University of Southern California Dissertations and Theses

Effects of age and gender on speed and accuracy of hand movements: and the refinements they suggest for Fitt's Law

(USC Thesis Other)

Effects of age and gender on speed and accuracy of hand movements: and the refinements they suggest for Fitt's Law

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content EFFECTS OF AGE AND GENDER ON
SPEED AND ACCURACY OF HAND MOVEMENTS:
AND THE REFINEMENTS THEY SUGGEST FOR FITTS’ LAW
by
George Erich Brogmus
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(Human Factors)
May 1991
Copyright 1991 George Erich Brogmus
UNIVERSITY O F SOUTHERN CALIFORNIA
THE GRADUATE SCHOOL
UNIVERSITY PARK
LOS ANGELES, CALIFORNIA S 0 0 0 7
This thesis, written by
George Erich Brogmus
under the direction of Ms. Thesis Committee,
and approved by all its members, has been pre
sented to and accepted by the D ean. of The
Graduate School, in partial fulfillment of the
requirements for the degree of
Master of Science, Human Factors
Dean
Date.
THESIS COMMITTEE
1&/W-U>
DISCLAIMER
This study was supported in part by the Baltimore Longitudinal Study of Aging
(Max Vercruyssen, Principal Investigator, George Brogmus, Research Assistant;
James L. Fozard, Technical Contract Officer). The opinions and ideas expressed in
this thesis are those of the author and his adviser (Max Vercruyssen) and do not
necessarily reflect those of the United States National Institutes of Health, National
Institute on Aging, or the Baltimore Longitudinal Study of Aging,
TABLE OF CONTENTS
Page
DISCLAIMER.................................................................................................. iii
LIST OF TABLES........................................................................................... vii
LIST OF FIGURES........................................................................................viii
LIST OF SYMBOLS AND ABBREVIATIONS..............................................x
ABSTRACT.................................................................................................... xii
CHAPTER
I. INTRODUCTION......................................................................1
Statement of the Problem..............................................4
Hypotheses......................... 4
Definitions......................................................................5
Basic Assumptions........................................................ 7
Delimitations..................................................................7
Limitations.......................................................... 8
Theoretical Significance................................................9
Practical Significance.................................................... 9
IL REVIEW OF LITERATURE...................................................11
Historical Roots............................................................ 11
Paul M. Fitts (1954)......................................... 13
Fitts & Peterson (1964)....................................16
Welford (1960)................................................ 18
Crossman & Goodeve (1963,1983)................21
Theoretical Developments...........................................25
Summary..........................................................42
Generalizability of Fitts' Law ..................................... 44
Age and Gender Studies..............................................49
Page
III. METHOD..........................................................................................62
Subjects..........................................................................62
Apparatus and Task...................................................... 63
Procedure .........................................................65
Independent Variables.......................................68
Dependent Measures.........................................68
Treatment of the Data...................................... 68
Step 1 - Purifying of Data.................... 69
Step 2 - Finding a Formula..................70
Step 3 - Evaluate Age and Gender
Effects Cross-Sectionally 75
Step 4 - Create new Formula with
Age and Gender Included 76
Step 5 - Test New Formula..................77
Step 6 - Spline Used to Interpolate
Equally Spaced Visits.............77
Step 7 - Evaluate Age Effects
Longitudinally ................... 78
IV. RESULTS AND DISCUSSION............................................... 80
Experimental Results.................................................... 80
The "Best" Formula..........................................80
Descriptive Statistics.........................................86
Age and Gender Differences............................86
Y-Intercepts...................................................... 91
Note on Negative Y-Intercepts............95
Slopes ..................................................... 96
A Further Improvement - Arc Estimates 100
Speed-Accuracy Tradeoff.............................. 101
Note on Changes with Age for SW Target... 102
Longitudinal Analysis.....................................104
General Discussion....................................................112
Hypotheses......................................................112
Interpretation of Formulas 73 and 6 9 ...........113
V. SUMMARY AND CONCLUSIONS............................................. 115
Summary of Procedures.............................. 115
Summary of Findings..................................................115
Conclusions..................................................................116
Recommendations for Future Research......................117
REFERENCES.................................................................................................120
V
Page
APPENDICES............................ !.................................................................... 128
A. Informed Consent Form........................................................... 128
B. Target Configurations.............................................................. 130
C. Samples of Actual Used Targets.............................................. 139
D. Instructions to Subjects............................................................ 145
E. Balanced Order of Targets Presented......................................146
F. Input File Format......................................................................147
G. Sample of Input File D ata........................................................149
H. Output File Format....................................................................150
I. Sample of Output File Data............................................. * .......151
J. Formula Numbering System.................................................. 152
K. Comparison of Prominent Formulas........................................153
L. Means of Each Basic Measure for Each Group.................. 161
M. Detailed Descriptive Statistics for MT, WL, WR, and D'
for All Subjects, Males, and Females.....................................167
N. Movement Time ANOVA Table with Bonferoni Critical
Values...................................... 170
O. Y-Intercept and Slope ANOVAs with Bonferoni
Comparison Tables..................................................................171
P. Predicted Versus Actual MT Using Formulas 73A, 73B,
69A and 69B.............................................................................179
Q. Summary of Equations From Chapter II................................. 194
R. Formulas Used to Calculate a, b, r^, Se, and Wo*.................. 196
S. Movement Time ANOVA Table with Bonferoni Critical
Values for Longitudinal Data..................................................197
T. Y-Intercept and Slope ANOVA Tables for Longitudinal
Data with Bonferoni Critical Values for Slope Data.............198
U. Descriptive Statistics for Movement Time for Longitudinal
Data...........................................................................................199
V. Descriptive Statistics for Y-Intercept and Slopes for
Longitudinal Data....................................................................208
ACKNOWLEDGMENTS................................................................................209
RESUME..........................................................................................................214
vi
LIST OF TABLES
Table Page
1 Target Amplitude/Width Measures....................................................... 64
2 BLSA Test Interval Schedule........................................................... 65
3 Longitudinal Distribution of Subjects....................................... .....78
4 Rank Order of Best 11 Formulas ................................................81
vii
LIST OF FIGURES
Eigum Bags
1 MT versus ID, Fitts's Data, 1954...................................................... 14
2 BLS A Participant Performing the Reciprocal Tapping Task...........63
3 Basic Measurements of Target and Scatters..................................... 67
4 MT versus ID, Formula 73, All Subjects......................................... 82
5 MT versus ID, Formula 73, Subjects 45 - 54 Years of Age.............83
6 MT versus ID, Formula 69, All Subjects......................................... 84
7 MT versus ID, Formula 69, Subjects 45 - 54 Years of Age.............85
8 MT versus ID, Formula 73, All Subjects by Gender....................... 87
9 MT versus ID, Formula 73, All Subjects by Decade........................88
10 MT versus ID, Formula 73, Males by Decade.................................89
11 MT versus ID, Formula 69, Females by Decade..............................90
12 Y-Intercept versus Age, Formula 73, All Subjects.......................... 91
13 Y-Intercept versus Age, Formula 73 and 69, All Subjects by
Gender, 2nd Order Splines for Males and Females........................92
14 Y-Intercept versus Age, Formula 73 and 69, All Subjects by
Gender, 2nd Order Spline for Males, Linear Regression for
Females............................................................................................ 93
15 Y-Intercept versus Age, Formula 73 and 69, All Subjects by
Gender, 2nd Order Spline for Males, Linear Regression for
Females, Based on Each Subject’ s Y-Intercept............................... 94
16 Slope versus Age, Formula 73, AH Subjects....................................97
17 Slope versus Age, Formulas 73 and 69, All Subjects by
Gender............................................................................................. 98
viii
Figure Page
18 Slope versus Age, Formulas 73 and 69, All Subjects by
Gender Based on Each Subject's Slope................ 99
19 MT versus Age for SW Target, All Subjects..................................103
20 MT versus Age for SW Target, Males............................................ 103
21 MT versus Age for SW Target, Females......................................... 104
22 MT versus Age for target SW for each age group using
longitudinal visits for subjects with 9 or more splined visits........105
23 MT versus Age for target SI for each age group using
longitudinal visits for subjects with 9 or more splined visits........106
24 MT versus Age for target SN for each age group using
longitudinal visits for subjects with 9 or more splined visits........106
25 MT versus Age for target MW for each age group using
longitudinal visits for subjects with 9 or more splined visits........107
26 MT versus Age for target MI for each age group using
longitudinal visits for subjects with 9 or more splined visits........107
27 MT versus Age for target MN for each age group using
longitudinal visits for subjects with 9 or more splined visits........108
28 MT versus Age for target LW for each age group using
longitudinal visits for subjects with 9 or more splined visits........108
29 MT versus Age for target LI for each age group using
longitudinal visits for subjects with 9 or more splined visits........109
30 MT versus Age for target LN for each age group using
longitudinal visits for subjects with 9 or more splined visits........109
31 Y-Intercept versus Age for each age group using longitudinal
visits for subjects with 9 or more splined visits............................. 110
32 Slope versus Age for each age group using longitudinal
visits for subjects with 9 or more splined visits............................. I l l
ix
LIST OF SYMBOLS AND ABBREVIATIONS
For the reader's convenience, abbreviations and any unusual symbols have been
explained below. Accepted mathematical, statistical symbols and Greek letters
have been omitted.
A Amplitude of a hand movement during a reciprocal tapping
task, usually the center-to-center distance between
a Y-Intercept of a line fitted to experimental data.
ANOVA Analysis of variance.
b Slope of a line fitted to experimental data.
BLSA Baltimore Longitudinal Study of Aging.
cm Centimeter(s).
CNS Central nervous system.
DAS Data Analysis System software.
F Statistical F ratio (in ANOVA).
GRC Gerontological Research Center in Baltimore, Maryland.
ID Index of difficulty. The actual formula for the ID is
different depending on the equation being used for MT,
but ID is generally the value of the abscissa in a plot
of MT. For Fitts's original formula, ID = log2(2A/W).
M Mean.
Mdn Median,
mm Millimeter(s).
msec Millisecond(s).
MT Movement Time - usually of the hand during a reciprocal
tapping task.
p
Statistical probability of type I error.
RT Reaction time (usually given in milliseconds).
SD Standard deviation.
Se Standard error of estimate.
SE Standard error.
VDT Video Display Terminal.
W The width of a target in a reciprocal tapping task.
xi
ABSTRACT
While Fitts' Law has been found quite robust to a variety of circumstances, several
attempts have been made to modify Fitts's original formula (MT = Log2(2A/W)) of
the relationship between movement time and the parameters of movement distance
(A) and target width (W) to improve its fit to experimental data. These alternative
formulations have had varying degrees of success in improving upon Fitts's
original equation. In addition, there have only been a few attempts to examine the
changes in this basic relationship with changes in age or effects of gender. These
age studies have produced inconsistent results. Therefore, the purpose of this study
was to determine the best equation for Fitts' Law and examine age and gender
effects.
The data for this study was provided by the Baltimore Longitudinal Study of Aging
(BLS A). A. T. Welford designed a reciprocal tapping task which was administered
to all subjects taking part in the BLSA from 1960 to 1981 (Shock, 1984). During
this time over 1,300 subjects performed this task. Over 6,500 total visits were
made by these subjects in the 22 year period. The task was a reciprocal tapping
task using a pencil on two targets drawn on paper. All possible combinations of
three different target widths (4mm, 11mm, and 32mm) and three movement
distances (50mm, 142mm, and 402mm) were used to produce a total of nine target
configurations.
The data were analyzed using over 400 different formulas. The best formula was
chosen based on the standard error of estimate of the regression line fitted to the
data.
xii
Significant age differences were found for movement times. The best formula for
males differed from that found for females. Some implications for gender
differences (perhaps related to performance strategy) are implied. Age differences
were also found in the slopes of the regression lines. As one ages a
disproportionate slowing occurs in movement for tasks with a high index of
difficulty. Surprisingly, females were found to be faster than males on this tapping
task for all age decades and all target configurations although not significantly so.
For both the females and (especially) the older subjects, a speed-accuracy tradeoff
is apparently in effect. The older a subject is, the more accurate the subject is in
hitting the targets (i.e., the smaller the actual scatter of hits). The same pattern was
observed with the males as compared to the females.
The best equation for males turns out to be of the form:
MT = a + bLog2(D'/W + 1)
which is of the form of Shannon's Theorem 17 (which is presumedly where Fitts
derived his original formula from) with the primary distance of measure D' - the
distance between the far edges of the scatters of hits. W is the constructed target
width(s) and "a" and "b" are the empirically derived y-intercept and slope of the
line fitted to the actual data. The best equation for females is the same except D' is
replaced by D - the constructed distance between the far edges of the targets.
Changes with age result in changes in the y-intercepts and slopes. For males the
changes can be modeled with a quadratic change in the y-intercept with age, with
xiii
young males having a higher y-intercept, middle aged males having the lowest y-
intercepts and old males having high y-intercepts. Changes in slope for males can
best be modeled by a linear increase in slope with increasing age. For females the
same pattern for slope was observed but the best fit of the data for the y-intercept
appears to be a linear decrease in the y-intercept with increasing age. While the
above patterns appear clearly, analysis of variance of the slopes and y-intercepts
when calculated from data collected on each visit indicates that only the slope
differences are significant for age and gender effects.
The resulting "best" formula for males is given by:
MT = -40 + [-15 + 0.3(AGE)]2 + [69 + l.l(AGE)]Log2(D'/W + 1)
The resulting "best" formula for females is given by:
MT = 28 - 0.75(AGE) + (64 + AGE)Log2(D/W + 1)
A further (yet slight) improvement in the fit of the above formulas can be achieved
if, instead of D' and D, the length of the arc between the far edges of the scatters of
hits and the length of the arc between the far edges of the constructed targets is
used where the radius of the arc is given by the average length of the distance
between the elbow and the tip of the thumb.
Longitudinal analysis of data for subjects (n=154, all males) who had completed
nine or more splined visits yeilded similar results as the cross-sectional analysis
xiv
except that a dramatic learning effect was apparently present up to about 10 years
after the first visits, after which time the changes in slope were relatively linear and
similar for each age group.
Fitts1 Law has important human factors implications for the design of products and
systems that require rapid hand movements. The Fitts’ Law reciprocal tapping
task, because of its simple design, may also have applications in assessing levels of
psychomotor performance and decrements of psychomotor performance due illness
or injury. The factors of gender, and, especially, of age, must also be considered in
the application of the underlying principles of Fitts' Law.
xv
CHAPTER I:
INTRODUCTION
The field of Human Factors can claim only two fundamental principles which have
risen to the status of "laws": Hick-Hyman Law and Fitts' Law. The latter is the
subject of this thesis. Long before Fitts (1954) described the relationship between
movement time, amplitude, and accuracy (target width), the qualitative nature of
the relationship between these elements were well known and were documented by
Woodworth (1899). Fitts, however, has been credited with consolidating the
concepts into an information theory law, now known as Fitts' Law, the most
frequently cited form of which is:
MT = a + bLog2(2A/W)
Since Fitts (1954) proposed this relationship between movement time, amplitude,
and target width, there have been numerous attempts to develop a formula that
would better fit his original data as well as data from subsequent investigations
(Bullock & Grossberg 1988; Crossman & Goodeve 1983; Howarth & Beggs 1981;
Howarth, Beggs, & Bowden, 1971; MacKenzie, Martiniuk, Dugas, Liske, &
Eickmeier, 1987; MacKenzie, 1989; Meyer, Abrams, Komblum, Wright, & Smith,
1988; Meyer, Smith, & Wright, 1982; Schmidt, 1988; Schmidt, Zelazink, Hawkins,
Frank, & Quinn, 1979; Wallace, Hawkins, & Mood, 1983; Welford, 1958, 1960,
1961, 1968; Welford, Norris, & Shock, 1969; Wright, & Meyer, 1983). With these
modifications have come additional theoretical considerations for the information
processing aspects of movement as well as methodological considerations for the
design of tapping tasks.
Surprisingly, although much work has been done in substantiating (or attempting to
refute) Fitts' Law under various conditions and for many different applications, and
even though there has been some work done to improve the formula itself and to
advance the psychomotor theory, there has been little work examining age and
gender differences (Crossman & Goodeve, 1983; Murrell & Entwisle, 1960;
Welford, 1958,1960,1961,1968; Welford, Norris, & Shock, 1969). Furthermore,
those studies that did examine age differences produced inconsistent results. (Two
studies found a complex relationship between movement time, error rate, and age
on a reciprocal tapping task while another found a slightly linear increase in
movement time with age.) Finally, these studies were cross-sectional in design, not
longitudinal. (Cross-sequential analysis is similar to longitudianal analysis and
shares some of the same advantages.)
Since cross-sectional studies have been criticized for overestimating slowing,
longitudinal analysis might manifest the individual differences contributing to the
appearance of slowing of all individuals. Longitudinal, combined with cross-
sectional analyses, may distinguish between within- and between-subject effects.
The disadvantages to using longitudinal analysis in the study of aging are practice
and period effects, recruitment of an "elite" subject pool, and subject drop-out.
Nevertheless, these are far outweighed by the advantages of longitudinal research,
which include eliminating birth-cohort effects, and identifying changes in
individuals' performance as they age.
Furthermore, with longitudinal research, reliability increases with increased
duration and frequency of testing, while cross-sectional analyses can only identify
differences between age groups. Even though practice and period effects are not
usually a problem, the performance differences observed may be partly a result of
factors other than age, such as cohort effects or selective survival (Shock, 1984).
Based on past research it is safe to say that a large sample size would probably be
needed to identify gender differences. This, combined with the desire for
longitudinal research on the subject, makes it economically difficult to conduct
such research. (It is understandable why such little research has appeared in the
literature so far!) Fortunately, however, the data gathering for such a project had
actually already been done. The Baltimore longitudinal study of aging (BLSA), a
federally-sponsored research project, (Shock, 1984) is considered to be the "gold
standard" of longitudinal research. This extensive research project has been
ongoing since 1958 and continues to conduct a multitude of tests including a
battery of psychomotor performance measures on its subjects.
Welford (Welford, Norris & Shock, 1969) designed a reciprocal tapping task
(similar to Fitts’ s original tapping task) that was administered to BLSA participants
on each visit from 1960 to 1981. The nature of Welford’s design allowed recording
of each "hit" of the tapping stylus. In this case, the simple design was a pencil and
paper to record the actual hits made. Three target widths (W) and three movement
amplitudes (A) were used to produce a total of nine width/amplitude combinations.
Initial testing of 325 males who were participating in this study was reported in
Welford, Norris, and Shock (1969). In January, 1978 women began to be tested as
part of the BLSA. "As of June 30, 1981, more than 300 [women] had been
examined and tested at least once, 150 two or more times." (Shock, 1984 p.l) The
3
data foT the present study includes usable data from 1,047 male subjects and 271
female subjects with a total of 6,375 visits. Subjects ranged in age from 17 to 100
years old.
Statement of the Problem
This study was designed to answer the following questions:
1. What equation fits the data (including age and gender) best?
2. Are longitudinal changes with age consistent with the equation obtained
above?
3. How does movement time vary with age?
4. Are there gender differences for movement time?
Hypotheses
Cross-sectional and longitudinal analysis of the BLSA tapping data will yield the
following results:
1.The best fit of the data to a formula will be a function of actual
actual amplitude, age and gender.
2.Movement time will increase with age for all age decades
as cross-sectionally for each test condition.
3.Movement time will be disproportionately higher for the more difficult
target width/amplitude combinations (e.g. small width and large
amplitude) for the older subjects (i.e. there will be an interaction
between age and the index of difficulty).
4. Males will be faster than females through all age decades and for all test
conditions. It is expected that this will be true longitudinally as well as
cross-sectionally.
Definitions
Human Factors - The multidisiplinary field of study that concerns itself with
human capabilities and limitations so that jobs, products, and systems can be
designed with these capabilities and limitations in mind to the end that those jobs,
products, and systems will be safe, productive, and enjoyable to do and use.
Hick-Hyman Law - The law that relates in a mathematical formula the relationship
between the time it takes to make a choice and the number of choices presented.
The formula is: Choice RT = a + b log2(N) where N is the number of choices and
a and b are empirically derived constants.
Fitts' Law - The law that relates in a mathematical formula the relationship
between the time it takes to make a movement and the amplitude and target width
for the movement in a reciprocal tapping task. The formula is: MT = a + b
log2(2A/W) where A is the amplitude of movement, W is the target width, and a
and b are empirically derived constants.
Cross-sectional analysis - An approach to studying age effects that looks at the
effects between subjects like a "snapshot" in time. No subsequent gathering of data
is necessary beyond the first visit. (See also Longitudinal analysis.)
5
Longitudinal analysis - An approach to studying age effects that looks at the effects
within subjects as they age. Subjects are requested to be tested periodically over a
long period of time as they get older.
Manipulandum - An apparatus used to measure wrist movements. Often, it is used
to provide subjects with a means to perform accurate wrist movements within
specific target parameters.
Metronome - A device that marks an exact amount of time by a regularly repeated
"tick". The frequency of the tick can be altered as desired.
Reciprocal tapping task - A task used to study psychomotor behavior that requires
the subject to tap back and forth between two targets using a stylus held in the
hand. For some Reciprocal tapping tasks, the stylus is a pencil and the targets are
double lines, boxes, or ellipses drawn on paper.
Shannons Theorem 17 - A communication theory that states that the effective
information capacity (C) of a communications channel is given by the following
formula: C = b log2((P + N)/N) where P is the signal strength, N is the noise
power, and b is an empirically derived constant.
Speed-Accuracy Trade-off - The intuitive principle that any effort to produce more
accuracy in an action will require more time to perform the action, and conversely,
any effort to perform the action faster will result in decreased accuracy.
6
Basic Assumptions
1.All subjects were healthy and motivated to perform at their normal levels.
2.All subjects followed the instructions properly.
3.The movement times and scatter widths of hits are a representative index of those
of the respective groups from which they were drawn.
4.AU subjects accurately reported personal information such date of birth.
Delimitations
Only reasonably healthy subjects were used in this study. Subjects with serious
health problems or who developed serious health problems after being
indoctrinated into the BLSA project were excluded from some of the BLSA tests.
However, the reciprocal tapping task was not one of the tests excluded, therefore,
some of the subjects could have had disorders that affected their results.
No attempt was made to find a formula that fit the longitudinal better than that
derived from the cross-sectional analysis. Furthermore, formulas were delimited to
those that could be tested with the information gathered, (e.g. Since no third
dimensional data were gathered, formulas involving a third dimensional component
could not be tested.) Also, power functions (such as the square root Equation 17),
were not explored beyond a preliminary evaluation using Equation 17 and the
mean values of all data combined.
7
No attempt was made to analyze possible cohort effects since a simple task such as
the Fitts reciprocal tapping task would not be expected to be influenced by cohort
influences such as education.
Limitations
This study was limited to BLSA participants, who are known to be of above
average occupational class, educational status and economic status (Shock, 1984)
and intelligence (Welford, Norris, and Shock, 1969).
The design of the task, while simple and advantageous in many ways, may have
limited the accuracy by not using electrical means for recording at least the total
time for a trial of 100 hits. Furthermore, resting time on the targets was not
measurable using the present design.
Covariate analysis was not used to consider the influence of intelligence, neural
conduction velocity, aerobic capacity, medications, and clinical pathologies,
limiting the potential for additional insight into the underlying mechanisms
governing the Fitts' Law relationship.
A completely thorough testing of the formulas was not completed. All 482
formulas were not applied to each test visit, only to group means. (See the
Treatment of Data section for details.)
8
Theoretical Significance
Fitts' Law has been found to be relatively robust in applications as varied as the use
of joy sticks for the control of cursor movement on a VDT screen (Jagacinski &
Monk, 1985; Kantowitz & Elvers, 1988) underwater hand movements (Dixon,
1985; Hoffmann, 1988; Kerr, 1973; and Kerr, 1978) an overarm throwing task
(Hoffman, Emwold, & Roller, 1983; Indermill & Husak, 1984) two handed
movements (Kelso, Southard, & Goodman, 1979) , movement under various levels
of hand loads, ratios of work to rest, and task duration (Wiker, Langolf, & Chaffin,
1989), for finger, wrist, and whole arm motions (Leisman, 1989) as well as other
body parts (head movement, Andres & Hartung, 1989, and lower limb movement,
Drury, 1975 and Williams & Werner, 1985). Fitts' Law has also been used as a
relative measure of psychomotor integrity for a variety of conditions including
hypoxia (Fowler, Taylor, & Porlier, 1987), alcoholism (York & Biederman, 1988),
stroke patients (Haaland, Harrington, & Yeo, 1987) learning disabled youngsters
(Kerr & Hughes, 1987) as well as the relationship between movement time and
intelligence (Mohan & Bhatia, 1985).
Practical Significance
Fitts' Law has implications for the design of control and display panels that may
require critical activation of knobs, switches, buttons, joy sticks or even the use of
a computer mouse, (e.g. stop buttons on machinery, the brake on a car, critical
display information, or a car's horn) . Fitts' Law has practical implications for user
interfaces in the design of high-tech equipment such as aircraft or even cars where
movement time can be crucial to safety, user satisfaction, and consumer purchasing
behavior. Fitts' Law can have an impact on the design of high-paced assembly or
production tasks that require fast and precise hand movements. Fitts' Law has
some logical applications to military and law enforcement combat situations.
Repetitive aiming requiring human motor output for control is a direct application
of Fitts' Law whether the device is being aimed directly (as in the use of a firearm)
or remotely (through mechanical or electronic control). A similar application of
Fitts' Law could be made to computer input devices. For example, the information
obtained from the present study could be used by software developers to design
user interface features such as the size buttons (on the VDT screen) that would take
into consideration age and gender differences.
As the United States population is increasing in average age (Czaja, 1990) the need
for better human factors data on aging is becoming more critical. Fundamental to
developing a useful information base for an aging population is pursuing an
understanding of some of the basic ways performance changes with age. Research
that seeks not only to understand the limitations of older individuals, but is open to
discovering superior capabilities and the positive aspects of the limitations of older
individuals will help to promote better utilization of the elderly in the workforce,
improve product design for the elderly, and educate the public in the limitations,
realities, and benefits of ageing. Since the reciprocal tapping task used to assess
Fitts' Law is fairly straightforward and easy to administer, it may provide a simple
way of assessing an individual's psychomotor performance and allow for an
estimate of any degradation of performance due to aging, illness, or injury. It may
even serve as an appropriate gauge of "biological age" as opposed to age based on
chronology alone. Most recently, Radwin, Vanderheiden, and Lin (1990) used
Fitts' Law to evaluate computer input devices for individuals with disabilities.
CHAPTER n :
REVIEW OF LITERATURE
This chapter summarizes the historical development of Fitts' Law, the effects of
age and gender on (hand) movement time as it relates to Fitts’ Law, the
generalizability of Fitts' Law, and the theoretical models proposed to explain Fitts'
Law as presented in the literature. This chapter is divided into the following
sections: (1) historical roots, (2) theoretical developments, (3) the generalizable of
Fitts' Law, and (4) the effects of age and gender as they relate to Fitts’ Law.
Historical Roots
Although there had already been a few investigators that studied the accuracy of
voluntary movements under various conditions, Woodworth (1899) is generally
credited with the first qualitative evaluations of the accuracy of voluntary
movement in relation to the speed of movement. Woodworth (1899, p. 16) noted
that, "the accuracy of a movement varies with its speed, so that the mere statement
that such a movement or such a person is so accurate has no definite meaning
unless the speed is specified." Earlier investigations by other researchers had
neglected the speed element.
Based on simple repetitive line drawing movements, Woodworth was unable to
develop a quantitative description of the speed accuracy trade off. However, in
qualitative terms he was able to show clearly that: the accuracy of a movement
diminishes as the speed increases; when the eyes are not used in the task the
accuracy does not vary much with speed; the right hand is more accurate than the
left hand; and accuracy of the left hand decreases more quickly with speed than
with the right hand. Woodworth only used four subjects, three males of 25 to 30
years of age and one female (specified as "a young lady")* Five additional subjects
(identified as students) are mentioned as participating in occasional experiments.
Based on the date of Woodworth’ s work, these subjects were probably males.
It is important to note the significance of Woodworth's 1899 work (which was his
Phd thesis). Howarth and Beggs (1981, p.94) note that "more recent experiments
have added remarkably little to Woodworth’ s data and analysis," Schmidt (1988,
p.268) endorses this view stating ’ ’ most of his results have not, in general terms at
least, been contradicted since." Howarth and Beggs (1981), and Schmidt (1988)
also note the significant theoretical contributions of Woodworth, by highlighting
his observation that a control system exists with an "initial adjustment" phase and a
"current or contemporary control" phase. Howarth and Beggs (1981, p.93) note
that "these two concepts are still central to theories of movement. [The first] is
now usually called the 'motor program', while [the second] is usually called
'feedback'."
The relationship that Woodworth found between speed and accuracy has been
(Howarth & Beggs, 1981) expressed as follows:
Error = k Sn (1)
Where n is some number less than one, k is a constant, and S is a measure of speed
of the task in "beats per minute". (Woodworth used a metronome to pace the
drawing tasks.)
12
PAUL M. FITTS (1954)
The individual generally credited with making the greatest contribution to the
psychomotor study of the relationship between speed and accuracy is Paul M. Fitts.
(See Grether, 1986, for biographical information and an account of his contribution
to the beginnings of Human Factors.) In his 1954 work "The information capacity
of the human motor system in controlling the amplitude of movement", using
information theory, Fitts formulated a relationship between movement time (MT),
the amplitude of the movement (A), and a measure of error tolerance. The measure
of error tolerance is the permissible range of the finished movement and is
generally specified as W (corresponding to a target width). Fitts1 Law, as it has
come to be known, is generally expressed as follows:
MT = a + b log2 (2A/W) (2)
(Fitts originally did not include the constant, "a"; it was added later in order to
compensate for an experimentally derived negative y-intercept.) Fitts (1954)
conducted three experiments that provided a reasonable fit of this formula to the
data. In the first experiment Fitts designed a reciprocal tapping task whereby the
subject would tap alternatively using a stylus between two six-inch metal strips of
varying widths and varying distances apart. Two stylus weights were used (one
which weighed one ounce and the other which weighed one pound), four different
target widths were used (2, 1, .5, and .25 inches each) and four center-to-center
distances between the target plates were used (2, 4, 8, and 16 inches) for a total of
16 combinations of amplitude (A) and target size (W). The apparatus also allowed
recording of misses since it provided additional recording plates on each side of the
13
target to record when an overshot or undershot of a hit was made. Subjects for the
first experiment were 16 right-handed college males. (It is assumed that these were
young males.) Figure 1 gives the data for Fitts’ s first experiment in graphical form.
1600
o' 1200
6
H 800
H
2
U
S
w
| 400
0
0 1 2 3 4 5 6 7
IN D E X O F D IFFIC U LTY
L0Gg(2A/W)
Figure 1. Movement time as a function of the Index of Difficulty
for the data collected by Fitts (1954).
The second experiment consisted of washers being transferred from one post to
another. The size of the washer hole was varied to allow for manipulation of the
"W" measure. No errors could be made on this particular task since the washer was
either on or off the post - no in-between. Again, 16 right-handed college males
participated as subjects. These subjects were different from experiment 1.
Fitts Data, 1954, for loz Stylus
14
The third experiment was a peg transfer task. This task consisted of transferring
small cylindrical pegs from a vertically aligned set of holes to another vertically
aligned set of holes. Both peg diameters and whole diameters were varied so that
each set of holes had a diameter that was twice that of the corresponding pins.
Four different pin sizes and four different amplitudes were used in this task.
Twenty college students, ten males and ten females served as subjects for this
experiment. These were different subjects than those which participated in
experiments 1 or 2. In all three experiments the subjects were instructed to work at
maximum rate and to "emphasize accuracy rather than speed" (p.384).
Fitts’ s work was a breakthrough in that it provided a simple formula for relating
movement time to the amplitude of the movement and the size of the target (a
relative measure of the accuracy of the movement). Subsequent researchers have
found this finding to be relatively robust to various applications as will be seen in
the review of literature in this chapter. At the same time, psychomotor
performance theorists have made Fitts’ work the focus of much criticism and
attention. The information-theoretic basis for Fitts’ Law has been criticized.
Furthermore, even those researches that have accepted this basis, have made
modifications to the formula in order that it may better fit the data.
Two important articles (Crossman & Goodeve, 1963, and Welford, 1960) will be
included in this section since they made lasting contributions to the debate as to the
theoretical basis for and specific formulation of what is now known as Fitts' Law.
Before this is done, however, it is appropriate to review a frequently cited article
by Fitts and Peterson (1964).
15
FITTS & PETERSON (1964)
This article, entitled "Information Capacity of Discrete Motor Responses",
examined the effects of response amplitude and terminal accuracy on reaction time
(RT) and on movement time (MT) for a two-choice task. Movement time and
reaction time were found to be relatively independent of one another for variations
of amplitude and target width (terminal accuracy). The authors concluded that this
result supports the view that perceptional and motor processes are serial and
independent in nature. "Apparently RT reflects the time required for perceptional
or cognitive processes, and is determined in part by the preparations which S [the
subject] makes prior to a stimulus, such as those resulting from his knowledge of
stimulus probabilities. Movement time, in contrast, appears to reflect the duration
of motor system processes that are necessary for the control of the timing and
patterning of a movement, and which begin after the decision is made to execute a
movement." (Fitts & Peterson, 1964, p. 110.)
Also noteworthy in this article is inclusion of a discussion on corrections to the
Fitts' Law that had been proposed by other researches. Specifically, the suggestion
that instead of using the actual target width, a corrected estimate of W, adjusted for
errors, should be used in computing ID values (ID is the Index o f Difficulty and is
equal to Iog2(2A/W)). This was suggested by Crossman (1960) and Welford
(1960). Unfortunately, in applying this type of correction (with W = + 2SD) the
Fitts’ Law equation yielded a poorer correlation between ID and RT (changing it
from .995 to .993).
16
However, using Welford's additional correction on the Fitts' Law formula where
ID = log2 ((A+.5W)/W) = log2 (A/W + .5) (3)
Fitts and Peterson found that the data yielded a correlation between ID and RT of
.997. (The reason for Welford’ s use of this correction will be addressed as part of
the review for Welford, 1960.)
The authors also found that the motor system is apparently more efficient in
producing low information than high information responses. They found that the
human performance capacity would vary from about 22 bits per second for a value
of ID equal to 2.5 to just over 14 bits per second for ID equal to 7.5 (for the most
difficult movement studied - high amplitude and small target width). The
researchers also found that a linear combination of the equations for RT and MT
would predict better performance for more difficult tasks as long as the effect of
RT was weighted sufficiently to give a positive value for the y-intercept constant,
a. It was found that a 4 to 1 weight for MT relative to RT would give a predicted 0
intercept, or equivalent information rates at all difficulty levels. Fitts and Peterson
(1964, p.l 11) found that "it appears that the processing of feedback data in serial or
continuous tasks introduces some small delay relative to simple open loop
movements, but less delay than would be expected if every response involved a
separate reaction time."
The experiment involved six male subjects, 18 to 25 years of age. The task
involved tapping a light-weight stylus from a center start button to one of two four-
17
inch high targets which were on the right and left of the center start button. The
target width and distances from the center start button were varied. Three distances
between the starting button and the midline of the target were used (3, 6, and 12
inches) and four target widths (0.125, 0.25, 0.5, and 1 inch values) were used,
making for a total of 12 target configurations. A series of separate experiments
were conducted whereby different target parameters were used for the right and left
sides as well as varying the proportion of "hits" required for a particular side.
WELFORD (1960)
This article is a historical review of the work done in sensory motor performance.
Welford summarizes past work as well as reappraises some of the theoretical bases
for the conclusions represented at that point in time. Welford concludes that there
is a need for joint psychological and physiological research "which would be able
to go beyond descriptive mathematical formulae to the study of detailed
micro-behavior and neuromuscular mechanisms." (Welford, 1960, p. 189) Welford
categorizes the research done into five main areas including the information theory
models relating to the speed and accuracy of movement.
Welford noted that (by Fitts's own admission) the multiplication of A by 2 was
arbitrary. Fitts (1954) does indicate that this choice was arbitrary, however, in Fins
and Peterson (1964) a more detailed justification of the use of twice the amplitude
is given based on communications theory (Shannon, 1948, Theorem 17, The
Channel Capacity formula).
18
Welford raised three important objections to the traditional Fitts' formulation of:
MT = a + b log2 (2A/W) (Equation 2)
The objections were:
1. Fitts's data for movement time as a function of the index of difficulty (equal to
log2(2A/W)) yields a best fit line to the majority of data which has a negative
y-intercept (i.e. below the origin). (Welford comments that Crossman (1957)
suggested that this difficulty can be eliminated by omitting the multiplication
of A by 2 so that the new formula would be:
MT = a + b log2 (AAV) (4)
With a = 0.05 seconds, purportedly relating to the time the stylus remains on
the target. However, Welford argues that more uniform results are obtained if
the total time is considered - time spent on and between the targets.)
2. The best fit of an equation to Fitts’ s data would actually be a curve and not a
straight line. However, Welford proposed that the curve can be substantially
removed by making a further modification to the equation as follows:
MT = K log2 ((A + .5W)/W) = K log2 (AAV + .5) (5)
Theoretically, Welford (1960, p.207) explains this formulation as a kind of
Weber fraction whereby, "the subject is called upon to distinguish between the
distances to the far and near edges of the target. To put it another way, he is
called upon to choose a distance W out of a total distance extending from his
starting point to the far edge of the target. The formulation also preserves the
advantage which Fitts claimed for the procedure of multiplying A by 2, in that
the logarithm can never be negative, since in the extreme case when the
movement begins at the edge of the target A = .5W."
3. Fitts's data (see Figure 1) shows a flattening at the lower end (for the smallest
values of ID), In this regard Welford postulates that this flattening is probably
due to a minimum time per movement as a result of the amount of target used.
According to Welford (1960, p.207), "When the targets are wide and the
distance short the subject uses very much less than the full target width. He is,
in fact, transmitting more information than a calculation in terms of [Equation
5] would assume because the effective W is narrower. The narrowing of W is
to some extent reflected in a reduction of errors and if due allowance is made
for them [Equation 5] still holds reasonably well.".
Welford argues that an "effective" target width can be determined assuming a
normal distribution of "hits". The determination of the effective target width
can be based on the number of misses. Using this correction along with his
formula (Equation 5) Welford achieves a much better fit of Fitts's data to a
straight line. (Welford did not provide an actual correlation coefficient for the
relationship between the movement time and the corrected ID, however, Fitts &
Peterson, 1964 did - see pages 35-36 of this chapter.)
20
Welford comments on the work of Crossman (1957) in that it agrees strongly with
Fitts’ s original observations. (An interesting note is that Crossman, 1957, found
that the length of the target strip as well as its width affects the movement time,
although to a smaller extent.)
Welford (1960, p.211) finally concludes that the conceptional model which best
explains the observations is one in which "the subject starts a movement fast and
gradually slows down as he approaches the target." This is a type of "ballistic and
homing-in composite movement" theory.
The major contribution of this article by Welford in terms of psychomotor
performance, is in regard to his altered formulation of movement time so that:
MT = K log2 (AAV + 0.5) (Equation 5)
With the target width, W, being modified as a function of the actual scatter of hits,
as determined by assuming a normal distribution and measuring the number of
misses.
CROSSMAN & GOODEVE (1963,1983)
In July, 1963, Crossman and Goodeve presented a paper entitled "Feedback control
of hand-movement and Fitt's [SIC] Law" at the Oxford meeting of the
Experimental Psychology Society. There was no publication of this paper made
until 1983. However, even though it was unpublished, it was frequently cited by
the meeting participants who received an informal typed document of the paper
21
presented. "Over the years, the original copies have been photocopied and passed
around. In this way a number of psychologists have had the opportunity to
appreciate that this paper contained a significant contribution to our understanding
of the relationship between the speed and accuracy of voluntary arm movements as
embodied in Fitts’ Law (Fitts, 1954). Indeed this paper is probably the most often
cited unpublished work in the current literature on human movement control."
(Wing, 1983, p.245)
Crossman and Goodeve reject Fitts's theoretical interpretation of his results from
the information theory basis. They (Crossman & Goodeve, 1983, p.256) suggest
that information theory "is concerned with statistical coding of messages for
efficient transmission over noisy channels... rather than with control of physical
systems." Furthermore, "the algebraic form of an empirical relationship does not
of course establish that statistical coding occurs in a system under investigation,
and in Fitts' [SIC] case it seems that the goodness of fit may have been
coincidental."
Using linear feedback theory, Crossman and Goodeve present a feedback
hypothesis to explain Fitts' Law. Crossman and Goodeve present two models to
explain Fitts' Law. These models are the continuous velocity control and the
intermittently sampled proportional control of limb position. The continuous
velocity control system model proposes that the actual position of the limb is
continuously compared with the "command position", providing an error term
which is assumed to determine the instantaneous limb velocity. This model yields
an identical formula for movement time as Fitts’ Law. However, Crossman and
22
Goodeve identify certain theoretical difficulties with the model and they present an
"intermittent proportional correction of position" model. In this theory it is
assumed that an exponential pulse passes through what is equivalent to a Gaussian
filter. The expectation is that a small but perceptible ripple should be seen in the
records of motion. Crossman and Goodeve devised an experiment which would
accentuate this ripple. They used an apparatus for rotary wrist motions. This
apparatus did in fact show the ripple that they were looking for. Briefly, this
model states that accurate motions are made up of sequences of discrete changes of
position, based on intermittent sampling and proportional correction of position
rather than on continuous velocity feedback.
Crossman and Goodeve explored some of the possibilities of how positional errors
might be signaled - either visually or kinesthetically. They (Crossman & Goodeve,
1983, p.277) found that, "because under non-visual conditions the angular
positional output of the forearm/wrist system is subject to offset by torque
disturbance, it seems that the effector's 'positional' feedback cannot be derived from
a sense organ that indicates true position." They also found that visual and
kinesthetic command signals are connected by a proportional link capable of
changing its gain slowly if persistent error occurs. They also found that visual
feedback can exert effects with quite short latency periods.
They found "the elementary positional corrective (impulse) motion exhibits an
approximately Gaussian integral trajectory which can be explained (at least in
outline) by reference to known dynamic properties and interactions of peripheral
effector system components." Furthermore, "the feedback signal that effectively
23
controls the amplitude of these positional correction impulses, and hence
determines the exponential form of the overall trajectory of accurately target-aimed
reciprocal tapping motions in Fitts’ [SIC] experimental paradigm, is probably
derived from the limb's input signal, i.e. level of nervous excitation to the muscle,
rather than from sensors monitoring its output, i.e. linear or angular position."
Crossman and Goodeve suggest mechanical and physiological interactions which
are capable of explaining the corrective impulse trajectory based on a balance of
forces between agonist and antagonist muscles.
The contribution by these authors in this article is important in relation to Fitts'
Law in that they provides alternative theories for the basis of Fitts' law while
maintaining an equivalent mathematical formulation. Furthermore, Crossman and
Goodeve have made a methodological contribution to the study of psychomotor
performance in that their experimental design consisted of wrist rotation
movements as opposed to the Fitts' paradigm reciprocal tapping task. The wrist
rotation apparatus has the advantage that the motions have low inertia compared to
the whole arm reciprocal tapping motions. Finally, as Wing (1983, p.246) points
out, "the disadvantage of the typical arrangement [the Fitts' reciprocal tapping task]
is that it confounds the target impact with any controlled deceleration imparted by
the muscles." Although some subsequent researches have employed the Crossman
and Goodeve methodology, most have remained with the traditional Fitts'
reciprocal tapping task.
24
Theoretical Developments
Theoretical developments have taken three basic directions, these have been in
regard to the exactness of the mathematical representation of Fitts’ Law, the
theoretical basis for the formulation, and methodological considerations. In regard
to the accuracy of the formulation itself, the earliest and most lasting of
contributions has been made by Welford. As mentioned previously under the
review of Welford (1960), Welford suggests that a more accurate fit of the data
would be to express movement time as follows:
MT = K log2 (AAV + 0.5) (Equations)
This formulation has been shown by Fitts and Peterson (1964) to have a better
correlation between movement time and the index of difficulty than Fitts' original
formulation.
Fitts's original methodology did not allow for recording the distribution of actual
hits. Crossman and Goodeve (1963, 1983) overcame this difficulty in a somewhat
awkward methodology of using a cable and pulley system attached to the recording
stylus in order to record the actual trajectory of hits. Welford (1960 and 1968) and
Welford, Norris, and Shock (1969) eliminated the awkwardness of this recording
process by simply using a pencil and paper to record the actual distribution of hits.
This methodological improvement allows for a more detailed assessment of the
accuracy of hits. In addition, the actual amplitude of movements and the actual
scatter of hits can be used for relating movement time to the parameters of resultant
target width and resultant amplitude.
25
Welford (1968) found that this recording methodology produced similar results to
Fitts, except with the narrower targets. Welford explains this difference by the fact
that Fitts’s apparatus may have emphasized accuracy more than the paper targets
would. Welford (1968, p. 154) offers another possible explanation: "...the point of
the stylus used by Fitts must have had an appreciable diameter and the electrical
insulation between the targets and the surrounding metal plate must have had an
appreciable thickness, so that all his targets might have been effectively wider by a
small constant amount than he claimed them to be. This extra amount would be of
little importance with the widest targets but it would be a substantial portion of the
narrowest." From these observations it is clear that a substantial improvement to
the Fitts’ Law reciprocal tapping task is to use the simple apparatus of a pencil and
a piece of paper with targets drawn on the paper.
Welford (1968) and Welford, Norris, and Shock (1969) have made four
modifications to Fitts' Law. The first modification (introduced first in Welford,
1960) as previously mentioned, takes the following form:
MT = K log2 (A/W + 0.5) (Equation 5)
Welford (1960 and 1968) and Welford, Norris, and Shock (1969) do not provide
significant theoretical justification for the above modification of Fitts’ Law.
However, they do relate it to a kind of Weber Fraction: "This formulation makes
movement time dependent upon a kind of Weber Fraction in that the subject is
called upon to distinguish between the distances to the far and near edges of the
target. To put it another way, he is called upon to choose a distance W out of a
26
total distance extending from his starting point to the far edge of the target The
formulation also preserves the advantage which Fitts claimed for the procedure of
multiplying A by 2, in that the logarithm can never be negative, since in the
extreme case when the movement begins at the edge of the target A = .5W."
(Welford, 1960 and 1968, pages 207 and 147 respectively.)
The second correction that Welford (1968) and Welford, Norris, and Shock (1969)
provided was:
MT = K log2 (A'/W + 0.5) (6)
Where A' is the distance between the centers of the scatters of actual "hits", and W
is the mean width of these two distributions. This formula is only available if a
recording methodology is used that allows A1 and W' to be recorded. This
formulation provided a good fit to the data with some slight differences as
explained above. (The times for narrow targets were too high which Welford
explained by methodological differences of the target use and the insulating
material around the stylus used in Fitts's original tapping task.) Welford was not
satisfied by these explanations and therefore discussed three others.
First, it may be that movement time depends more on aim than on accuracy
actually achieved. In this regard, movement time would depend more on the target
presented than on the actual scatter of the hits. Welford (1968, p. 155) considerd
this view to be "untenable because it would assume no relationship between
observed scatter and movement time for any given target and amplitude."
27
The second explanation leads into the third modification of the formula: The
third modification that Welford made was to subtract a small constant (c) of
approximately three millimeters from the observed widths of the distribution of
shots which would yield the following equation:
MT = K log2 (A7(W‘ - c) + 0.5) (7)
Welford (1968) and Welford, Norris, and Shock (1969) found that this
modification of the formula provides a much better fit to the data. Welford
postulates that, "the constant c might perhaps be attributed to tremor which would
increase the scatter slightly and mean that, in order to attain a given level of
accuracy, the subject would have to aim at a corresponding higher level. Such
tremor might arise from the fact that the time taken to traverse the servo
mechanisms controlling movement implies a period of at least about 0.1 sec during
which operation is open loop. Alternatively it might be due to the muscular action
of a large member such as the arm not being very finely graded, or to its
movements being liable to slight disturbance by factors such as the pulse."
(Welford, Norris, & Shock, 1969, p.8.)
Again, Welford (1968) and Welford, Norris, and Shock ( 1969) have problems
with this modification since it falls apart for very small target widths (3 millimeters
or less). Furthermore, Welford notes that it would make more sense that such a
2 2
tremor effect would add to the overall variance (i.e. square root of W' -c , rather
than W'- c). Unfortunately, the variance formulation does not provide a good fit to
the results.
' 28
The third explanation leads into the fourth modification. Welford (1968) and
Welford, Norris, and Shock (1969) make the very interesting observation that if the
points for any one target width at different amplitudes of movement are fitted to a
line, an even better fit of the data is obtained. This means that they are treating the
different target widths separately and seeing how movement time chsnges with
different amplitudes. They note (Welford, Norris, & Shock ,1969, p.10.) that "this
suggests that two control processes ought perhaps to be distinguished: A faster one
concerned with distance covering, and a slower one of 'homing' onto the target. It
seems reasonable to regard the former as an essentially motor control shown in a
relatively pure form in ballistic movements aimed at achieving a given amplitude
but not at a definite target, and the latter as implying an additional process of visual
control. If so, the appropriate equation would be of the type:
movement time = a log2 A' + b log2 1/W' (8)
Where a and b are the slope constants for amplitudes and targets respectively."
Welford (1968) and Welford, Norris, and Shock (1969) argue that ballistic
movements have been shown to be substantially accurate without concurrent visual
control by Vince (1948) and if the accuracy of ballistic movements is independent
of their extent, the best fit of the data can be given by the following formula:
MT = b log2 (A'/W'i) + (b - a) log2 C (9)
Where C = W'q/A' and W j is the scatter width observed for any particular target
width under consideration. W'0 is the scatter of shots for ballistic movements of
29
amplitude A’. Welford found values for W'0 of 23.7 and 31 millimeters with
constants of a and b respectively being approximately 9.6 and 5.6 bits per second.
Welford, Norris, and Shock (1969) note that the value for a of 9.6 bits per second
is close to the figure for Fitts's results and the value of b of 5.6 bits per second is
close to that found by Hick (1952) for choice reaction times. "It is tempting to
suppose that while the former represents some capacity of the motor mechanism,
the latter is limited by the same elements of the sensory-motor chain as
choice-reactions," (Welford, Norris, & Shock ,1969, p. 12.) As can be seen from
the preceding discussion, A.T. Welford has made substantial contributions to the
theoretical development of psychomotor performance in regard to precision of
movements.
Knight and Dagnall (1967) found Welford's formulation of
MT = K log2 (A/W + 0.5) (Equation 5)
to be the best fit of their data using an apparatus that provided a pointer which was
swiveled by the subject through a vertical plane between two separate targets (i.e.
this was a wrist-rotation-type of movement task).
Keele (1968) provides a concise reiteration of the control feedback model
developed by Crossman and Goodeve (1963) but also introduces the concept of
"motor programs" that provide a pre-structured set of muscle commands that can
be executed independently of visual or kinesthetic feedback. Keele mentions that
this type of program control has three advantages. The first is that the degree of
30
attention required would be reduced. (Keele mentions that there has been very
little research in this regard.) Secondly, "successive stimuli may be anticipated so
that appropriate movements may coincide with the stimuli rather than lag behind."
And third, "it may be possible for movements to be made at a much faster rate."
(Keele, 1968, p.397) Keele provides an excellent review of past and current
(according to the date of his publication) evidence for the existence of
pre-programmed motor programs.
Beggs and Howarth (1970) have demonstrated that "a visually mediated
intermittent correction mechanism operates, since removing visual feedback, when
the hand is close to the target, has very little effect on the terminal accuracy,
provided that there is less than one corrective reaction time between the removal of
the feedback and the hand reaching the target. At greater times and distances away
from the target, the removal of visual feedback has an effect on terminal accuracy
which depends mainly on the distance the hand moves in the dark. This finding
suggests a simpler way of looking at the relationship between speed and accuracy
than has been suggested by either Fitts or Crossman." (Quoted from Howarth,
Beggs, & Bowden, 1971, p.208.)
Howarth, Beggs, and Bowden (1971) have a very interesting speed accuracy
equation derivation. Starting from the common observation that as a hand
approaches the target, it slows down, they postulate that during the ballistic phase,
the hand travels in an uncontrolled manner over the distance over which it is
accelerating. They reason that there should be a simple relationship between the
length of the uncontrolled part of the movement and the terminal error. They also
31
reason that the total time available for the entire movement will also be a function
of the total terminal error. From these assumptions they developed the following
equation for specifying the hand-to-target distance at the beginning of deceleration:
d = 814.9 (t/T) 1,4 (10)
Where d is the distance of the hand from the target in millimeters, t is the time
remaining before the target is hit in seconds, and T is the time for the total
movement in seconds. They also found the following relationship holds:
Where E is the root mean square of the deviations from a target line, E0 and < y g are
empirically determined constants, and dy represents the distance over which the
movement is uncontrolled for different values of T. Together with the previous
equation they arrive at the following equation for the total measure of error:
The authors state that "this equation does in fact describe the observed relationship
between speed and accuracy which justifies our basic assumption that the decrease
in accuracy with the decrease in time for the total movement is solely due to the
increase in the length of the ballistic phase of the movement." (Howarth, Beggs, &
Bowden, 1971, p.209.) However, they also note that this relationship and this
theoretical basis only holds for the slower movements.
E2 = E02 + (o5 du)2
(11)
E2 = E02 + (814.9)2 (og2 (t/T )2* 8
(12)
32
Several things are noteworthy for these researchers' results. First, they found that
E0 has a value of about 2.42 millimeters and they postulated that this may be due
to some kind of uncontrollable tremor. Even though they ended up rejecting the
concept, Welford (1968) and Welford, Norris, and Shock (1969) include a term for
tremor effects as part of their correction to Fitts' Law with an order of magnitude in
the same general vicinity of this value (a value of three millimeters). The other
term for the error equation is used by the authors as a variance due to the length of
the uncontrolled movement. On this assumption the constant value of 05
represents the angular accuracy in radians with which a movement can be directed
towards a target. The authors found a value of approximately 36 minutes of angle
for C T g . "This is a surprisingly small figure, much less than the accuracy of
kinesthetic localization (about 3°). Since the movement is always under visual
control, Gg may be a function of our ability to control movements visually, to
detect errors visually, rather than being a measure of the accuracy with which
predetermined orders are carried out by the motor system." (Howarth, Beggs &
Bowden, 1971, p.217.) Finally, it is extremely important to note the experimental
design used by these researchers. The orientation of the target and the home
position of the recording instruments (in this case a pencil) were dramatically
different from the traditional fits reciprocal tapping task. (In fact, the researchers
did not find a close fit of Fitts's results with their data.) In their experiment the
subject (only one male subject was used - no further data on the subject was given)
sat facing a vertically placed paper target in front of him. The subject was asked to
hit the target from the home position (which was located approximately 50 cm
away from the target, approximately at shoulder height, while holding the pencil in
his right hand) to the target. In time with alternate beats of a metronome.
While the experimental design and use of only subject makes it difficult to transfer
over these findings to those of Fitts and subsequent researchers using the Fitts's
reciprocal tapping task, it is certainly an interesting and well thought out approach
which has some parallel (i.e. the tremor effect aspect) to the theoretical
developments based on the information theoretic and feedback control models used
to interpret Fitts’ Law.
Klapp (1975) found that Fitts' Law held for long movements, but a different pattern
emerged for very short movements. Klapp interpreted these findings as implying
that long movements are under feedback control, whereas short movements are
predominantly programmed and ballistic. Klapp supported this finding by showing
that the elimination of visual feedback was more disruptive to the long movements
as opposed to the short movements.
Schmidt, Zelaznik, Hawkins, Frank, and Quinn (1979) found results that seemed
consistent for rapid (less than 200 msec) but not for longer movement times. The
researchers derived relationships among movement amplitude, movement time, the
mass to be moved, and movement error based on "two apparently fundamental
principles of movement control. These principles are: (a) the variability in the
force produced is linearly related to the amount of force produced, and (b) the
variability in the intervals of time produced is directly proportional to the amount
of time produced." (Schmidt, Zelaznik, Hawkins, Frank, & Quinn 1979, p.446.)
These researchers applied these principles and came up with relationships for 3
psychomotor tasks: single-aiming responses, reciprocal movements, and rapid-
timing tasks. In the single-aiming responses, they found that the variable error in
the subjects' end points was directly and linearly related to the amplitude of the
movement and inversely and linearly related to the movement time. Inserting
constants that can be empirically derived and solving for movement time yields:
MT = a + b (AAV1 ) (13)
Where W' is the actual width of the scatter of shots. As mentioned, the
researchers found this relationship to hold true only for movement times of
less than 200 msec. The single-aiming task involves moving a stylus from a fixed
resting point to a target.
For the rapid-timing tasks, the researchers found that the variable error in timing is
proportional to the movement time, independent of the movement amplitude and
independent of the mass to be moved. This rapid-timing task requires the subject
to provide a movement through a fixed distance (with the follow-through) in a
certain interval of time. For the reciprocal movements (the traditional reciprocal
Fitts tapping task) the researchers found that the variability in movement end points
(Wf ) is linearly and directly related to the movement amplitude, independent of the
movement time and independent of the mass to be moved. Again, it must be
emphasized that these results were found to hold only for movement times of less
than approximately 200 msec.
Meyer, Smith, and Wright (1982) reject the theoretical interpretations of Schmidt,
et al. (1979) and instead present a symmetric impulse-variability model that
explains the linear relationship found by Schmidt, et al. (1979) between movement
35
error, movement distance and movement time. Their model "assumes that a limb is
driven by the product of a force parameter and a time function with certain well-
defined qualitative properties, including symmetry, curvilinearity, and force-time
rescalabality." (Meyer, Smith, & Wright 1982, p.449) Their research is
noteworthy in that they utilize the principles underlying mass-spring biomechanical
systems and neurophysiology including electromyographic mechanisms to explain
their model and are able to unify the linear relationship found by Schmidt, et al.
(1979) and the general logarithmic formation of the Fitts' Law formula.
Wright and Meyer (1983) also found a linear (rather than logarithmic) formulation
to describe the accuracy of hand movements as did Schmidt, et al. (1979).
However, Wright and Meyer (1983) found this relationship to hold for movement
times "significantly" exceeding 200 msec. They conclude (p.279) that "the
linearity does not depend on movement brevity and/or feedback deprivation per se.
Instead it supports a temporal-precision hypothesis that the linear trade-off occurs
when aimed movements must have precisely specified durations."
Briefly stated, the temporal-precision hypothesis says that precisely timed
movements are mediated by a single pair of opposing force pulses which minimize
temporal but not spatial variability. This means that spatially precise movements
(as required by the Fitts' reciprocal tapping task) would be mediated by a
pre-programmed series of overlapping force pulses, which increase temporal
variability. The use of overlapping impulses should lead to a logarithmic trade off,
whereas a single pair of pulses would yield a linear trade off. (See Meyer, Smith,
& Wright, 1982, for further details.)
36
Wallace and Newell (1983) using five female and four male right handed students,
using a reaction time/movement time apparatus similar to that used originally by
Fitts and Peterson (1964) found support for Fitts' Law. However, they were most
concerned with investigating the visual control of discreet rapid arm movements.
In this regard, their findings indicated that vision was only used when movement
time was over 200 ms (as indicated by Klap, 1975) and even then it was only used
to varying degrees. On the basis of their findings these researchers rejected the
finding of Keele (1968) in regard to his discreet correction model.
Wallace, Hawkins, and Mood (1983) present an argument for enhancing Fitts' Law
by including the constant and variable errors of the subjects' end points in two
dimensions as well as the vertical component of the movement trajectory.
Although they did not provide a formulation which included the vertical
component of the movement trajectory, the following formula includes the
effective target width and effective target depth: ,
MT = b log2 (effective amplitude/effective target area) (14)
or
MT = b log2 (Ae/(tt(We/2) (De/2))) (15)
Where Ae is the effective amplitude, We is the effective target width, De is the
effective target depth, and b is the empirically defined constant for the slope of the
line fitted to the data. Using data from an obscure paper (Wallace, S.A.,1983), the
37
researchers found a correlation of 0.99 for this formula as compared to 0.97 for
Fitts's original equation as well as Crossman's (Crossman, 1957):
MT = b log2 (A/Wa) + b log2 (A/Da) (16)
Where A is the amplitude of movement, Wa is the actual target width, Da is the
actual target depth (perpendicular to the X-dimension) and b is the empirically
derived slope.
It is also extremely interesting for this author to note that Wallace, et al. (1983)
found Welford's use of log2 (AAV + 0.5) to have a correlation of 0.93 to the data.
This is quite surprising since when Welford used this formula to compare Fitts's
original data and when Fitts used it to compare his formula to subsequent research
(Fitts & Peterson, 1964), Welford's equation supplied a much closer correlation
between his index of difficulty and that originally derived by Fitts. It may be that
each researcher has come upon formulations which simply fit a particular set of
data better than another, and, in fact, have questionably sound bases theoretically!
MacKenzie, Marteniuk, Dugas, Liske, and Eickmeier (1987) made some interesting
contributions to the understanding of the different planning and control processes
as a function of movement amplitude and target size. While validating Fitts' Law
in its original formulation, they also found significant effects related to the velocity
profiles of the three dimensional trajectories of the stylus motion. The researchers
summarized their findings as follows: "As amplitude of movement increased, so
did the time to peak resultant velocity; peak resultant velocity increased slightly
38
with target size and to a greater extent with increases in the amplitude of
movement; the time after peak resultant velocity was a function of both amplitude
and target size. Resultant velocity profiles were normalized in the time domain to
look for scalar relation in the trajectory shape. This revealed that: resultant
velocity profiles were not symmetrical; the proportion of time spent prior to and
after peak speed was sensitive to target size only, i.e. as target size decreased, the
profiles became more skewed to the right, indicating a longer decelerative phase;
for a given target size, a family of curves might be defined and scaled on
movement amplitude.
These results suggest that a generalized program (base trajectory representation)
exists for a given target width and is parameterized or scaled according to the
amplitude of movement." (MacKenzie, Marteniuk, Dugas, Liske, & Eickmeier,
1987, p.629) Stated somewhat differently, "amplitude affects acceleration time,
deceleration time and peak velocity; target width affects deceleration time and to a
lesser extent, peak velocity." (p.642) Furthermore, "target size determines the
shape of the trajectory in terms of relative time spent in acceleration and
deceleration, and amplitude determines the shape of the trajectory in terms of a
gain factor." (p.644) As is clear from the previous two studies reviewed, three
dimensional analysis of movements may become an essential part of future
psychomotor performance research.
Langolf, Chaffin, and Foulke (1976) found that Fitts’ Law holds for finger, wrist,
and arm movements, but with clearly systematically different slopes. Schmidt
(1988) postulates that the slope increases progressively as the limb used changes
39
from the finger, to the wrist, to the arm, because the larger the limb, the more
sensitive it may be to changes in the index of difficulty. (There may also be some
question as to greater muscle group enlistment corresponding to more overlapping
motor programs and thus poorer performance on the more difficult tasks.)
Schmidt (1988) provides an excellent overview of the development and current
theory of the laws of simple movement. Schmidt argues strongly for the validity of
Fitts’ Law under a variety of conditions. He also presents a thorough discussion of
the various theories accounting for Fitts' Law as well as alternative theories such as
those described in this review. Schmidt (1988) also points out that there are some
instances in which the commonly accepted speed accuracy principle of greater
speed demanding less accuracy, does not hold. Schmidt (1988) also reviews his
own as well as other researchers' work on force-variability principles,
impulse-variability principles and the applications of the laws of movement to real
skills. It is one of the most comprehensive reviews of the relatively current
literature on the subject of psychomotor performance for hand and arm movement.
Meyer, Abrams, Komblum, Wright, and Smith (1988) developed a model called
the "stochastic optimized-submovement model". This model says that aimed
movement toward a target involves a primary submovement and an optional
secondary corrective submovement. "The submovements are assumed to be
programmed such that they minimize average total time while maintaining a high
frequency of target hits. The programming process achieves this minimization by
optimally adjusting the average magnitudes and durations of noisy neuromotor
force pulses used to generate the submovements." (Meyer, Abrams, Kornblum,
40
Wright, & Smith, 1988, p.340) This theoretical basis leads to a formulation based
on the square root of the ratio of the distance from the starting point to the target
and the target width:
Although the authors of this work argue that "numerous results from the literature
on human motor performance may be explained in these terms" (p.340) the
correlations presented for the experiments performed in association with these
theoretical considerations are not impressive.
Leisman (1989) showed that Fitts' Law holds for finger, wrist, and whole arm
motions. Furthermore, observation of motion trajectories supported a visually
mediated discrete correction control model. However, the researcher rejected the
use of linear control models in explaining Fitts' Law since there was severe
non-linearity in the movement responses.
Returning to the information theoretic basis for Fitts' Law, MacKenzie (1989)
proposed that a better fit of Fitts's data could be achieved if a more exact
representation of Shannon's theorem 17 is used:
(17)
MT = a + b log2 ((A + W)/W) = a + b log2 (A/W + 1) (18)
Using this formula MacKenzie (1989) found significantly higher correlations
between movement time and this new form of the index of difficulty with the data
41
for Fitts’ s reciprocal tapping task as compared to Fitts's original formulation as well
as Welford's most commonly cited formulation (MT = a + b log2 (A/W + 0.5)).
This is certainly an interesting and long overdue observation and was tested with
the data for the present study.
SUMMARY
As Schmidt (1988) and others note, there really has been very little real progress to
improve the formulation of Fitts' Law. The mathematical superiority of corrections
proposed thus far is negligible from a practical standpoint as compared to Fitts’ s
original formulation. Furthermore, while theories, both simple and complex,
abound, minimal (albeit questionable) progress has been made in establishing a
theoretical basis for the general validity of Fitts' Law. Nevertheless, important
methodological refinements and improvements have been made on the original
apparatus and procedures used by Fitts for the reciprocal tapping task. These
methodological considerations have included the use of the simple apparatus of a
pencil and paper for recording the actual scatter of hits for any given target.
There may be one problem with this simple apparatus that has not been brought up
in the literature thus reviewed. This is the potential problem of subjects being
influenced by the visual presence of a growing scatter of hits. It may be that
subjects tend to use the dots already made as a new target area. The results
presented in this thesis provide some support for this conjecture. An interesting
experiment would be to devise an apparatus that would allow for recording of the
actual scatter of hits while eliminating the visual cues accrued from a pencil and
paper recording system, while maintaining a consistent presentation of the target.
42
Electronically recording wrist rotations may have this advantage, as well as the
aforementioned advantage that the ballistic movement of the hand is not artificially
terminated by the surface of the target, but allows for continuous control of the
stylus or pencil by the subject
For the literature reviewed thus far, tasks that have been studied include the
traditional Fitts' reciprocal tapping task using electronic monitoring of hits and
misses, Fitts' reciprocal tapping task using other more complicated apparatus for
recording hits and misses (Crossman & Goodeve, 1963), Fitts' reciprocal tapping
task using pencil and paper (in various orientations and target shapes and sizes),
stylus moving tasks whereby the stylus starts in a resting position and is moved to a
target upon a "go" signal, peg transferring tasks (used by Fitts originally), washer
transferring tasks (also used in Fitts's original work), and wrist rotation type tasks
with various recording apparatus. Of these tasks, the most preferred (on the basis
of "tradition" as well as methodological considerations) have been forms of the
Fitts' reciprocal tapping task and wrist rotation type tasks. As described previously,
wrist rotations have some definite methodological advantages. In contrast,
Welford (1968) has mentioned some disadvantages of pin transfer and washer
transfer tasks. Other researchers have made similar observations. (It is interesting
to note that the work by MacKenzie, 1989, to provide a more direct application of
Shannon's theorem 17 did not produce the desired results for disk (washer) transfer
and pin transfer tasks.)
The basic relationships evident in Fitts' Law have been studied extensively as can
be seen from the preceding review. The work done has contributed to
43
methodological improvements, theoretical developments, and improvements in the
actual formulation of the equation. The methodological developments have
included simplifying and improving the apparatus (e.g. using pencil and paper or
wrist motion). Theoretical developments have helped in the understanding of the
underlying basis for this simple mathematical relationship. Finally, improvements
in the actual formulation of the equation have been made so that it better fitts the
actual data and provides a better tool for predicting movement time based on the
basic parameters of target size and a measure of movement distance. The
following section will briefly review some of the many different applications of
Fitts' Law that both support and confute the various formulations of Fitts' Law.
The Generalizability of Fitts' Law
What is commonly known as the "speed-accuracy trade-off1 (Schmidt, 1988) states
that accuracy of a movement is compromised by emphasizing speed, and likewise,
speed is compromised by an attempt to achieve more precise accuracy. From an
intuitive and experiential basis, it is no surprise that this general principle is an
overwhelmingly predominant finding with virtually all movement tasks. What
may be somewhat surprising is that a simple mathematical formula (Fitts' Law) has
been found to be almost as robust as this general speed-accuracy trade-off
principle. What follows is a brief review of some of the different types of tasks
and applications where Fitts' Law has been shown to be valid as well as those
situations where the formula does uoi fit the data.
Meyer, Smith and Wright (1982) argue for the generalizability of Fitts' Law to a
variety of applications. (The following references in this paragraph are quoted
44
from Meyer, et al., 1982.) Langolf, Chaffin, and Foulke (1976) showed Fitts' Law
to hold in an experiment where minute finger movements were observed while
looking at targets through a microscope. Jagacinski, Repperger, Moran, Ward, and
Glass (1980) found Fitts' Law to hold for a step-tracking task using a joystick that
had either a position control or velocity control mechanism. (Note that previous
references have identified some step-tracking tasks as failing to provide a speed-
accuracy trade-off that "obeys'' Fitts' Law.) Kerr and Langolf (1977) found that
Fitts' Law holds for throwing as well as tapping tasks. Dixon, (1985), Hoffmann
(1988), Kerr (1973, 1978) found Fitts' Law to hold for rapid movement
underwater.
Wallace & Newell (1983) also argue that Fitts' Law is still considered one of the
most stable relationships in the perceptional motor domain. (The following
references in this paragraph are quoted from Wallace & Newell, 1983.) As well as
mentioning some of the above supporting research, they also mention that Fitts'
Law has shown to hold for different populations such as mentally retarded
individuals (Wade, Newell & Wallace, 1978), pre-school children (Wallace,
Newell & Wade, 1978) and older children (Sugden, 1980). Meyer, Abrams,
Komblum, Wright, and Smith (1988) also mention that Fitts’ Law has shown to
hold for patients with Parkinson’s disease (Flowers, 1976).
Kelso, Southard, and Goodman (1979) did not find Fitts' Law to hold when
subjects performed two-handed movements to targets of extremely different
difficulty. Instead, they found these movements to be simultaneous and
constrained by the more difficult of the target configurations. Kelso, Southard, and
45
Goodman (1979, p. 1029) conclude that "this result suggests that the brain produces
simultaneity of action not by controlling each limb independently, but by
organizing functional groupings of muscles that are constrained to act as a single
unit."
In a study of handwriting, Viviani and Terzuolo (1982) found that Fitts' Law
applies to hand writing tasks. It is interesting to note that Woodworth (1899) made
some early observations on the accuracy of hand movements in relation to
handwriting.
Indermill and Husak (1984) found Fitts' Law to be applicable when they
investigated the principles of force and variability of force in relation to an
over-arm throwing task. Jagacinski, and Monk (1985) found that Fitts' Law held
for hand movement using a joystick as well as for head movement using a
helmet-mounted sight, with better performance on the joystick. Kantowitz, and
Elvers (1988) also found Fitts' Law to hold consistently for four separate
combinations of position, velocity, and two levels of control display gain using an
isometric controller.
As mentioned previously in the reviews from other sources, Kerr (1973 and 1978)
found Fitts' Law to hold for underwater reciprocal tapping tasks. Dixon (1985),
Hoffmann (1988), and Kerr (1973 and 1978) also found Fitts' Law to hold for
underwater movement. Dixon (1985) found no gender effects.
46
The Fitts' reciprocal tapping task has been used to test psychomotor performance
for a variety of conditions. Yamada (1986) used the number of tappings and
percent of correct detections of a target in order to test the hypothesis that high
performance (type-P) behavior becomes more effective when affected by high
maintenance (type-M) behavior. Mohan and Bhatia (1985) used a tapping task to
examine the relationship of psychomotor performance with intelligence and gender
using 30 boys and 30 girls with between the ages of 10 and 14 years. Normal and
gifted subjects performed consistently better on the tapping tasks than did mentally
retarded subjects. It was interesting to note that they found the boys to perform
significantly better than the girls on the tapping task. Fowler, Taylor, and Porlier
(1987) studied the effects of hypoxia on movement time using the traditional Fitts'
reciprocal tapping task. They found that the slope of the Fitts' function was
increased by hypoxia effects. They also found the slopes to increase when target
width and movement amplitude were analyzed separately. Fowler, Taylor, and
Porlier (1987, p. 1475) postulated that movement time "is also slowed due to a
disruption of both the aiming and ballistic processes controlling movement."
Kerr and Hughes (1987) did not find any difference between learning disabled
students (age 6 to 8 years) and a control group of normal students using the
traditional Fitts’ reciprocal tapping task. Kerr and Hughes (1987, p.72) concluded
that "getting information into the system may be the processing problem."
Haaland, Harrington, and Yeo (1987) conducted a study on the effects of task
complexity on movement ipsilateral to lesion using the traditional Fitts' reciprocal
tapping task. A control group consisting of 20 subjects were compared to 10 left
hemisphere and 9 right hemisphere stroke patients with similar lesion volumes. It
was noted that the left hemisphere group's lesions were more anterior. The results
of the study found that only the left hemisphere group showed significant deficits
with greater impairment found in the wide target condition. (Target widths of one
or four centimeters were used.)
Andres and Hartung (1989) cite Drury (1975) and Williams and Werner (1985) as
finding Fitts' Law to hold true for lower limb movements. In their own research,
Andres and Hartung (1989) found that Fitts' Law held for head movement using a
reciprocal tapping task. They found a mean information processing rate for the
experimental head movement of about 7 bits/second.
Wiker, Langolf, and Chaffin (1989) evaluated the effects of arm posture on the
performance of a reciprocal peg-to-hole movement task and, while Fitts’ Law held
for all postures, a decrement of performance was observed such that positioning
times increased 15.3% and 26.5% respectively with elevation of the hand from -
15° to 60° respective to shoulder level. This has important ramifications for the
design of tapping tasks so that arm posture is kept consistent between
subjects.
In one of the most interesting applications of Fitts' Law encountered by this author,
Georgopoulos and Massey (1987) found that Fitts' Law holds for a hypothesized
rotary motion of an imagined movement vector, and that both real and imagined
movements may be governed by the Fitts' Law relationship. Using a
manipulandum, subjects were instructed to generate a movement (using wrist
rotation) at an angle from a stimulus direction which varied in two dimensional
48
space from trial to trial in a pseudorandom fashion. The angles were 5, 10, 15, 35,
70, 105, and 140 degrees. The movement of the manipulandum was almost
frictionless with negligible inertia. The researchers interpreted their results in
terms of an internal rotation of an image of the movement vector. "Since this
model postulates a mental motion of an imagined vector, we were interested to find
out whether Fitts' Law, which holds for real movements, will also hold in the
present case." (Georgopoulos & Massey, 1987, p.365) The researchers treated the
reaction time as a mental movement time. They found that Fitts' Law described
very well the results of their study. "This suggests that both real and imagined
motions may be governed by the same principles in the amplitude/accuracy
domain." (Georgopoulos & Massey, 1987, p.369) The concept that a cognitive
process itself, in this case the cognitive process involved in reaction time, would
actually follow a Fitts' Law relationship, speaks of the extreme robustness and
generalizability of Fitts' Law.
Age and Gender Studies
With all that has been written and studied in regard to Fitts' Law, it is astounding
that so little has been done in regard to studying age and gender effects. While
some studies have peripherally analyzed gender effects, age related investigations
have been extremely limited. Virtually all research (as is true for other fields, as
well as psychomotor performance) have used university students as subjects.
While there has been some work done involving children, there has been little work
with older individuals, the only substantial work having been initiated by Welford.
49
Welford (1961, p.138) states, "evidence relating age systematically to the accuracy
in speed of movement is extremely limited, and only one, somewhat preliminary
experiment, by N. Welford (see Welford, 1958) will be considered." Welford
begins his discussion with a generalized statement of Hick's Law:
T = a + b log2 N (19 - equivalent to Equation 5)
Where, for accurate movements, T = movement time and N = the ratio between the
distance from the starting point to the far edge of the target and the distance
between the near and far edges of the target (A/W + .5). This corresponds to the
most commonly used form of Welford's modification of Fitts' Law (Equation 5).
The aforementioned research regarding age showed that holding target size
constant shows a proportional rise with age, meaning that the slope, b, in the above
equation increases with age. However, holding distance constant yields a rise with
age of an absolute amount, corresponding to "a" in the above equation. Regarding
these results Welford (1961, p. 143) states, "age effects are shown in some cases of
each kind of performance as an increase in a, and in others as increase in b. The
reasons for the discrepancies between different results are not clear, but detailed
examination of performances and inferences about the mechanisms underlying
them, suggests that the increase of a with age occurs when the signals for action are
effectively brief, and an increase of b when their effective duration is longer." In
the experiment described, subjects’ age ranged from the 20's to 60's and evaluation
was made for each decade. This was a cross-sectional study.
50
Welford, Norris, and Shock (1969) cite Morikiyo and Nishioka (1966) and the
above study as two studies indicative of an analysis of Fitts' Law in relation to age.
Morikiyo and Nishioka (1966) found that differences in performance between
groups in their 20's and 50's could be accounted for with a slight rise in the value
for b in the above Equation (19).
With these two studies in mind, Welford, Norris and Shock (1969) designed a
reciprocal tapping task (similar to Fitts's original tapping task) that was
administered to subjects participating in the Baltimore longitudinal study of aging
(Shock, 1984). The test was administered to all participants on each visit from
1960 through 1981, including women as of January, 1978. Results of analysis of
the first visits of 325 men in their twenties through seventies was reported in
Welford, Norris, and Shock (1969). These results are described below.
Two equations were used to evaluate the changes of performance with age. The
first of these (mentioned previously) is:
MT = K log2 (A7(W' - c) + 0.5) (Equation 7)
Where A’ is the actual amplitude - the distance between the centers of the actual
scatter of hits - W' is the actual scatter width, and c is a constant with a variety of
explanations including a tremor effect.
Using this equation, performance tended to rise from the 20's to the 40's and
decline thereafter. Welford, et al. (1969) comment that peak performance is
51
usually reached somewhat earlier (presumably for psychomotor performance). The
constant, c, attributed to tremor, showed no consistent trend in relation to age.
The second equation used by Welford to evaluate age was a somewhat complex
derivation starting in the form:
MT = a log2 A * - b log2 W'j + (b - a) log2 W'0 - (20)
The terms of this equation have the same meaning as discussed earlier (see
Equation 9), "where W'0 is the scatter of shots that would be observed with
ballistic movements of amplitude A', and W'j is the scatter observed with any
particular target width under consideration." (Welford, Norris, & Shock, 1969,
p. 11.) This formulation has the advantage that it yields interesting conclusions
depending on the way in which the formula is applied. Welford, Norris, and Shock
(1969, p .ll) explain:
The part played by (b - a) log2 W'0 depends on whether or not W'0
increases with A'. This, as Woodworth (1899) pointed out, is
difficult to measure directly as it involves controlling both
movement time and also vision, but if eq. [20] is valid an answer
can be inferred from the present data. Suppose, for example, that
Weber's Law held and that W'0 rose in proportion to A'; it would
then be possible to rewrite eq. [20]:
movement time = a Iog2 A'/(C A') + b logj (C A'/Wj)
b log2 (A'/W’ j) + (b - a ) log2 C [Equation 9]
where C = W’ q/A = the Weber fraction.
5 2
Welford states that the above equation implies that all the points plotted from any
data in terms of time per movement versus log2 (A'/W1 + 0.5) should lie on the
same straight line with slope b. This did not fit the observed data in this
experiment. Welford continues, however, "If alternatively W'0 is constant at all
values of A', the expression (b - a) log2 W'0 becomes a constant and the data
should fall on a straight line described by eq. [20], provided suitable values are
chosen for a and b." (Welford, et al.. 1969, p .ll) This formulation, did in fact fit
the data well.
Using Equation 20, a pattern similar to Equation 7 was found in relation to age
effects. However, Welford, et al. (1969, p. 12-13) note "interesting differences
between the several measures." They explain their results in terms of motor
control and decisional processes:
Slope a and its reciprocal in bits per second for variation of
amplitude with W constant, indicate performance at a peak in the
thirties. Slope b and its reciprocal in bits per second for variation
of W' with amplitude held constant, show maximum performance
in the forties. W'0 is at its lowest, implying greatest accuracy of
absolute positioning, in the twenties. The percentage change with
age from the best scoring age group to the seventies is greatest for
W'0 and least for b suggesting factors of position sense and motor
control decline more with age than do the decisional processes
responsible for accuracy of homing on a target, although the
period over which the decline takes place is longer.
Welford, et al. (1969) note that these results may be specific to the subject
population who were of a notably higher intelligence. In other words, the high
performance peaking out in the 30's and 40's, may be indicative of a more
intelligent population sample. Welford, et al.(1969, p. 13) note that "previous
53
evidence suggests that people of high intellectual grade show less than average
decline with age of intellectual capacities but about the same decline of motor
functions as the general population (e.g. Gilbert 1941; Pacaud, 1955; Ctement
1969). A more representative sample might therefore have shown greater decline
of performance in terms of b, but would have been unlikely to have shown less in
terms of a or W'0."
The study by Welford, Norris, and Shock (1969) is of particular interest to this
author since the data that was analyzed by these authors continued to be collected
until 1981 and has been used in the present study to evaluate these findings in more
detail, in a longitudinal, rather than strictly cross-sectional manner, and to examine
possible gender effects.
Murrell and Entwisle (1960), while not addressing speed-accuracy trade-offs, made
some interesting observations between young and old subjects (the younger group
was in the age range 20 to 25 years and the older group was in the age range 60 to
65 years). Murrell and Entwisle (1960, p.948) found that the movement pattern in
responding to a four-choice stimulus consisted of a "very rapid acceleration at the
outset, followed by an equally rapid decrease in acceleration to a minimum at
approximately 0.1 sec. from the commencement of the movement, which was in
turn followed by a second acceleration to a 'peak' of approximately half the value
of the first. This whole phase occupied approximately a third of the total
movement time. While the characteristic pattern at the outset of the movement was
found in both young and old subjects, the old subjects accelerated less rapidly than
the young and the "dip" past below the 0-acceleration line showing that the older
men had a short negative acceleration phase." No significant differences were
found between movement times for the young and old subjects.
Schellekens, Kalverboer, and Scholten (1984, p.20) found that "Age differences
appeared mainly in the homing time, not in the duration of the distance covering
movement phase (DCMP). Accuracy and velocity of the DCMP differed with age.
results suggest that age differences in homing time may be related to both the
accuracy of the DCMP and the Ss' rate of information processing." The subjects
for this study involved 25 children aged 5 to 9 years old and 5 adults with a mean
age of 28 years. A reciprocal tapping task was used.
In a traditional Fitts' reciprocal tapping task, Wallace, Newell, and Wade (1978,
p.509) found that movement time "was greatly affected by these variables
[amplitude and accuracy - target width] in a manner predicted by Fitts' Law. Also,
the difficulty of movement appeared to effect MT of pre-school children to a
greater degree than that found previously with adults. Information processing
differences between children and adults were used as a tentative explanation for
these results." In other words, for the children, they found that performance was
inhibited significantly with the index of difficulty of the task for the children, while
such effects were found to be less apparent in previous studies on adults. (For a
review of literature which includes a validation of Fitts' Law as it relates to
development of skilled motor behavior, see Gaadgold-Edwards, 1984 and
McCracken, 1983.)
5 5
Hay (1981) found similar results for subjects of the ages 5, 7, 9, and 11. Hay
(1981, p. 177) concludes: "the analysis of movement time showed that, as children
grow up, the movement speed increased and was gradually less affected by the
level of difficulty of a given task; moreover the respective effects of accuracy and
amplitude requirements on movement time changed with age, resulting in distinct
evolutive patterns." Twelve subjects for each age group were evaluated (6 boys
and 6 girls for each group). Similar increasing slopes of the fit of the data to Fitts’
Law for each age group were found to be similar to that found by Welford, Norris,
and Shock (1969). Hay (1981, p.185) summarizes his findings as follows:
In 5-yr-old children, the weak effect of amplitude and the strong
effect of accuracy on movement time indicate that the feedback
control processes, when they occur, are generally limited to the end
of the movements, which allows the hand to cover rapidly any
distance to the target; but the adjustment onto the target requires a
long time because, for lack of practice, the guiding activity is not
yet efficient enough and well integrated to the whole motor process.
On the contrary, in 7-yr-old children, the data suggest that
movements are chiefly controlled by the feedback processes of that
age, even during the initial approach of the hand, which makes
movement time more dependent on amplitude than it is at 5. Then
this dependence decreases between 7 and 11, while movement time
decreases too, which could be related to a decrease of the feedback
processes, or rather, to a better integration of these processes with
the ballistic component, during a movement. The efficiency of the
guiding processes seems to improve regularly with age, as shown
by the decrease of the accuracy effect between 5 and 11, with a
particularly important improvement between 5 and 7.
While Hay (1981) did not report gender differences, as noted earlier, Mohan and
Bahatia (1985) found that boys (age 10 to 14) perform significantly better than did
girls on a tapping task.
56
Stelmach, Amrhein, and Goggin (1988) using unimanual, bimanual symmetrical,
and bimanual asymmetrical movements for young subjects (5 males and 5 females
of mean age 22.4 years) and elderly participants (5 males and 5 females of mean
age 69.8 years) found that the elderly participants showed a proportional increase
over the young participants in movement time. Stelmach, Amrhein, and Goggin
(1988, p.18) also found that "compared with the young participants, the elderly
participants showed greater asynchrony in response initiation of bimanual
movements; increased inability to subsequently compensate during response
execution also resulted in a greater asynchrony in response termination. These
results suggest specific aging deficits in bimanual coordination processes." (See
comment on Kelso, Southard, & Goodman ,1979.)
Darling, Cooke, and Brown (1989) using a manipulandum for a visual step-
tracking task found older subjects to be less accurate in terms of the control of the
movement trajectories; however, the elderly subjects improved with practice. The
subjects were nine elderly (68 to 95 years of age, no mean given) and six young
(21 to 24 years of age). The researchers did not provide an evaluation of Fitts'
Law, but examined EMG (electromyography) readings and explained their findings
in terms of tonic coconcentration of agonist and antagonist muscles prior to and
during movement, abnormal phasic antagonist EMG activity, and non-existent or
inappropriate timing of an antagonist muscle burst associated with the deceleration
phase of movement. In a similar experiment Cooke, Brown and Cunningham
(1989) found "variability was most apparent in the deceleratory phase of movement
where the elderly subjects often showed hypermetria. Some elderly subjects also
57
showed movement decomposition, the movements being made as a series of
discrete submovements.’ ’ (p. 159).
With the intent to examine possible gender-related speed-accuracy tradeoffs that
may take place with age, York and Biederman (1990) administered the Fitts’
tapping task to 62 males and 84 females, 20 to 89 years of age. They found that
women appear to perform better than men on the Fitts tapping task. They also
found that the young men seem to favor speed over accuracy. The slopes for the
lines fitted to the data using Fitts's original formula showed that women perform
better on the more difficult tasks than the men and that, with age, women show less
slowing. This work by York and Biederman is the first to examine the factors of
speed, accuracy, age, and gender using the Fitts' tapping task.
Most recently, Welford (1990) reviewed the current literature, including York and
Biederman (1990), and concluded that the best formula for Fitts’ Law is given by
either Log2(A/W + 0.5) (Equation 5) or Log2(A/W + 1) (Equation 18).
Furthermore, Welford outlines an explanation for a shift from and emphasis on
speed for the young to an emphasis on accuracy for the old.
While this concludes the review of relevant data regarding Fitts’ Law, a few brief
comments are relevant regarding the general finding of behavioral slowing with
age. Vercruyssen (1991) states that "one of the most robust findings in behavioral
research is the general slowing in behavior with age." Bitten, Woods, and
Williams (1980) in an already classic review of the causes, organization, and
58
consequences of behavioral slowing with age, present some concise findings on
this subject. These findings and conclusions can be summarized as follows:
l.The loss in behavioral speed with age is a reflection of a general mediating
process within the central nervous system.
2.0ne property of the slowing appears to be a pervasive influence on all events
mediated by the nervous system.
3.Reduction in synaptic density with age appears to be a good observed change
accounting for the slowing.
4.Reduction of cells within the reticular system is a possible contributor.
5.Reduction in neurotransmitters, neurofacilitators, or neuroinhibitors may also
contribute.
ti.Changes in activity level may also play a causative role in changes of the nervous
system.
7.Speed of behavior might be of great practical use in determining the level of an
individuals' biological functioning and perhaps even in predicting longevity.
The above conclusions must be considered in an overall evaluation of the
implications and meaning of Fitts’ Law as applied to changes due to aging.
59
Reviewing primarily reaction time studies, Salthouse and Somberg (1982) found
that improvement in performance with practice is evident in both young and old
subjects and is perhaps greater in old subjects than in young subjects. Furthermore,
sizeable age differences still remain even though the improvements with practice
are considerable. They also found that there is little evidence that the way in which
subjects perform or improve in the tasks differs between young and old subjects.
Interestingly, they found that older subjects appear to operate with a greater
relative emphasis on accuracy than younger subjects. (This finding was supported
by the results of the present study.) They conclude that a fundamental
physiological change in the nervous system seems to be responsible for age related
performance differences. The consequence of this "physiological change" is a
slower rate of processing for nearly all types of information.
In studying adult visual choice-reaction time in relation to age, gender and
preparedness, Lahtela, Niemi, and Kuusella (1985) provided some interesting
insights into age and gender differences. First, in regard to gender differences,
they brought up the fact that there has been conflicting information as to the speed
of response between older men and women. One study reviewed indicated that
women were faster than men. The researchers postulated that this finding was a
result of the fact that on the average, elderly women are healthier than elderly men,
and hence, more capable of producing faster responses. In their present study, they
found that old people show exceptionally long reaction times with a short inner-
stimulus interval, suggesting that they have difficulty in getting prepared for an
uncertain event. They also found that men were consistently faster than women
across all age levels. However, while this finding confirms their suspicion that the
other study showed a fast reaction time for elderly women, there is a trade-off
involved since they found that while the men performed faster, they had an
increased error rate. The researchers concluded that men may have faster
movement times as has been indicated by some studies. They also made the
interesting suggestion that there may be gender differences due to some task
specific effects (e.g. a gender difference in spatial abilities). In other words, men
are known to be better at spatial processing and women better at semantic code
processing. These results were considered in the present study.
61
CHAPTER III:
METHOD
The method used to determine the effects of age and gender on the speed and
accuracy of hand movements is presented in the following sections: Subjects,
Apparatus and Task, Procedure, and Treatment of Data.
Subjects
The subject pool was composed of 1338 individuals: 1060 males and 278 females
(aged 17 to 100), participants in the Baltimore Longitudinal Study of Aging
(BLSA) who performed a reciprocal tapping task on each visit from 1960 to 1981.
The BLSA began in February, 1958 and originally recruited only men. In January,
1978 women began to be included in the study. The main purpose of the BLSA is
to study "normal" aging. Study participants were self-recruited volunteers from the
Baltimore area, and therefore were neither a random sample nor a representative
sample of the Baltimore population.
Originally, subjects recruited their relatives, friends, and co-workers. This has led
to a somewhat homogeneous group of subjects from the upper-middle
socioeconomic bracket who differ from the general population in that they are
happier, healthier, and more likely to be married than the general population
(Andres, 1978). Over 70 percent of the subjects were college graduates, and over
40 percent held advanced degrees. See Appendix A for the informed consent form
signed by each participant.
62
Apparatus and Task
The following apparatus and task description is based on information derived from
Shock, 1984, Welford, Norris, and Shock, 1969 and Cathy Dent, Baltimore
Longitudinal Study of Aging, personal communication, October 12, 1990.
Subjects performed a reciprocal tapping task designed by Welford (Shock, 1984).
Using a number 2 pencil subjects tapped alternately on each of two targets drawn
on paper. (See Figure 2.) The pencil was sharp for each subject and was modified
by the use of a non-slip tape to provide a good coupling between the subject's hand
and the pencil. The tape did not add appreciably to the pencil diameter.
p j v ^ Tl Vj Y L '4iu5 It I
^ v' ^ 'i t mi
i HfL-J^rn 1 M
Figbre.2. BLSA participant (Leslie Higbie) conducting the task.
63
Each target configuration consisted of four parallel lines - two lines per target
Each line was approximately 4 1/2 inches (115 millimeters) long. Three different
target widths were used (4, 11, and 32 millimeters) in conjunction with three
different movement requirements (50, 142, and 402 millimeters) for a total of nine
target configurations. (See Appendix B for replicas of the target configurations
and Appendix C for samples of the first six actual used targets. The targets with
the largest amplitudes were not included as examples.) The constructed amplitudes
of movement (center-to-center distance between targets) were equal to the
"movement requirement" minus one-half of the target width for that target
configuration. This means the constructed movement amplitude was different for
each target configuration and is given in Table 1.
Table 1
Target Amplitude/Width Measures (given in millimeters!
Center to Center
Width Amplitude Constructed Amplitude Constructed Width
Small Wide 34 32
Small Intermediate 44.5 11
Small Narrow 48 4
Medium Wide 126 32
Medium Intermediate 136.5 11
Medium Narrow 140 4
Large Wide 386 32
Large Intermediate 396.5 11
Large Narrow 400 4
64
Procedure
The following section is based on information derived from Shock, 1984, Welford,
Norris, and Shock, 1969 and Cathy Dent, Baltimore Longitudinal Study of Aging,
personal communication, October 12, 1990. All testing took place at the
Gerontological Research Center (GRC) in Baltimore, Maiyland. Subjects were
tested according to the test interval schedule given in Table 2.
Table 2
BLSA Test Interval Schedule
Yea:
Age Test Interval
February, 1958 to July, 1970 2 0-70 18 months
February, 1958 to July, 1970 over 70 12 months
July, 1970 to July, 1981 20-59 24 months
July, 1970 to July, 1981 60-70 18 months
July, 1970 to July, 1981 over 70 12 months
July, 1981 to Present All 24 months
Women began to be tested as part of the Baltimore Longitudinal Study of Aging
(BLSA) in January, 1978. Each subject participated in a battery of tests during a 2
1/2 day period. The reciprocal tapping task was administered on each visit from
1960 to 1981.
Subjects could select a pencil from several offered, but the pencils were similar
except for the length (due to repeated sharpening). Each subject had a practice trial
with one target configuration, followed by the recorded trial of each of the nine
65
target configurations. Subjects were seated at a desk and given the target
configuration to be used. They were allowed to position the paper in front of them
so that they were comfortable with its orientation. The subject would hold the
paper with the non-dominant hand and tap back and forth from one target to the
other using the dominant hand.
The instructions read to the subjects are given in Appendix D and include the
instruction to "be accurate in hitting the target and at the same time maintain
maximum speed". A total of 100 hits were made on the targets (50 each side). The
administrator of the test counted the hits and, using a stopwatch, recorded the time
for the total 100 hits. The administrator would say. "ready", pause, say "go"
starting the stopwatch, begin counting until 100 hits had been made, stop the
stopwatch, and tell the subject to stop tapping.
Four parameters were recorded for each of the nine target configurations:
1. Total time in minutes (to two decimal places) for all 100 hits to be
accomplished. (Seconds were converted to hundredths of a second.)
2. The resultant width of the left target, WL.
3. The resultant width of the right target, WR.
4. The distance between the leftmost hit and the rightmost hit, excluding
any wild deviant hits, D\
Figure 3 shows an example of these measurements.
66
- \
\—\
Figure Basic measurement parameters of targets and scatters of hits.
67
The nine target combinations were presented in different orders to different subjects
in such a way that the serial positions both of the conditions and of the transitions
from any condition to any other were appropriately balanced. The orders of targets
presented are given in Appendix E.
Independent Variables
The independent variables in this study were: 1) age, 2) gender, 3) measures of the
distance between targets, 4) measures of the target width, and 5) visit number -
which was used for the longitudinal analyses as a measure of aging within subjects.
The Index of difficulty (ID), which was a function of 3) and 4) above also served as
an independent variable.
Dependent Measures
The primary dependent measure was movement time. However, the slopes (b) and
y-intercepts (a) of the lines fitted to the "best" equation were treated as dependent
measures to gain insight into age and gender effects.
Treatm ent of Data
In order to fairly evaluate age and gender differences, it is critically important to
have a formula that provides a good fit to the data for each age group by gender.
Therefore the pursuit of the "best" equation was of primary initial concern. The
treatment of data can be outlined as follows: 1) first, "suitable" data was selected
from the raw data, 2) next, formulas were tested to see which one provided the best
fit to the first visit data, 3) this formula was used to evaluate age and gender effects
based on first visit data, 4) based on this evaluation, a new formula
68
was created which incorporated age and gender* 5) this new formula was then
tested similar to step 2 above to evaluate how well this formula fit the first visit
data, 6) starting with the first visit and using a straight line spline between visits,
data for bi-annual visits (one visit every other year) were interpolated for those
subjects that had more than one visit, 7) finally, the formula found in step 2 above
was used to evaluate longitudinal age effects using the data obtained in step 6
above for subjects that had nine or more interpolated (splined) visits. The data for
visits 1-9 (representing data for 16 total years) were used in this longitudinal
analysis. There were a total of 154 (male) subjects that had at least 9 visits. These
steps are described in more detail in this section.
STEP 1 - PURIFYING OF DATA
Elaborate methods to maintain as much of the raw data as possible were not felt to
be necessary since such a large amount of data existed. Therefore, all data for any
visit that was missing any portion of the data under investigation or had any data
out of acceptable ranges would be eliminated. Out-of-range data was defined as
values for WL, WR, D', and MT that were at the upper (99mm, 99mm, 999mm,
and 5994ms respectively) or lower (0 for all measures) limits of the original
parameter’s range. By this process only 126 (1.9%) out of an original 6,501 visits
were eliminated and only 17 of these visits were for subjects with data for that visit
only (i.e.. resulted in the elimination of a subject).
This step also involved reorganizing and transforming some data into more easily
analyzable units. No precision was lost with this conversion. Appendix F contains
the file formats for the raw input files (the format the data was in when it was
69
received from BLSA), Appendix G contains a sample of input file data, Appendix
H the format for the subsequent output file that was used in the data analysis and
Appendix I a sample of output file data. Movement times, which were recorded in
minutes to the hundredth of a minute for 100 total taps, were transformed to
milliseconds for the average time per movement (thus the value of 5994ms per
movement = 9.99 minutes per 100 taps for the upper range limit on MT).
STEP 2 - FINDING A FORMULA
Two hundred and forty one (241) unique formulas were applied to several
groupings of the data to determine which formula was the best representation of the
data. The 241 formulas were derived from all possible combinations of six (6)
basic logarithmic expressions, two (2) logarithmic bases, five (5) different
measures of movement amplitude,four (4) different measures of target width, and
Welford's formula (Equation 20). (6x2x5x4+l - 241.) The six basic logarithmic
expressions were:
log(A/W)
log(2A/W)
Iog(A/W + 0.5)
log(A/W + 1)
log(A/(W - c) + 0.5) where c = 3mm
log(A/(W - c) + 1) where c = 3mm
Except for the last expression, each of the above have been described in Chapter II.
This last expression was included as a logical synthesis of the fourth and fifth
70
expressions. Except for Welford's formula (Equation 20), which is handled
separately, these six expressions represent most of the formulas introduced in
Chapter II for which data needed to solve the formula was gathered during the
BLSA experiment. (Since no data was gathered for the height of the pencil during
movement, formulas calling for this data were not evaluated.) A preliminary
evaluation of the square root formula (Equation 17), which is a form of power
function, did not yield correlations and standard error of estimate values which
warranted investigation.
It was felt that a natural log (In) might provide a more desirable slope even though
the y-intercept, the standard error of estimate, and the coefficient of determination
would remain equal to the log2 counterpart. As it turned out, no additional insight
was gained through this addition.
Figure 3 provides a diagram of the various ways movement amplitudes and target
widths can be represented. All of the measures given were calculated from data
collected. (See the Procedure section for a description of what data was collected.)
The notation used for the five measures of movement were:
A center-to-center distance between constructed targets
A' center-to-center distance between resultant scatters of hits
D distance between outside edges of constructed targets
D' distance between outside edges of resultant scatters of hits
I distance between inside edges of constructed targets
71
(A sixth logical measure of movement amplitude would have been I’, the distance
between the inside edges of the resultant scatters of hits, but because this measure
could be negative for overlapping scatters, it was eliminated.) The notation used
for the four measures of target width are:
W width of the constructed target
WL width of the left side scatter of hits
WR width of the right side scatter of hits
W' average of WL and WR
The form of the formula for all possible combinations of the above elements is:
MT - a + b(expression)
For each of the 240 formulas thus formed, a, b, r^ (the squared coefficient of
correlation, also known as the coefficient of determination) and Se (the standard
error of estimate) were calculated for first visit data as described below. For
Welford's formula (Equation 20),a, b, W0, r^, and Se were also calculated for first
visit data. The constants a, b, and WO were already calculated for most visits as
part of the original recording of data but for consistency, these were recalculated
by groups in the way described below. The squared coefficient of correlation, also
known as the coefficient of determination, was used since it provided more
precision than r to differentiate between formulas.
72
Using the means of MT, W, W’ , D, D’ , etc., for each group (all subjects combined,
males, females, decade2, ... decade2 males, ... decade9 females) the four or five
parameters ( a, b, r^, Se, and W0) were calculated using the first visit data for each
of the 241 formulas. The calculations were carried out in two ways: first, for all
test conditions; second, omitting the "easiest" condition (i.e. small movement
amplitude and wide target - SW) on the grounds that it does not fit the major trend
of the data and instead represents a lower limit to movement time of about 200
msec (Welford, Norris and Shock, 1969, and Welford, 1990). The primary
justification for the omission of this data point is that movement times of less than
about 200 msec are too fast to be part of an information processing loop and thus
are not indicative of the process being modeled by Fitts' Law. On the other hand,
as Birren has pointed out (J. E. Birren, personal communication, December 4,
1990), the goal in investigating the relationship between movement time and
movement parameters should be to gain a comprehensive understanding of the
phenomenon being examined and not to restrict the scope of investigation to the
areas that are the easiest to explain. Therefore, the formula that fits all the data,
including the easiest target has been discussed in the Results section.
In total, 482 unique formulas were applied to the data. A limitation to the present
study is that each formula was not tested on each visit individually and then mean
Se's and r^'s evaluated.
While there is some theoretical satisfaction for a formula that has a y-intercept (b)
close to zero (0), the "best" formula was considered to be the one that produced the
lowest Se and highest r^ for the highest number of groups described above.
73
NOTE: Even though and Se are related mathematically, Se, technically, is the
appropriate measure to evaluate how well an equation fits a set of data since it is
directly related to the difference between the true value of a data point and the
value predicted based on the formula in question. It should be noted that of all
literature reviewed by the present author, none of it has included an evaluation of
the various formulations in terms of the standard error of estimate. While the
correlation reflects how strong the relationship is between the variables in question,
the standard error of estimate is intended to reflect how good a fit the formulation
is to the actual data. The standard error of estimate, therefore, is, technically
speaking, a more appropriate measure of "fit" between any formula and the actual
data observed.
The above calculations were carried out using several software packages. Group
means were produced using BMDP (PC90 version) program module 9D. (Detailed
descriptive statistics were produced by program module 2D.) These means were
imported into LOTUS 123 (release 2.01) spreadsheets (one spreadsheet for each
group) where each set of means for an individual group (e.g.. males in the third
decade) were arranged for easy analysis. Another LOTUS 123 spreadsheet was
created so that all 241 formulas were represented. Since not enough memory was
available to easily contain all 241 formulas on one spreadsheet on the IBM PS 2/50
being used, the spreadsheets were transferred (using Dyna Systems DOS Mounter
software) to a Macintosh II Si where they were converted to Wingz (Informix
Software, Inc.) spreadsheet files. Once in Wingz, each spreadsheet of means was
copied one at a time to the spreadsheet with the formulas and the y-intercepts (a's),
slopes (b's), r^'s, and Se's were calculated. These values were then brought
together onto one spreadsheet where they were analyzed to determine the best
formula. The analysis to determine the best formula proceeded as follows. For
each group (all subjects, males, females, decade2,..., females decade9) the formula
numbers were sorted by Se. The best 5 formulas from each group were then made
"semi-finalists" in the formula competition. There were 10 different "semi-finalist"
formulas in first place in at least one of the groups, 10 in second place, 11 in third
place, 12 in fourth place, and 16 in fifth place. There were 36 different formulas in
total. The 11 most prominent of these 36 formulas were selected as "finalists".
The rank order (based on Se - best being "1", worst being "482") of each of these
11 formulas was ascertained for each group. The formula(s) with the lowest rank
order for the greatest number of groups won the selection as the best formula(s).
STEP 3 - EVALUATE AGE AND GENDER EFFECTS CROSS
SECTIONALLY
The midpoint of the age ranges was taken at the decade such that decade3, for
example, represents subjects aged 25 through 34. The calculations performed in
Step 2 provided much of the data necessary to examine age and gender effects.
Differences between the a's and b's of different groups could be compared by
inspection to get a general idea of the way in which age and gender affects hand
movement. In addition, the a’ s and b’ s were calculated for each visit using only the
"best" formulas.
Descriptive statistics on the means of a’s and b's for each group(e.g. males, females,
decade 3, males decade 3, etc.) were calculated using BMDP program module 9D.
An ANOVA was performed on the a's and b’ s obtained using BMDP (BMDPEM -
75
the expanded memory version) program 7D on a Compac 386 20Mhz computer
with a math coprocessor and four megabytes of RAM.
The ANOYA used an 8 X 2 (age decade X gender) between subjects design with
the dependent measures being the a’s and b's. The males over age 94 (only two
subjects) were included with the males aged 85 thru 94 to avoid an empty cell and
yet not lose the data. Bonferoni and Tukey Post Hoes were included with the
ANOVA produced by BMDPEM program module 7D. (BMDP uses the
studentized range method and for unequal sample size, as here, BMDP uses the
Tukey-Cramer adjustment - harmonic mean.)
The ANOVA for movement time was analyzed using BMDPEM program module
2V on the aforementioned computer. The ANOVA used a 9 X 8 X 2 (Target X
Age X Sex) mixed ANOVA design with repeated measures on the first factor
(target configuration). Since post hoes are not produced by program module 2V
(automatically) and since program module 7D cannot process more than a two-way
ANOVA, post hoes were calculated by hand. The Bonferoni Post Hoc was utilized
since it is preferred for unequal numbers of subjects per cell.
STEP 4 - CREATE NEW FORMULA WITH AGE AND GENDER
INCLUDED
Based on the patterns observed in Step 3, above, for age and gender effects, the
"best fit" formulas were modified. Linear and quadratic regressions were
performed on the slopes and intercepts over age ranges to model the changes with
age. In general, the data points obtained from decade9 males, decade 10 males,
76
decade2 females, decade8 females, and decade9 females were omitted from the
regressions due to small sample sizes (5, 2, 4, 9, and 1 subject(s) respectively).
However, these groups were included in calculation the regressions where they
clearly fit the major trend of the rest of the data (such as decade9 males for the y-
intercept). The factors of age and gender were incorporated into the slope (b) and
y-intercept (a) coefficients.
STEP 5 - TEST NEW FORMULA
The formula obtained in Step 4 was used to predict values of MT for the mean
values of MT for the various age decades and genders. A comparison of predicted
MTs and actual MTs is included in the Results section.
STEP 6 - SPLINE USED TO INERPOLATE EQUALLY SPACED
VISITS
In order to get the most accurate representation of age-related changes within
subjects and to overcome problems of irregularly spaced visits, each subject's basic
measures (MT, WL, WR, and D') for each of the nine target configurations were
interpolated using a linear spline between actual data points to coincide with one
visit every two years starting with the first visit (the first visit data remained
intact). In this way, data were obtained from all subjects, regardless of how erratic
the time intervals between visits were. However, in no case were data points
extrapolated beyond the last actual data point. This splining procedure resulted in
5,571 splined visits total.
77
For each subject with more than one visit, visits were spaced at 2-year intervals.
Males accounted for 5,215 of the visits and females made up the remaining 356
visits. Table 3 gives the number of visits by gender for each visit. Since there
were only 2 females with visits 3 or more, the females were not included in the
longitudinal analysis.
Table 3
Longitudinal Distribution of Subjects
VISIT
NUMBER
NUMBER OF
MALES
NUMBER OF
FEMALES
NUMBER OF YEARS
REPRESENTED
1 1058 273 0
2 883 81 2
3 774 2 4
4 677 0 6
5 578 0 8
6 475 0 10
7 364 0 12
8 242 0 14
9 154 0 16
10 10 0 18
STEP 7 - EVALUATE AGE EFFECTS LONGITUDINALLY
The formula obtained in Step 2 above (the formula unmodified by age and gender)
was used to evaluate age and gender effects longitudinally in a similar fashion as
78
was done in Step 3 for the cross-sectional analysis. Technically, this analysis was
cross-sequential and not a true longitudinal analysis. In a true longitudinal
analysis, all subjects in a particular age group would have to be bom about the
same time (within several years). In the present analysis subjects were included in
whatever age group represented their age upon entry into the program.
ANOVAs were performed for subjects that had visit data for visits 1-9. The data
were analyzed using an 8 X 2 X 9 (age X gender X visit) mixed ANOVA design
with repeated measures on the third factor with dependent measures being the
slopes (b's) and y-intercepts (a's). For these ANOVAs, a’ s and b's were calculated
based on the raw measures for each visit. As in Step 2, a's and b's were also
calculated based on the means of these measures for the data grouped by age
decades and gender. ANOVAs were also performed on movement time using a 9
X 8 X 2 X 9 (Target X Age X Sex X Visit) mixed design with repeated measures
on the first and fourth factors. Since there were no females who had more than
three splined visits, they were not included in the longitudinal analysis.
79
CHAPTER IV
RESULTS AND DISCUSSION
Experimental Results
THE "BEST” FORMULA
Table 4 shows the number of subjects for each group and a list of the 11 most
prominent formulas found within the first top five formulas (in terms of the
standard error of estimate) for each group. (For a more detailed explanation of the
derivation of this table see Step 1 of the Treatment of Data section.) The numbers
on this table indicate the rank order in terms of Se of that formula for the group
specified. The lower the number, the better the fit of the data (for the group
indicated) to the formula listed on the left hand side. (See Appendix J to determine
the exact formula from the formula number.) From Table 4, it can be seen that
formula 69 (without the SW data point included in the calculations) fits the female
data particularly well, while formula 73 fits the male data best. Formula 189 is the
same as 69 except it is the natural log version. The same is true of 193 in relation
to 73. Formula 73 is:
MT = a + bLog2(D'/W + 1)
Formula 69 is:
MT = a + bLog2(D/W + 1)
80
Ranlc Order of Best 11 Formulas
TOTALS MALES FEMALES DECADE2 DECASE3 DECADE4 DECADE5 DECADE6 DECADE7 DECADES DECADE9 DECADZ10
Humber of Subjects: 1318 1047 271 35 244 250 271 212 217 81 6 2
69 WITHOUT SW 5 12 1 1 1 5 14 5 9 3 317 85
73 WITHOUT SW 1 1 16 18 13 1 1 1 1 6 377 41
69 WITH SW 11 13 7 3 15 15 15 7 7 1 274 29
189 WITHOUT SW 6 11 2 2 2 6 13 6 10 4 318 86
193 WITHOUT SW 2 2 15 17 14 2 2 2 2 5 378 42
189 WITH SW 12 14 8 4 16 16 16 8 8 2 273 30
53 WITHOUT SW 3 3 21 24 19 3 3 3 3 9 386 33
169 WITHOUT SW 10 15 3 5 3 10 18 11 17 7 327 80
173 WITHOUT SW 4 4 22 23 20 4 4 4 4 10 385 34
49 WITHOUT SW 9 16 4 6 4 9 17 12 18 8 328 79
65 WITHOUT SW 7 9 5 7 5 8 9 9 5 17 355 96
MDECADE2 MDECADE3 MDECADE4 MDECADE5 MDECADE6 MDECADE7 MDECADE8 MDECADE9 MDECADE10
Humber of Subjects: 31 197 203 229 144 164 72 5 2
69 WITHOUT SW 3 1 5 20 7 27 3 253 85
73 WITHOUT SW 21 8 1 1 1 1 5 355 41
69 WITH SW 1 16 15 17 15 19 1 233 29
189 WITHOUT SW 4 2 6 19 8 28 4 254 86
193 WITHOUT SW 22 7 2 2 2 2 6 356 42
189 WITH SW 2 15 16 18 16 20 2 234 30
53 WITHOUT SW 27 17 4 3 3 3 15 366 33
169 WITHOUT SW 5 3 13 22 19 34 13 260 80
173 WITHOUT SW 28 18 3 4 4 4 16 365 34
49 WITHOUT SW 6 4 14 21 20 33 14 259 79
65 WITHOUT SW 7 6 12 10 18 14 20 304 96
FDECADE2 FDECADE3 FDECADE4 FDECADE5 FDECADE6 FDECADE7 FDECADE8 FDECADE9
Humber of Subjects: 4 47 47 42 68 S3 ‘9 1
69 WITHOUT SW 1 1 1 1 1 1 12 101
73 WITHOUT SW 3 24 19 19 3 16 39 167
69 WITH SW 29 13 13 5 7 5 35 13
189 WITHOUT SW 2 2 2 2 2 2 11 102
193 WITHOUT SW 4 23 20 20 4 15 40 168
189 WITH SW 30 14 14 6 8 6 36 14
53 WITHOUT SW 10 33 22 23 11 24 46 190
169 WITHOUT SW 7 4 3 3 9 3 17 121
173 WITHOUT SW 9 34 21 24 12 23 45 189
oo 49 WITHOUT SW 8 3 4 4 10 4 18 122
— 65 WITHOUT SW 5 5 12 14 6 7 19 161
If the target configuration SW (Small amplitude and Wide target) is to be included,
formula 69, provides the best fit for most groups. However, as discussed in the
Treatment of Data section, SW should be excluded from the rest of the data.
Figure 4 shows Formula 73 applied to the data for all subjects combined for each
target configuration.
1600
o 1200
O
' B Q
E
w>
C d
5 6
P 800
Z
W
5 8
W
| 400
0
0 1 2 3 4 5 6 7
INDEX O F D IFFICULTY
L0Ga(D’/ff + 1)
Figure 4. Movement time versus the index of difficulty using
Formula 73 for all subjects combined. Standard error bars are
smaller than the symbols and therefore are not observable. Target
configuration SW (the point with the lowest index of difficulty) has
been omitted from the regression line drawn.
All S u b jects Com bined
1-SW:
2-SI:
3-SN:
4 -M W
5-MI:
6-MN:
7-LW:
8-LI:
9-LN:
Small Distance, Wide Target
Small Distance, Intermediate Target
Small Distance, Narrow Target
: Medium Distance, Wide Target
Medium Distance, Intermediate Target
: Medium Distance, Narrow Target
Long Distance, Wide Target
Long Distance, Intermediate Target
Long Distance, Narrow Target
82
While it could be argued that the mean of all subjects for each target configuration
is not the best baseline since it may emphasize the largest population age group, a
nearly identical plot is achieved if the mean of the means of each age group are
used instead- Nevertheless, Figure 5 shows the plot for all subjects 45 to 54 years
of age.
1600
1200
V
I D
&
w
3
h 900
H
55
E d
>
3 400
0
0 1 2 3 4 5 6 7
INDEX OF DIFFICULTY
log8(D '/w + l)
Figure 5. Movement time versus the index of difficulty using
Formula 73 for all subjects 45 to 54 years of age. Target SW has
been omitted from regression line.
Figures 6 and 7 provide the fit of the same data using Formula 69. It may seem at
first glance that Formula 69 provides the best fit, but the data near the ID of four
83
All S u b jects, 4 5 -5 4 Years
1-SW:
2-SI:
3-SN:
4-MW:
5-MI:
6-MN:
7-LW:
fl-LI:
9-LN
Small Distance, Wide Target
Small Distance, Intermediate Target
Small Distance, Narrow Target
Medium Distance, Wide Target
Medium Distance, Intermediate Target
Medium Distance, Narrow Target
Long Distance, Wide Target
Long Distance, Intermediate Target
Long Distance, Narrow Target
are farther from the line than for Formula 73 and even though the lowest ID data
point (SW) is closer to the line, it was not included in the regression of the line to
the data.
1600
o' 1200
u
m
£
w
3
5 800
a
H
I
1 400
0
0 1 2 3 4 5 6 7
INDEX OF DIFFICULTY
L O G 2(D/W + 1)
Figure 6. Movement time versus the index of difficulty using
Formula 69 for all subjects combined. Target SW has been omitted
from regression line.
If SW were to be included, as mentioned earlier, Formula 69 would indeed have a
better fit to the data than Formula 73. It is more likely that a radically different
formula would include SW and provide a better fit for the other points as well.
The pursuit of such a formula, would have little practical value, but there may be
theoretical insight gained as to the controlling relationships that underlie Fitt's Law.
84
All S u b jects C om bined
1-SW: Small Distance, Wide Target
2 - SI: Small Distance, Intermediate Target
3-SN: Small Distance, Narrow Target
4-MW: Medium Distance, Wide Target
5-MI: Medium Distance, Intermediate Target
6-MN: Medium Distance, Narrow Target
7-LW: Long Distance, Wide Target
8-LI: Long Distance, Intermediate Target
9-LN: Long Distance, Narrow Target
All Subjects, 45-54 Years
1600
IT 1200
e
I D
a
W
5
“ 800
H
S 5
W
2
H
| 400
0
0 1 2 3 4 6 6 7
INDEX OF DIFFldULTY
log2(d/ w + 1)
Figure 7. Movement time versus the index of difficulty using
Formula 69 for subjects 45 to 54 years of age. Target SW has been
omitted from the regression line.
Since much past work has been done using log2(A/W) (Formula 1 - not the Review
of Literature Equation 1, but the one used for the formula test - see Appendix J for
the number system), log2(2A/W) (Formula 21 = Fitts' Law), log2(A/W + 1)
(Formula 41), and log2(A/W + 1) (Formula 61), Appendix K compares the
resulting a's, b's, r^'s, and Se's for each of these formulas for all groups (all
subjects, men, women, etc.).
1-SW: Small Distance, Wide Target
2-SI: Small Distance, Intermediate Target
3-SN: Small Distance, Narrow Target
4-MW: Medium Distance, Wide Target
5-MI: Medium Distance, Intermediate Target
6-MN: Medium Distance, Narrow Target
7-LW: Long Distance, Wide Target
8-U : Long Distance, Intermediate Target
9-LN: Long Distance, Narrow Target
85
While formulas 1, 41, and 61 have positive y-intercepts for essentially all groups,
and formulas 21, 69 and 73 have negative y-intercepts for over half the groups
(formula 21 having the greatest number of negative y-intercepts), the magnitudes
of the y-intercepts for formulas 1, 21, 41, and 61 are greater than those for
formulas 69 and 73. In other words, the y-intercepts for formulas 69 and 73 are
actually closer to zero than formulas 1, 21, 41, and 61. Slopes show a fairly
consistent trend across formulas, increasing from a low for formulas 1 and 21 to a
high for formulas 69 and 73, with 69 and 73 essentially equal. The coefficient of
determination (r^) shows a similar trend of increasing from formulas 1 and 21 to
formula 73. Here, formula 73 is slightly better than 69 for males but not for
females. The same trends are observed for the Standard Error of Estimate (Se)
with the highest Se's for formulas 1 and 21 and the lowest for formulas 69 and 73.
DESCRIPTIVE STATISTICS
Appendix L contains the means of all the basic parameters (A, A', WL, D', etc.) for
each target for all subjects combined, males, females, each age decade, and each
age decade by sex. Mean age of and number of subjects in each group is also
given. Appendix M contains detailed descriptive statistics (means, standard
deviations, skewness, and kurtosis) for MT, WL, WR, and D’ for all subjects
combined, males, and females.
AGE AND GENDER DIFFERENCES
Unexpectedly, females showed lower movement times than men for each target
configuration and for every age range except those with very few subjects. The
main effects of gender were not significant (F=2.58, p=0.1083). However, there
86
was a marginally significant interaction between sex and target configuration
(F=1.85, p=0.0625). See Appendix N for the ANOVA table.
1600
A . M ales
v F em a les
o 1200
no
800
400
1 0 2 3 5 6 4 7
INDEX OF DIFFICULTY
L0G2(D'/W + 1)
Figure 8. Formula 73 fitted to the mean movement times for males
and females separately. Standard error bars are smaller than the
symbols and therefore are not observable. Target SW has been
omitted from the regression lines
The consistent trend of females being faster than males for each age group and for
nearly every target within each age group suggests that women may have a slight
advantage in rapid hand movements that require precision. Whether this is the
result of a biological advantage, performance strategy, or gender difference due to
work and hobby stereotypes is open to question. However, as will be discussed
later, this study provides some support for an advantage due to strategy. Part of
this difference may also be explained in terms of a speed accuracy tradeoff. Except
87
for on the widest targets, the males have consistently smaller scatters of hits for
both the right and the left targets - indicating a possible emphasis on accuracy.
Another explanation may be related to the smaller average mass of female
forearms, which might be allowing for fewer corrections to be made to the arm
trajectory in order to overcome the inertia of the arm during deceleration.
All Subjects Combined
1600
o' 1200
G J
m
%
w
£
H B O O
H
Z
W
s
w
1 400
0
0 1 2 3 4 5 6 7
INDEX O F DIFFICULTY
L0G a(D’/W + 1)
Figure 9. Formula 73 fitted to each age decade's movement times for
all subjects.
It was no surprise that significant main effects were found for age. Age differences
in movement times were significant between every age group (F=38.03, p<0.0001).
(See Appendix N for the Anova table and the Bonferoni Post Hoc critical
difference values.) As expected, older subjects experience a disproportionate
88
8 5 -9 4 (n=6)
7 5 -8 4 (n = 8 l)
6 5 -7 4 (n=217)
^ 55-64 fn=212j
4 5 -5 4 (n = 27l)
3 5 -4 4 (n=250)
2 5 -3 4 (n=244)
Under 25 (n=35)
slowing on more difficult targets (i.e. targets with a high index of difficulty - ID).
Nevertheless, even for the target with the lowest index of difficulty (SW),
movement time was significantly higher for the older subjects than the young.
Figures 9, 10 and 11 illustrate the age and gender differences in movement time.
(Sample size for each group is given in parenthesis.) A steady increase in the
slopes is evidence of a disproportionate slowing of performance on the more
"difficult" tasks.
Males
1600
8 5 -9 4 (n = 5)
o* 1 2 0 0
v
Q L
- 7 5 - 8 4 (n = 72)
--6 5 -7 4 (n =164)
/ 5 5 — 64 (n = 144)
- 4 5 - 5 4 (n =229)
^ 3 5 -4 4 (n = 203)
''“ 2 5 -3 4 (n =197)
''“ Under 25 (n = 31)
800
400
1 0 3 2 4 6 7 5
IND EX O F DIFFICULTY
LOGgfD’/W + 1)
Figure 10. Lines fitted to the data for each decade of males using
Formula 73 and omitting the easiest targets (SW).
89
Fem ales
1600
8 5 -9 4 (n = l)
e » 1500
09
« L
6
-75-84 (n=9)
6 5 -7 4 (n=53)
5 5 -6 4 (n = 6 8)
4 5 -5 4 (n=42)
3 5 -4 4 (n=47)
2 5 -3 4 (n=47)
u
S
H 800
e-
2
Ed
s
W
>
§ 400
U nder 25 (n=4)
1 0 3 2 6 7 4 5
INDEX O F DIFFldULTY
L0Gg(D/W + 1)
Figure 11. Lines fitted to the data for each decade of females using
Formula 69 and omitting the easiest targets (SW).
The patterns of change with age can be seen more clearly if the slopes and
intercepts are graphed in relation to age. First the y-intercepts are examined for
males and females, then the changes in slope will be addressed. (The reader should
note that even though second order regression splines have been fitted to the data in
many of the graphs, the regression equations given wee not derived from the
software - Sigmaplot, 1990 - that generated the graphs, but were estimated "by
hand".)
90
Y-INTERCEPTS
All Subjects Combined
200
150
I
> *
-50
100
0 10 20 30 40 50 60 70 80 90 100
AGE
Figure 12. Y-intercept values for each age group using Formula 73.
With the exception of the groups with very small sample sizes, all y-intercepts are
near zero and most are negative. Differences in y-intercepts between age groups
were not statistically significant. (See Appendix O.) Nevertheless, a trend is
indicated: Young subjects tend to have a positive y-intercept. As they age this
drops below zero and bottoms out around -30 ms around the 50's. It then begins to
rise in the latter years. The y-intercepts for the females appear to decrease more
linearly with age.
91
200
150
Males—
Female
M
I
-50
-100
0 10 20 30 40 50 60 70 80 90 100
A G E
Figure 13. Y-intercept by age for males and females using formula
73 for males and 69 for females. The second order regression curves
omit the most extreme points.
Figure 13 shows second order regressions for the y-intercepts of males and females
plotted against age. While a curve gives a reasonable fit for both the males and
females, the females are more appropriately modeled with a straight line as can be
seen from figure 14.
Figure 14 is based on the means of the relevant parameters (D' and MT for all
males and D and MT for all females) taken together by age ranges. Another way to
look at the changes with age is to calculate the slopes and intercepts for each
subject and then to take the mean of the values of the slopes and intercepts instead
92
of taking the means of the basic parameters (D\ D, and MT) and calculating the
slopes and intercepts from these means.
200
150
H 100
&
w
o
Pi
S 50
H
Z
> 0
A Males—
v Females,
-50
-100
0 10 20 30 40 50 60 70 80 90 100
AGE
Figure 14. Y-intercept by age for males and females using formula
73 for males and 69 for females. The second order regression curve
and the linear regression omit the most extreme points.
Figure 15 is based on the means of the y-intercepts which have been calculated for
each visit (subject). As can be clearly seen, the data fits just as well if not better
than the data calculated using the mean values of D, D1 , and MT and then
calculating the y-intercepts.
93
200
150
A Males— _
v Females,
M
I
-5 0
-100
0 10 20 30 40 50 60 70 80 90 100
AG£
Figure 15. Y-intercepts for males and females by age using the
means of the y-intercepts calculated for each subject. Formula 69
was used for females and formula 73 was used for males.
The curve of the y-intercept for males and the line for females can be approximated
by the following formulas:
a (Males - Formula 73) = -40 + [-15 + 0.3(AGE)]2
a (Females - Formula 69) = 28 - 0.75(AGE)
As an alternative, since the changes in y-intercept with age are not statistically
significant, a mean value of a of about -5 to -30 msec for males and -9 to -20 msec
for females can also be used.
94
Note on Negative Y-Intercepts
Traditionally, it has been viewed as desirable to have a y-intercept as close to zero
as possible, but not be negative. The rationale is that a task with no difficulty
(Index of Difficulty = 0) would require zero movement time. A negative
movement time for a task is impossible, of course. This rationale, while sound on
the surface, breaks down on two points: 1. What is being modeled here is a small
(supposedly linear) section of observation of MT and ID - a "fuller" formula would
include the SW target configuration and would probably not have a y-intercept.
Justifying the omission of SW in the regression of the data is, in a way, admitting
that we are only modeling a portion of what's going on. If we were truly modeling
all observed data, we would have justification for insisting on reasonable values for
the entire range of ID. 2. An ID = 0 should not mean a MT = 0, it would mean a
tapping in place task movement time and would be non-negative and about 100 -
200 ms (depending on age). If desired, the y-intercept could simply be set at zero
or about 100 - 200 ms for these formulas and new regressions could be made based
on this constraint. The resulting regression lines would not be expected to deviate
far from the original lines in terms of Se, but they wouldn't be as good as the
original regressions. However, a better approach, of course, would be to pursue
that (elusive) formula that fits the low, middle, and high ID’s in and of itself and
produces the lowest Se in the process.
For the present analysis, the formulas that give the best fit (low Se's) and yet have
positive y-intercepts near zero for most of the groups are formula 53 (MT = a +
bLog2(D’ /W + 0.5)) and formula 65 (MT = a + bLog2(A'/W + 1). The formulas
that give the best fit (low Se's) and yet have positive y-intercepts near 100ms for
95
most of the groups are formulas 1 (MT = a + bLog2(A/W)) and formula 5 (MT = a
+ bLog2(A'/W)). It is interesting to observe that, except for D' in formula 53, these
formulas are the ones that have dominated the literature: Formula 53 is essentially
Welford's correction; Formula 65 is a form of Shannon's Theorem 17 (Shannon,
1948); and Formulas 1 and 5 are essentially Crossman's corrections.
SLOPES
The more prominent trend is for the slope. The differences in slopes with age was
significant at p<0.0001 for both Formula 73 and 69. (See Appendix O.) The
difference between slopes by gender was not statistically significant at the p=0.05
level of significance for both formulas, however, trends between males and females
can be seen. With the exception of the youngest females, the slopes for both
formulas have a strong linear increase with age for all groups. The slopes for
females do not change quite as much as those for males.
96
All Subjects Combined
250
200
u
o 150
1 0 0
0 10 20 30 40 50 60 70 80 90 100
A G E
Figure 16. Changes in slope with age using Formula 73. The linear
regression omits the last (oldest) two ranges (only one of which is
shown here).
Figure 16 gives the slopes for all subjects by age range. The regression that fits the
data is remarkably linear for the 20's through the early 80's. Figure 17 brakes out
males and females separately. A very slight interaction of age and gender can be
seen in the slopes.
97
250
200
A M a l e s - ^
v Females
100
0 10 20 30 40 50 60 70 80 90 100
AdE
Figure 17. Slopes by Age for males and females. The oldest point
shown for the males and females and the youngest point for the
females was not used in calculating the regression lines. Line for
males based on Formula 73; line for females based on Formula 69.
As was true for the y-intercepts, the preceding graphs are based on the means of the
raw data for calculating the slopes. Figure 18 shows that calculating the slopes
from the mean of slopes for each visit (subject) is very close to the value obtained
by the former method.
98
250
200
A M a l e s ^
v Females.
o 150
<00
0 10 20 30 40 50 60 70 80 90 100
AGE
Figure 18. Slopes for males and females using Formula73 for males
and Formula 69 for females. Slopes based on the mean of slopes of
each subject.
Linear regression on the data above yields the following approximations for the
changes in slope with age:
Males: (Formula 73) b = 69 + 1.1 (AGE)
Females: (Formula 69) b = 64 + AGE
99
The preceding formulas together with the formulas for the y-intercepts yield the
following modified formulas for predicting MT:
Males:
MT = -5 + [69 + 1. l(AGE)]Log2(D'/W + 1) (73A)
-or-
MT = -40 + [-15 + 0.3(AGE)]2 + [69 + U(AGE)]Log2(D’ /W + 1) (73B)
Females:
MT = -9 + (64 + AGE)Log2(D/W +1) (69A)
- or-
MT = 28 - 0.75(AGE) + (64 + AGE)Log2(D/W +1) (69B)
Appendix P provides a comparison of the actual movement times to those predicted
by the four formulas above. Summing the absolute value of the differences
between the predicted and actual movement times indicates that formula 73B,
overall, is the best predictor of movement time. This is true for males by decade
and, surprisingly, it is also true for females by age range.
A FURTHER IMPROVEMENT - ARC ESTIMATES
In attempting to make more and more exact representations of precise movements,
some researchers have incorporated two and three-dimensional parameters into the
formula for movement time (Wallace, Hawkins, and Mood, 1983 and Mackenzie,
Martiniuk, Dugas, Liske, and Eickmeier, 1987). Along this same line of reasoning,
100
a two-dimensional correction was informally tested. A slight improvement in Se
for both formulas can be achieved if D’ and D are substituted with their
corresponding arc distances with the radius of the arc being the distance between
the elbow and the tip of the thumb (which is approximately where the pencil is
held). The rationale behind this modification is that most people perform the
reciprocal tapping task by swinging their arm at the elbow, thus proscribing an arc
defined by the length of their forearm. While this does improve the fit of the data
to the formulas slightly, it is somewhat in opposition to the finding that women are
faster on this task. Since women have shorter forearms, you would expect them to
be proscribing an arc with a smaller radius and thus traversing more distance than
someone with a long forearm and thus a larger radius arc.
SPEED-ACCURACY TRADEOFF
It can be observed from Appendix L that for the older age ranges the average
scatter width (W') is much smaller for old subjects than for young. It appears that
older subjects are emphasizing accuracy more than the young subjects. This may
account for some of the increased speed with the old subjects. It may also account
for some of the gender differences as well since the males have smaller scatters of
hits than the females except for the target configurations with wide targets, where
the females have the (slightly) smaller scatters. Exactly how much of the variance
in MT can be accounted for the differences in W' is uncertain. Comparing Wr for
the decade2 males with W' for the decade8 males reveals a consistent trend. As the
target size gets smaller, for the same movement amplitude, the discrepancy
between the W’ s increases. In addition, as the amplitude gets bigger, for the same
constructed target width (W), the discrepancy between the W s again increases.
1 0 1
For the most difficult target configuration (LN - long amplitude, narrow target) the
scatter width (W') for the decade8 subjects is 42% of the W' for the decade2
subjects. In other words, the scatter of hits for the older subjects for the most
difficult target width is less than half the scatter of hits made by the young subjects
on the same target!
NOTE ON MT CHANGES WITH AGE FOR SW TARGET
Since the data for the SW target were not included into regressions to find a "best"
formula, Figures 19, 20, and 21 present the pattern of change for MT with age for
the SW target. As can be seen, the trend is for escalating movement times past
about the sixth decade. Both the male and the female data suggest a slight, but
perceptible decrement in performance for the youngest age groups with an increase
in performance in the third decade for males and the fourth decade for females.
(Again, because of a sample size of four subjects, the data for the second decade
females should be omitted from consideration.) This trend of lower performance
for the young females was also found by York and Biederman and Welford, 1990.
102
M O V E M E N T T I M E (msec) M O V E M E N T T I M E (m sec)
All Subjects Combined
450
400
350
300
250
200
150
10 20 30 40 50 60 70 80 90 100 0
A C J E
Figure 19. MT for target SW by age, all subjects combined.
Males
450
400
350
300
250
200
150
10 20 30 40 50 60 70 80 90 100 0
AdE
Figure 20. MT for target SW by age for males.
Fem ales
450
C 400
V L
350
H 300
S 250
S 200
150
0 10 20 30 40 50 60 70 80 90 100
a c I e
Figure 21. MT for target SW by age for females.
LONGITUDINAL ANALYSIS
Significant differences in movement time for the longitudinal data (subjects with
nine or more splined visits) were found for target configuration, age, and visit
(F=1926.95, p<0.0001; F=11.52, p<0.0001; andF=25.09, p<0.0001 respectively).
Significant interactions were also found for visit by age, target by age, visit by
target, and visit by target by age (F=1.82, p=0.0036; F=3.75, p<0.0001; F=5.36,
p<0.0001; F=1.47, p<0.0001 respectively). The ANOVA table for movement time
is given in Appendix S and includes the Bonferoni Post Hoc critical difference
values. Appendix U contains the descriptive statistics for movement time for these
longitudinal data.
104
The results support the cross-sectional findings but reveal what appears to be a
training effect. Movement times increase between the age groups, as was true with
the cross-sectional analysis of first visit data, and also across visits as the subjects
aged. However, the change with age longitudinally (across visits) is not a linear
change. Instead, it appears that as the subjects aged, their movement times
decreased up until about the fifth to seventh visit. This seems to imply the effects
of age were being counteracted by a learning effect up till about 10 years after their
first visit! This effect is most apparent on the more difficult target configurations.
Figures 22 through 30 show the movement times by age for each age group for
every target configuration with standard error bars included. (For the number of
subjects per group, see Appendix U.)
Target
1000
I 800
E
a
s
„ 600 -
b *
| 400 -
u
s
a 200 -
30 40 GO 70 90 50 80
A C | E
Figure 22. MT versus Age for target SW for each age group using
longitudinal visits for subjects with 9 or more splined visits.
105
Target ( i l l 1000
o
e
800 'm
£
u
3 600
M
H
Is
g 400
u
>
o
* 200
30 40 50 70 60 80 90
A G l E
Figure 23. MT versus Age for target SI for each age group using
longitudinal visits for subjects with 9 or more splined visits.
1000
1 800
s
w
W
a 6oo
* ■ *
“ 400
sa
2
* 200
0
30 40 50 60 70 80 90
A d E
Figure 24. MT versus Age for target SN for each age group using
longitudinal visits for subjects with 9 or more splined visits.
Target
3 ' 3 . 4' \ . - “ 'B n
J ____________ 1 ____________ I ____________ L
106
1000 Target M W
8. 800
B
w
3 600
E -
£
£ 400
g
o
a 200
30 40 50 80 60 70 90
A d E
Figure 25. MT versus Age for target MW for each age group using
longitudinal visits for subjects with 9 or more splined visits.
1000
i -----
- Target M I
r -i— " _i --- - - - i
1 800
6
- -
U
2 600
H
e-
| 400
g
7'7~7~7~7-7-7-l~l
o
a 200
- -
0
i
--- - - - - - 1 _ _ _ _ __ __ j___ ___ ___i_. i—
30 40 50 60 70 80 90
A d E
Figure 26. MT versus Age for target MI for each age group using
longitudinal visits for subjects with 9 or more splined visits.
107
1000
o
£. 800
£
u
g 600
£
g 400
8 3
o
5 6 200
0
30 40 50 60 70 80 90
A (^E
Figure 27. MT versus Age for target MN for each age group using
longitudinal visits for subjects with 9 or more splined visits.
1000
I 800
E
U
3 600
£
jj 400
S 3
* 2 0 0
0
30 40 50 60 70 80 90
A C l E
Figure 28. MT versus Age for target LW for each age group using
longitudinal visits for subjects with 9 or more splined visits.
Target L W
Target M N
10S
1 0 0 0
a t 8 0 0
w
3 600
s 4 0 0
&
o
* 200
Target L I
- n7-7 t ^ % r 7
* 7'Z ^
L 3-3 4-4
30 40 50 60
A C i E
70 80
Figure 29. MT versus Age for target LI for each age group using
longitudinal visits for subjects with 9 or more splined visits.
SO
o
©
w
3
£
§
1000
800
u
a eoo
b *
400
200
Target L N
3X ,
3
4s
30
5 - 5 - 6 ■ L - g i J-'Z J. 1
40 50 60
A C | E
70 80 90
Figure 30. MT versus Age for target LN for each age group using
longitudinal visits for subjects with 9 or more splined visits.
109
Using Formula 73 the y-intercepts and slopes were calculated for each subject
(who had nine or more splined visits) and ANOVAs were computed. No
significant differences were found for age or visit for the y-inteicepts (F=1.77,
p=0.1379 and F=0.8, p =0.6025 respectively), however, a significant interaction
was found for visit by age (F=1.73, p=0.0073). The relationship of the interaction
is not clear from the data as represented, with standard error bars, in Figure 31.
The ANOVA table for the y-intercepts and slopes is given in Appendix T along
with the Bonferoni post hoc critical difference values for the slopes. No post hoes
were calculated for the y-intercepts.
100
50
H
o.
u
K -5 0
u
£
i-i'*
i - 5 ^ 1 1 'b t T ^
s-3 T t 5 4 A 1
-150
-200
30 40 80 50 60 70 90
A G E
Figure 31. Y-Intercept versus Age for each age group using
longitudinal visits for subjects with 9 or more splined visits.
Significant main effects were found for age and visit for the slopes (F=5.33,
p=0.0005 and F=6.11, p<0.0001 respectively). Also, a significant interaction was
found for visit by age (F=1.8, p=0.0044). The apparent learning effect is readily
visible in the plot of slope versus age given in Figure 32. The best performance
seems to be for the subjects who entered the study when they were between 35 and
44 years old. The apparent learning effect seems less pronounced for the two
oldest groups.
160
1 T
■ v
140
Ed
I
x n .
120
100
70 40 50 90 30 60 80
A t i E
Figure 32. Slope versus Age for each age group using longitudinal
visits for subjects with 9 or more splined visits.
It seems that for all groups except the "sixties" group performance increases with
every visit up till the sixth or seventh visit and only then do any apparent
longitudinal aging effects become apparent. Nevertheless, excluding the youngest
group and taking the last three or four visits, a relatively linear increase in slope
can be observed. Including the youngest group yields a u-type function, indicating
a peak performance in the mid-years (late 30's to 50's).
Ill
General Discussion
HYPOTHESES
1. The hypothesis that the best fit of the data to a formula will be a function of
actual scatter width, actual amplitude, age and gender is only partially correct.
In the case of actual scatter width and amplitude, formula 73 is a function of
actual scatter widths and actual movement amplitude (D * = A' + (Wl + W^)/2).
Formula 73 is also gender dependent - it provides a better representation of
males than females. On the other hand, formula 69 is only a function of the
constructed target parameters. Nevertheless, it does share the gender dependent
applicability feature of formula 73. In relation to age dependency, a linear
increase of b (slope) is clearly indicated, at least for the mid-decades (30's
through 70's).
2. This study did confirm the hypothesis that movement time would increase with
age for all age decades. This was true longitudinally as well as cross-
sectionally.
3. The expected disproportionate slowing for more difficult target configurations
was confirmed. This was true longitudinally as well as cross-sectionally. The
unexpected result was that this slowing is not as pronounced in females.
4. Related to this is the failure to show males faster than females for this sample.
1 12
INTERPRETATION OF FORMULAS 73 AND 69
The essential form of these formulas is the same, with the basic measures being the
distance between the outside edges of the target and the target width. The slight,
but consistent, difference between the fit of these two formulas for males and
females presents some interesting possibilities for explaining the difference.
First, the basic form of these formulas suggests again that Fitts's original
inspiration from Shannon's Theorem 17 may, in fact, for whatever real reason,
have been the best form of the formula. This supports the findings of MacKenzie
(1989), and more recently of Welford (Welford, 1990) using Fitts's original data
and some of the first visit data from the present study (approximately 300 visits).
The basic form of Formulas 73 and 69 may provide the most intuitive explanation
of what is really going on in terms of information processing. Two features of
theses formulas make them distinctive: 1) They have the form of a channel
capacity formula which has relevance to information flow, and 2) They use the
outer edges of the targets (or scatters) rather than the traditional center-to-center
measures. Perhaps the programmed motor responses are constrained in execution
according to the relationship developed by Shannon. In addition, the measures of
D and D' provide a much more intuitive measure of distance than A. (For the brain
to utilize the measure of A means that an estimation must be made between the
centers of the targets or else recognition of the outside edge of one target and the
inside edge of the other target must be made. It seems far simpler to input the
readily available outside edges of the targets!)
113
Nevertheless Formulas 73 and 69 present some interpretive difficulties. Intuitively,
what does D/W + 1 (= (D + W)/W) represent? What is D + W? While it could be
that subjects are constrained not by the amplitude of movement but by the outer
edges of the targets, it seems difficult to apply to this formula. A more appropriate
formula might have been Log2(A/W + 1) which is equivalent to LogjfD/W). The
following is an attempt to explain this finding: Perhaps as one taps back and forth
between two targets, motor programing takes into consideration the total possible
distance to be covered (D) and a basic parameter o f the constraint o f that distance
(W). If this is the case, the W in the numerator becomes a constraining parameter -
the bigger W is, the more control must be exercised so as not to miss the
opportunity to hit just inside the close edge of the target being hit. In the
denominator, W would then have to take on a different meaning - it would have the
traditional interpretation that more control is needed to hit a small target, and
therefore more time-consuming motor programs to be executed.
The difference between the males' formula (73) and the females' formula (69) may
suggest a difference in perception of the task as it proceeds. It may be that males
tend to use existing hits (as they are being made) for the parameter of the "outside
edges", while the females may be focusing on the constructed edges thought the
tapping task. If this is true, it may be that the "strategy" of the females results in
better performance - perhaps more information is processed/programmed by the
males to account for a variable "hit edge". This might be testable by providing a
recording device that would record the location of actual hits without providing
any visual clues of where those hits were made. (However, subjects might still use
the temporal position of the stylus to judge where their hits were being made.)
CHAPTER V:
SUMMARY AND CONCLUSIONS
Summary of Procedures
A large sample of subjects (over 1,300) completed over 6,300 batteries of
reciprocal tapping tasks over a period of 22 years. The data were analyzed to
determine the best formulation of Fitts' Law, taking into consideration age and
gender effects. Past investigators had made various modifications to Fitts’ original
formula, but no extensive evaluation of a large sample had been conducted which
would take into consideration age, gender, and visits over a long period of time.
Therefore, this study was undertaken to find the best formula, based on the
standard error of estimate, that would take into consideration age (between
subjects, cross-sectionally and within subjects, longitudinally), and gender effects.
Summary of Findings
There were two formulas which were deemed to be best fits of the data for males
and females respectively. While they are identical in basic form, they differ in the
way in which one of the parameters is measured. The best formulas for males and
females respectively are:
MT = a + bLog2(D’ /W +1) (For Males)
MT = a + bLog2(D/W + 1) (For Females)
Where "a" is also close to zero and "b" increases with age.
115
Slight improvement to the formulas can be achieved by substituting D' and D with
the equivalent distances of arcs with a radius approximately equal to the subjects
forearm length.
Analysis of longitudinal data for subjects completing nine or more visits yeilded
similar results as the cross-sectional analysis but implied a learning effect was
realized across visits up to about the fifth to seventh visit which represented about
10 years since the first visit. After this time, the changes with age seem linear and
similar for all but the youngest subjects.
Conclusions
The implications for this research are several. First, a new formulation of the Fitts'
Law relationship has been indicated as superior over past formulations in
representing the data. Unfortunately, this new formula, while mathematically
superior, has produced more questions than answers in the effort to provide an
explanation of the workings of psychomotor performance. As Welford (Welford,
1990) has pointed out, a choice of formulas must consider the theoretical
implications.
Some researchers may feel more comfortable with the standard formulations since
they may provide for easier interpretations. Nevertheless, these new formulations
have some interpretive benefits. Furthermore, the superior fit of the formulas
described in this study indicate that a re-thinking of the theory underlying rapid
aimed hand movements should be considered.
116
The present study has contributed to the overall understanding of psychomotor
behavior in at least three ways:
1. It has demonstrated that there is a linear increase with age in the slope of the
Fitts' Law equation (modified - equations 73 and 69), implying that as we age
we tend to take a disproportionately greater amount of time on difficult rapid
hand movement tasks.
2. Different formulas for males and females provide a better representation of the
data.
3. The decrease in performance with age appears to be partially, if not substantially
the result of an emphasis on greater accuracy with age.
A possible fourth contribution is in disturbing the common assumption that males
have faster movement times than women. These contributions can be applied, in a
more quantitative way, to the design of products, systems, and jobs, so that the
capabilities of the people using those products or systems or performing those jobs
are adequately considered.
Recommendations for future research
Of primary concern would be the need to duplicate the formula testing procedure
on the data used in this study. This should preferably take place on a mainframe
system which could more readily support an exhaustive evaluation of formulas
already proposed as well as other possible formulas. Before serious debate is made
117
regarding the findings of this study, this step is warranted. In addition, since no
statistical tests were applied to the formula-testing step, this should, be included in
future tests to determine if differences in the Se's for different formulas are
statistically different. A more thorough screening of outliers should also precede
the data analysis.
Secondly, any future research should adopt the sound practices that have been
developed by the researchers reviewed in this study. These practices include the
use of apparatus that records actual hits made (such as pencil and paper for the
present study). Consideration should also be given to designing the task so that
visual clues of the hits is minimized so that the theoretical implications of
Formula73 can be tested.
Of great concern is the effect of practice on performance. As was seen with the
longitudinal analysis, a very significant learning effect may be going on as long as
10 or more years after the first visit before the real effects due to aging are
apparent. An analysis of the data for subjects who had less than nine splined visits
should be conducted to see if the same learning effect is seen.
A more detailed investigation should be made into the contribution of the speed
accuracy tradeoff that was observed. This speed-accuracy tradeoff was observed
for the females as well as the younger subjects. An analysis of covariance using
1/W' is recommended.
118
It must be pointed out that even though the formulas proposed in this paper do
appear to improve the fit of the formulas to the data, there is still the hint of
something missing from the formulas. The graphs of the data seem to indicate
times for the most difficult task which are disproportionately slower than the rest
and thus these points end up off of the recession line. A second order spline of all
points fits remarkably well and should be researched more thoroughly.
One final note. As part of the tapping experiment, subjects also performed a
tapping-in-place task. Three different target sizes were used. The smallest target
size yeilded the shortest movement times. It seems that as the target gets smaller,
less time is "wasted" in "wandering" around the target. This should be explored in
order to find out if this principle might carry over into reciprocal tapping. It might
be that there are two principles in play: 1. Smaller targets require more corrections
to home in on the target and thus require more time, but 2. Smaller targets help
constrain "wasted" movement and thus require less time. This may provide some
insight in the role that "W" the numerator is playing in formulas 69 and 73.
1 1 9
REFERENCES
Andres, R. O. (1978). The normality of aging: The Baltimore Longitudinal
Study. Part of the National Institute on Aging Science Writer Seminar Series.
Washington D.C.: U.S. Department of Health, Education, and Welfare.
Andres, R. O., & Hartung, K. J. (1989). Prediction of head movement time using
Fitts'Law. Human Factors. 31(6), 703-713.
Beggs, W. D. A., & Howarth, C. I. (1970). Movement control in a repetitive
motor task. Nature. 225.752-753.
Birren, J. E., Woods, A. M & Williams, M. V. (1980). Behavioral slowing with
age: Causes, organization, and consequences. In L. W. Poon (Ed.), Agm gJnjhs
1980s. Washington, D.C.: American Psychological Association.
BMDP (1990). BMDP version PC90. Computer software. BMDP Statistical
Software, Inc., Los Angeles, California.
BMDPEM (1990). BMDP Extended Memory version. Computer software.
BMDP Statistical Software, Inc., Los Angeles, California.
Bullock, D. & Grossberg, S. (1988). Neural dynamics of planned arm
movements: Emergent invariants and speed-accuracy properties during trajectory
formation. In S. Grossberg (Ed.), Neural networks and natural intelligence.
Cambridge, MA: MIT Press.
Cooke, J. D., Brown, S. H. & Cunningham, D. A. (1989). Dinematics of arm
movements in elderly humans. Neurobiologv of Aging. IQ, 159-165.
Cldment, F. (1969). The relative development of several psycho-physiological
and psychometric variables with different occupations and intellectual levels. In
A. T. Welford & I. E. Birren (Eds), Decision making and.aee. Basel: Karger.
Crossman, E. R. & Goodeve, P. J. (1963 and 1983). Feedback control of hand-
movement and Fitts' Law. Quarterly Journal of Experimental Psychology^Human
Experimental Psychology. 35A(2). 251-278, (originally presented at the Oxford
meeting of the Experimental Psychology Society in July, 1963).
1 2 0
Crossman, E. R. F. W. (1957). The speed and accuracy of simple hand
movements. In E. R. F. W. Crossman, & W. D. Seymour, The nature and
acquisition of industrial skills. Final report on research project sponsored by the
N.R.C. and D.S.I.R., Joint Committee on Individual Efficiency in Industry.
Department of Engineering Production , University of Birmingham. (Cited in
Welford, 1960).
Crossman, E. R. F. W. (1960). The information capacity of the human motor
system in pursuit tracking. Quarterly General of Experimental Psychology. 12.
1-16. (Cited in Fitts & Peterson, 1964).
Czaja, S. J. (Ed). (1990). Human factors research needs for an aging population.
Washington, D.C.: National Academy Press.
Darling, W. G., Cooke, J. D. & Brown, S. H. (1989). Control of simple arm
movements in elderly humans. Neurobiologv of Aging. 10.149-157.
DAS (1990). Data Analysis System. Computer software. Version 2.06.
Available from PS Y-MED Associates, Honolulu, Hawaii.
Dixon, D. J. (1985). Underwater movement and Fitts’ Law, Dissertation
Abstracts International. 4£ (8-B), 2845.
DOS Mounter (1989). Computer software. Dyna Systems.
Drury, C. G. (1975). Application of Fitts’ Law to foot pedal design. Human
Factors. 17.368-373.
Fitts, P. M. (1954). The information capacity of the human motor system in
controlling the amplitude of movement. Journal of Experimental Psychology.
4Z(6), 381-391.
Fitts, P. M., & Peterson, J. R. (1964). Information Capacity of Discreet Motor
Responses. Journal of Experimental Psychology. 67(21.103-112.
Flowers, K. A. (1976). Visual "closed loop" and "open loop" characteristics of
voluntary movement in patients with Parkinsonism and intention tremor. Brain.
22, 269-310.
Fowler, B., Taylor, M., & Porlier, G. (1987). The effects of hypoxia on reaction
time and movement time components of a perceptual-motor task. Ergonomics.
22(10), 1475-1485.
1 2 1
Gaadgold-Edwards, S. A. (1984). Motor learning as it relates to the development
of skilled motor behavior: A review of the literature. Physical and Occupational
Therapy in Pediatrics. 4(4), 5-18.
Georgopoulos, A. P., & Massey, J. T. (1987). Cognitive Spatial-Motor Processes.
Experimental Brain Research. £5, 361-370.
Gilbert, J. G. (1941). Memory loss in senescence. Journal of Abnormal
Sociology and Psychology. 2£, 73-86.
Grether, W. F. (1986). The genesis of human engineering. Aviation. Space, and
Environmental Medicine. October, 1986, A37-A43.
Haaland, K. Y., Harrington, D. L., & Yeo, R. (1987). The effects of task
complexity on motor performance in lift and right CVA patients.
Neuropsvchologia. 25(5), 783-794.
Hay, L. (1981). The effect of amplitude and accuracy requirements on movement
time in children. Journal of Motor Behavior. 13(31.177-186.
Hick, W. E. (1952). On the rate of gain of information. Quarterly Journal of
Experimental Psychology. 4, 11-26.
Hoffman, S. J., Imwold, C. H., & Koller, J. A. (1983). Accuracy and prediction in
throwing: A taxonomic analysis of children's performance. Research Quarterly for
Exercise and Sport. 54(1), 33-40.
Hoffmann, E. R., & Gan, K. (1988). Underwater ballistic movement.
Ergonomics. 31(9). 1305-1316.
Howarth, C. I., & Beggs, W. D. A. (1981). Discreet movements. In D. Holding
(Ed.), Human Skills, (pp. 91-117). Chichester: John Wiley.
Howarth, C. I., Beggs, W. D. A., & Bowden, J. M. (1971). The relationship
between speed and accuracy of movement aimed at a target. Acta Psvchologica.
25,207-218.
Indermill, C., & Husak, W. S. (1984). Relationship between speed and accuracy
in an over-arm throw. Perceptual and Motor Skills. 52(1), 219-222.
Jagacinski, R. J., Repperger, D. W., Ward, S. L., Moran, M. S., & Glass, B.
(1980). A test of Fitts' Law with moving targets. Human Factors. 22(21.225-233.
122
Jaquacinski, R. J., & Monk, D. L. (1985). Fitts1 Law in two dimensions with hand
and head movements. Journal of Motor Behavior. 12(1), 77-95.
Kantowitz, B. H., & Elvers, G. C. (1988). Fitts' Law with an isometric controller:
Effects of order of control and control-display gain. Journal of Motor Behavior.
2Q(1), 53-66.
Keele, S. W. (1968). Movement control in skilled motor performance.
Psychological Bulletin. 2Q(6), Part 1, 387-403.
Keele, S. W. (1981). Behavioral Analysis of Movement. In V. B. Brooks (Ed.)
Handbook of physiology: Section 1: The nervous system. Volume 2. Motor
Control. Part 2. Baltimore: American Physiological Society.
Kelso, J. A. S., Southard, D. L., & Goodman, D. (1979). On the nature of human
interlimb coordination. Science. 203(43841.1029-1031.
Kerr, B. A., & Langolf, G. D. (1977). Speed of aiming movements. Quarterly
Journal of Experimental Psychology. 22,475-481.
Kerr, R. (1973). Movement time in an underwater environment. Journal of Motor
Behavior. 5, 175-178.
Kenr, R. (1978). Diving, adaptation and Fitts' Law. Journal of Motor Behavior.
Ill, 255-260.
Kerr, R,, & Hughes, K. (1987). Movement difficulty and learning disabled
children. Adapted Physical Activity Quarterly. 4(1), 72-79.
Klapp, S. T. (1975). Feedback versus motor programming in the control of aimed
movements. Journal of Experimental Psychology: Human Perception and
Performance. 104(2). 147-153.
Knight, A. A., & Dagnal L. P. R. (1967). Precision in Movements. Ergonomics.
IQ(3), 321-330.
Lahtela, K., Niemi, P., & Kuusela, V. (1985). Adult visual choice reaction time,
age, sex and preparedness, a test of Welford's problem in a large population
sample. Scandinavian Journal of Psychology. 2£, 357-362.
Langolf, G. D., Chaffin, D. B„ & Foulke, J. A. (1976). An investigation of Fitts'
Law using a wide range of movement amplitudes. Journal of Motor Behavior. £,
113-128. (Cited in Schmidt, 1988)
123
Leisman, G. (1989). Limb segment information transmission capacity. Journal of
Manipulative Physiological Therapy. 12(1), 3-9.
Lotusl23 (1987). Computer software. Lotus Development Corporation.
Cambridge, MA.
MacKenzie, C. L., Martiniuk, R. G., Dugas, C., Liske, D., & Eickmeier, B.
(1987). Three-dimensional movement trajectories in Fitts’ task: Implications for
control. The Quarterly Journal of Experimental Psychology. 39A. 629-647.
MacKenzie, I. S. (1989). A note on the information-theoretic basis for Fitts' Law.
Journal of Motor Behavior. 21(3), 323-330.
McCracken, H. D. (1983). Movement control in a reciprocal tapping task: A
developmental study. Journal of Motor Behavior. 1^(3), 262-279.
Meyer, D. E., Abrams, R. A., Komblum, S., Wright, C. E., & Smith, J. E. K.
(1988). Optimality in human motor performance: Ideal control of rapid aimed
movements. Psychological Review. 22(3), 340-370.
Meyer, D. E., Smith, J. E. K., & Wright, C. E. (1982). Models for the speed and
accuracy of aimed movements. Psychological Review. 89.449-482.
Mohan, J., & Bhatia, S. (1985). Intelligence, sex and psychomotor performance.
Indian Psychological Review. 2£(3), 1-6.
Morikiyo, Y., & Nishioka, A. (1966). An Analysis of the control mechanism on
simple movement of the hands. Journal of Science and Laboratory. 42.238-243.
Murrell, K. F. H., & Entwisle, D. G. (1960). Age differences in movement
pattern. Nature. 185 , p. 948.
Pacaud, S. (1955). Le vieillissement des aptitudes. In: L. Binet et F. Bourliere
(Edsl. Precis de Gerontologie. Paris: Masson.
Radwin, R. G., Vanderheiden, G. C., & Lin, M. (1990). A method for evaluating
head-controlled computer input devices using Fitts' Law. Human Factors. 32(41.
423-438.
Salthouse, T. A., & Somberg, B. L. (1982). Skilled performance: Effects of adult
age and experience on elementary processes. Journal of Experimental Psychology:
General. 111(21.176-207.
124
Schellekens, J. N., Kalverboer, A. F„ & Scholten, C. A. (1984). The
micro-structure of tapping movements in children. Journal of Motor Behavior.
M D , 20-39.
Schmidt, R. A. (1988). Loss of simple movement. Motor control and learning: A
behavioral emphasis. Chapter 9, Champaign, IL: Human Kinetics Publishers.
Schmidt, R. A., Zelazink, H., Hawkins, B., Frank, J. S., & Quinn, J. T. (1979).
Motor-output variability: A theory for the accuracy of rapid motor acts.
Psychological Review. ££(5), 415-451.
Shannon, C. (1948). A mathematical theory of communication. Bell Systems
Technical Journal. 22, 379-423, 623-656. (Cited in Fitts & Peterson, 1964).
Shock, N. W. (1984). Normal human aging: The Baltimore Longitudinal Study
of Aging. (NIH publication no. 84-2450) U.S. Department of Health and Human
Services.
Sigmaplot (1989). Computer software. Jandel Scientific Corporation. Corte
Madera, CA.
Stelmach, G. E., Amrhein, P. C., & Goggin, N. L. (1988). Age differences in
bimanual coordination. Journal of Gerontology: Psychological Sciences. 42(1),
18-23.
Sugden, D. A. (1980). Movement speed in children. Journal of Motor Behavior.
I I , 179-188.
Vercruyssen, M. (1991). Ergonomics and human performance: An overview.
Author published textbook. Los Angeles: University of Southern California.
Vince, M. A. (1948). Corrective movements in a pursuit task. Quarterly Journal
of Experimental Psychology. .1, 85-103.
Viviani, P., & Terzuolo, C. (1982). Trajectory determines movement dynamics.
Neuroscience. 2(2), 431-437.
Wade, M. G., Newell, K. M., & Wallace, S. A. (1978). Decision time and
movement time as a function of response complexity in retarded persons.
American Journal of Mental Deficiency. S3,135-144.
Wallace, S. A. (1983). The use of vision in controlling limb movements which
vary in difficulty. Paper presented at North American Society for the Psychology
of Sport and Physical Activity, Michigan State University, East Lansing, MI.
1 2 5
Wallace, S. A., & Newell, K. M. (1983). Visual control of discreet aiming
movements. Quarterly Journal of Experimental Psychology. 35A. 311-321.
Wallace, S. A., Hawkins, B., & Mood, D. P. (1983). Can Fitts' Law be
improved?: Predicting movement time based on more than one dimension.
(Technical Report No. 126). Boulder, CO: University of Colorado, Institute of
Cognitive Science.
Wallace, S. A., Newell, K. M., & Wade, M. G. (1978). Decision and response
times as a function of movement difficulty in pre-school children. Child
Development. 49. 509-512.
Welford, A. T. (1958). Ageing and human skill. London: Oxford University
Press.
Welford, A. T. (1960). The measurement of sensory-motor performance: Survey
and re-appraisal of twelve years'progress. Ergonomics. 3(31. 189-230.
Welford, A. T. (1961). Age changes in the times taken by choice, discrimination
and the control of movement. Gerontologia. 5, 129-145.
Welford, A. T. (1968). Fundamentals of Skill, pp.137-160, London: Methuen
and Company.
Welford, A. T. (1990). Fitts' Law revisited, with a note on changes associated with
age. Private communication, December, 1990.
Welford, A. T., Norris, A. H., & Shock, N. W. (1969). Speed and accuracy of
hand movements and their changes with age. Acta Psychologic a. 30. 3-15.
Wiker, S. F., Langolf, G. D., & Chaffin, D. B. (1989). Arm posture and human
movement capability. Human Factors. 31(41. 421-441.
Williams, H. G., & Werner, P. (1985). Development of movement schema in
young children. Perceptual and Motor Skills. 6Q . 403-410.
Wing, A. M. (1983). Crossman & Goodeve (1963): 20 years on. Quarterly
Journal of Experimental Psychology. 35A. 245-249.
Wing, A. M., Church, R. M., & Gentner, D. R. (1989). Variability in the timing
of responses during repetitive tapping with alternate hands. Special issue: Rhythm
perception, rhythm production, and timing. Psychological Research. 51(1). 28-37.
(Not Cited.)
126
Wingz (1989). Computer software. Informix Software, Inc., Lenexa, Kansas.
Woodworth, R. S. (1899). The accuracy of voluntary movement. Psychological
Monographs. 2, (3, Whole No. 13), 1-114.
Wright, C. E., & Meyer, D. E. (1983). Conditions for a linear speed-accuracy
trade-off in aimed movements. Quarterly Journal of Experimental Psychology.
34A. 279-296.
Yamada, Y. (1986). The interaction effect of type-p and type-m leadership
behavior on the number of tappings and the percent correct detection of the target.
Japanese Journal of Psychology. 52(4), 193-199.
York, J. L,, & Biedeiman, I. (1988). Motor performance in detoxified alcoholics.
Alcoholism - Clinical and Experimental Research. 12(1), 119-124.
York, J. L., & Biederman, I. (1990). Effects of age and sex on reciprocal tapping
performance. Perceptual and Motor Skills. 71.675-684.
1 2 7
APPENDIX A
Informed Consent Form
V.
Form C (Revised 2/90)
CLINICAL INVESTIGATION CONSENT FORM
The Gerontology Research Center
(The National Institute on Aging)
(The Francis Scott Key Medical Center, etc.)
TIUe of Research Prefect:
Baltimore Longitudinal Study of Aging
Patient I.D. Plate
Explanation of Research Project to Subject:
PU RPO SE O F STUD Y:
The Baltimore Longitudinal Study of Aging (BLSA) is a
multidisciplinary research study of the physiological and
psychological aspects of human aging. As a BLSA volunteer, you
■arebeing asked to consent to participate in the tests listed in
the attached Consent Booklet, your participation in these
procedures will help add to knowledge about the relationships
.between age and .the areas under study, such as cardiovascular and
pulmonary function, memory, and personality (See Table of
Contents, pages 1 c 2, in Consent Booklet).
PROCEDURES:
The tests are described in the attached.BLSA Consent Booklet on
pages 4-18. All of the tests are performed for research purposes
and are not designed to improve your health at this time. You
will be scheduled for most, but not all, of these tests during
your two and one-half day visit at the Gerontology Research
Center. If, after reading the Consent Booklet, there are tests in
which you do not wish to participate, please list them on the back
of this form.
RISKS/DISCOMFORTS:
Risks and/or discomforts associated with the tests are explained
in Section IV of the Consent Booklet, pages 18-20. In the event
of physical injury resulting from the research procedures, whether
at the Gerontology Research Center, the Francis Scott Key Medical
Center, or The Johns Hopkins Hospital, emergency care will given
at the facility where the injury occurs. The Gerontology Research
Center will provide for short-term medical care as may be
necessary. The Francis Scott Key Medical Center., .the Gerontology
Research center, The Johns Hopkins Hospital, the investigator, and
the Federal government will not be able to pay far care beyond
this or provide you with long-term medical treatment or financial
compensation except as may be provided through whatever remedies
are normally available under law.
THIS CONSENT FORM CONTINUES ON THE REV ER SE SIDE
\
The procedures, risks and benefits of this study have been explained. You understand that this
is a research project, and alternative forms of therapy may be available to you. Any questions that
you have now, or in the future, -will be answered by the investigator, James L. F o z a rd . Ph.D.
at Xim) sen-17Rfi You will be informed.of any new information that may be learned during
the course of-this study that might affect yourwillingness to partidpate.
The records from this research study will be kept confidential and will not be given to anyone
who is not helping on this study, unless you agree to have the records given out. U the study uses
a new drug or device that is under the jurisdiction of the Pood and Drug Administration (FDA),
the FDA government officials may look at the relevant part of your medical records as part of their
job to review new drug and device studies.
In the event that you have questions about research subjects' rights, or believe that you have
received a research related injury, you may contact the investigator. Dr. Reubin Andres, 550-1784,
Clinical Director, Chairman of the Institutional Review Board for Human Research, 550-1853.
The known and suspected risks of this study are listed on the consent form. You understand
that in the event of physical injury resulting from the research procedures, the investigator will
attempt to provide you with emergency and/or short term medical care to be given at the facility
where the injury occurs. You also understand that neither the Gerontology Research Center, the
Francis Scott Key Medical Center, the Johns Hopkins Hospital, the Federal Government or the
Investigator will be able to provide long-term medical treatment or compensation beyond this or
to provide you with financial compensation except as may be provided through whatever remedies
are normally available under law.
Your cooperation in this study is entirely voluntary, and you may refuse to participate or with
draw at any time without prejudicing your care at the Gerontology Research Center, Francis Scott
Key Medical Center or Johns Hopkins Hospital. * *
I w ill p articip a te in the te s ts as lis te d in th is document.
I will not p articip a te in the following t e s t s i ^ ____________ _____________________
1 understand copies o f m y medical report w ill fie sent to m y physician lis te d below:
N a m e ; ____________________________________
Address r____________________________________________________ ;______________
Phone:______________ ___________
Subject's tijninUT
(Including children* when eppUobto)
Slgnanuv of Pimit or Guirdiin (when applicable)
Wltneu 6 1 Zbnscnt P tm d m ? f ^
SEjiururfottnveitigitor s J
-----------------
.. .-tOpdonal imlesa subject to fflitrrale. or wubfe to algn.
NOT VALID WITHOUT THE
COMMITTEE OR IRB STAMP
?N
m 18 13S 0
VOID ONE YEAR FROM ABOVE DATE
R P N N o , & d tl________
M OTE; Signed copies of this consent form must be a) retained on file by the Frindpal Investigator; b) deposited in th
patient's medical record: and c) given to the patient. Revised 2/90
A P P E N D I X B
T a r g e t C o n f ig u r a tio n s
Target SW
Target SI
T a rg e t S N
Target MW
Target MI
Target MN
/
7 r
35H m m
/
V
Target LW
136
/
7 T
3 8 5 , 5 mm
/ ( \ s
7
/
Target LI
137
3 16 m w\
Target LN
A P P E N D I X C
S a m p le s o f A c tu a l U s e d T a r g e t s
Target SW
V -
' '* r . i . , ' \
/ r -
- * * • *
• ?
................. ... - - ..........
t
* •* \ 1 ; i ' >*-
Target SI
140
Target SN
Target MW
Target MI
Target MN
APPENDIX D
INSTRUCTIONS TO SUBJECTS OF TAPPING TEST (REVISION 3/25/66)
1. The purpose of this test is to find out how fast you can perform different
tapping tests. The distance between targets will be changed from one trial to the
next. In each case, you are supposed to be accurate in hitting the target and at
the same time maintain maximum speed.
2. You will "dot" back and forth from one target to the other fifty times (100 dots
in all). There will be a total of 10 trials.
3. You may hold the pencil in either hand, but you must use the same hand
throughout the test.
4. You must nol rest your elbow or wrist on the table. You must let your arm
swing free.
5. You should nol try to count the dots since this will slow you down. I will count
for you. I will also tell you wen to start and when to stop.
6. You will find that you can work faster on some of the target sheets than on
others. In each case, you should work as fast as possible, whise making sure
that most of the dots - say all except about 4 on each sheet - fall between the
target lines.
1 4 5
APPENDIX E
Balanced Order of Targets Presented
1. SW M N LIL N SIM W M ILW SN
2. MW LN SI SN MI LW LI SW MN
3. SI MN LW LN SW MI MW LI SN
4. MI LN SW SN MW LI LW SI MN
5. SN MI LW LI SW MN MW LN SI
6. MN LI SW SI MW LN LW SN MI
7. SW LN MI MN SI LW LI MW SN
8. LW SN MI MN LI SW SI MW LN
9. SI LN MW MN SW LI LW MI SN
10. LI SN MW MN LW SI SW MI LN
11. SN LI MW MI SW LN LW MN SI
12. LN SI MW MI LW SN SW MN LI
13. MW SN LI LN MI SW SI LW MN
14. LW MN SI SN LI MW MI SW LN
15. MI SN LW LN MW SI SW LI MN
16. LI MN SW SN LW MI MW SI LN
17. MN SI LW LI MW SN SW LN MI
18. LN MI SW SI LW MN MW SN LI
19. MW LI SN SI MN LW LN SW MI
20. SW MI LN LI SN MW MN LW SI
21. MI LW SN SW MN LI LN SI MW
22. SI MW LN LW SN MI MN LI SW
23. MN LW SI SW MI LN LI SN MW
24. SN MW LI LW SI MN MI LN SW
25. LW SI MN MI LN SW SN MW LI
26. SW LI MN MI SN LW LN MW SI
27. LI SW MN MW LN SI SN MI LW
28. SI LW MN MW SN LI LN MI SW
29. LN SW MI MW LI SN SI MN LW
30. SN LW MI MW SI LN LI MN S W
31. LW MI SN SI LN MW MN SW LI
32. MW SI LN LI MN SW SN LW MI
33. LI MW SN SW LN MI MN SI LW
34. MI SW LN LW MN SI SN LI MW
35. LN MW SI SW LI MN MI SN LW
36. MN SW LI LW MI SN SI LN MW
146
APPENDIX F
Input File Format
FORMAT OF ORIGINAL DATA
INFORMATION TYPE 151 = TAPPING DATA
CARD 1
COLUMN(S) FORHAT UNITS CONTENTS
1-2 XX
T TW TI
WL for Target SW
3-4 XX m m WR for Target SW
5-7 XXX ram DPRIME for Target SW
8-10 XXX 0 *OlminutQB Total Time for Target SW
11-12 XX mm WL for Target SI
13-14 XX WR for Target SI
15-17 XXX mm DPRIME for Target SI
18-20 XXX 0.Olminutee Total Time for Target SI
21-22 XX mm WL for Target SN
23-24 XX r r t m
WR for Target SN
25-27 XXX ntm DPRIME for Target SN
28-30 XXX 0,01ml mitaa Total Time for Target SN
31-32 XX mm WL for Target MW
33-34 XX mm WR for Target MW
35-37 XXX mm DPRIME for Target MW
38-40 XXX O.Olmlnutes Total Time for Target MW
41-42 XX mm WL for Target MI
43-44 XX m m
WR for Target MI
45-47 XXX m m DPRIME for Target MI
48-50 XXX 0. Olminutee Total Time for Target MI
51-52 XX m m WL for Target MN
53-54 XX m m WR for Target MN
55-57 XXX mm DPRIME for Target MN
58-60 XXX 0.OlminuteB Total Time for Target MN
61-62 XX mm Width of tapping in place lX2cm
63-65 XXX 0.Olminutes Total Time for tapping in place
66-67 Blanks
68-68 X 0 = Left Band, 1 = Right Band
69-72 XXXX XRAY Number (Subject Number)
73-74 XX Visit Number
75-77 XXX Information Type = 151 (Tapping
78-79 XX Card Number => 01
80-80 Blank
CARD 2
COLUMN(S) FORMAT UNITS CONTENTS
1-2 XX mm WL for Target LW
3-4 XX mm WR for Target LW
5-7 XXX mm DPRIME for Target LW
8-10 XXX O.Olmlnutes Total Time for Target LW
11-12 XX mm WL for Target LI
13-14 XX mm WR for Target LI
15-17 XXX mm DPRIME for Target LI
18-20 XXX O.Olmlnutes Total Time for Target LI
21-22 XX mm WL for Target LN
23-24 XX mm WR for Target LN
25-27 XXX mm DPRIME for Target LN
28-30 XXX O.Olmlnutes Total Time for Target LN
31-32 XX mm Width of taking In place - 5X1Ocm Target
33-35 XXX O.Olmlnutes Total Time for tapping in place - 5X10cm Target
36-37 XX mm Width of tapping in place - 10X15cm Target
38-40 XXX O.Olmlnutes Total Time for tapping in place - 10X15cm Target
41-49 XXXXXXXXX "a" Constant X 100,000 - Wolford's Formula
50-58 XXXXXXXXX "b” Constant X 100,000 - Weiford's Formula
59-67 XXXXXXXXX "Wo"' Constant X 100,000 - Wolford's Formula
67-68 Blanks
69-72 XXXX XRAY Number (Subject Number)
73-74 XX Visit Number
75-77 XXX Information Type = 151 (Tapping Test)
78-79 XX Card Number = 02
80-80 Blank
1 4 7
INFO RM ATION TYPE 0 0 0 = ID E N T IF IC A T IO N RECORD
COLUMN (S) FORMAT UNITS CONTENTS
1-4 XXXX XRAY Number (Subject Number)
S-5 Blank
6-7 XX Visit Number
8-8 Blank
9-9 X SEX - Male = 1, Female = 2
10-10 Blank
11-18 HMDDYYYY BIRTBDATE
19-19 Blank
20-25 MMDDYY VISITDATE
26-26 Blank
27-27 X Number of Cards for this visit
28-74 Blanks
75-77 XXX Information Type = 000 (Identification type)
78-80 Blanks
148
APPENDIX G
Sample of Input Data
313107603812110580530405052088422516304810121500750608149125
193341208209154081220505406160 001360919002223418001557025
211111211
15150530330712058058050505410718171490571109147095040514413505022
1620396093091140514305054061830903310053001557725002804011000895998
2 1 1 2 1 1 2 1 1
13180440331717065050101306206817241610673927154045060914610704015
3539422068101240609804094061350904510045000877270001906181005150000
2 1 1 2 1 1 1 1 1
14180610351914065048111105906841271510481921151065080714510703017
3839420067131941210307094051350402705022001089629001757957006042507
211211111
20220530352418065043161106205826271490433321160058060714710305020
2941411077121841110407104111370603017038001336249005381263001596621
211211111
29240640382416067047060705607734321630530810148083422415705702017
1924408092152241210814174161130903813042000989835001701136008192307
23140610353018075038282608204244311670372826165043282716805310015
5044410070425243306711174111070803214035
19140350352119067038151306205245221540381717154065361816405505018
3749423062163141609014184181201303810042
2 1 1 2 1 1 1 1 1
21220600331720070042142006705035381700382121154055272216307204018
5244421067475744007332494340880602712040
211111111
102760215101
02760215102
02760215105
102760315101
02760315102
02760315105
102760415101
02760415102
02760415105
102760515101
02760515102
02760515105
102760615101
02760615102
02760615105
102760715101
02760715102
102760815101
02760815102
102760915101
02760915102
02760915105
102761015101
02761015102
02761015105
NOTE: Card 5 d a ta (e.g. l a s t l i n e above) was n o t u s e d i n t h i s s tu d y .
APPENDIX H
O u t p u t F ile F o r m a t
COLUMN(S) FORMAT UNITS CONTENTS
1-4 XXXX XRAY Number (Subject Number)
5-5 Blank
6-7 XX Visit Number
8-8 Blank
9-14 MMDDYY VISITDATE
15-15 Blank
16-23 MMDDYYYY BIRTHDATE
24-24 Blank
25-27 XXX years AGE on visit date
28-28 Blank
29-29 X SEX - Male = 1, Female c s 2
30-30 Blank
31-31 X 0 — Left Hand, 1 = Right Hand
32-32 Blank
33-35 XXX mm
AFIXED (A + 0.5W)
36-36 Blank
37-41 xxx.x mm A
42-42 Blank
43-44 XX mm H
45-45 Blank
46-50 xxx.x
nm
A'
51-51 Blank
52-56 xxx.x
|iffin
D
57-57 Blank
58-60 XXX M U D*
61-61 Blank
62-66 xxx.x mm I
67-67 Blank
68-69 XX mm WL
70-70 Blank
71-72 XX mm WR
73-73 Blank
74-77 XX.X
trim
W'
78-78 Blank
79-85 XX.XXXX A' /A
86-86 Blank
87-93 XX.XXXX
W'/H
94-94 Blank
95-98 XXXX msec Time per Movement (MT)
99-100 Blanks
101-101 X Target Configuration (1=SW, 2=SI
1 5 0
APPENDIX I
Sample of Output File Data
0 3 8 8 0 1 1 2 0 4 6 3 1 2 2 7 1 9 0 6 5 6 1 1 5 0 3 4 . 0 32 3 1 . 0 6 6 . 0 58 2 . 0 28 2 6 2 7 . 0 0 . 9 1 1 8 0 . 8 4 3 8 1 9 2 1
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 56 1 1 50 4 4 . 5 11 4 5 . 5 5 5 . 5 59 3 3 . 5 13 14 1 3 . 5 1 . 0 2 2 5 1 . 2 2 7 3 3 3 6 2
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 56 1 1 50 4 8 . 0 4 4 8 . 5 5 2 . 0 53 4 4 . 0 5 4 4 . 5 1 . 0 1 0 4 1 . 1 2 5 0 5 2 2 3
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 56 1 1 142 1 2 6 . 0 32 1 2 3 . 5 1 5 8 . 0 142 9 4 . 0 17 2 0 1 8 . 5 0 . 9 8 0 2 0 . 5 7 8 1 3 4 2 4
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 56 1 1 142 1 3 6 . 5 11 1 3 9 . 0 1 4 7 . 5 1 5 0 1 2 5 . 5 10 12 1 1 . 0 1 . 0 1 8 3 1 . 0 0 0 0 492 5
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 56 1 1 142 1 4 0 . 0 4 1 4 1 . 0 1 4 4 . 0 1 4 5 1 3 6 . 0 4 4 4 . 0 1 . 0 0 7 1 1 . 0 0 0 0 6 8 4 6
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 5 6 1 1 402 3 8 6 . 0 32 3 8 1 . 0 4 1 8 . 0 4 0 0 3 5 4 . 0 19 19 1 9 . 0 0 . 9 8 7 0 0 . 5 9 3 8 4 62 7
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 5 6 1 1 4 0 2 3 9 6 . 5 11 3 9 7 . 0 4 0 7 . 5 4 0 6 3 8 5 . 5 7 11 9 . 0 1 . 0 0 1 3 0 . 8 1 8 2 6 18 8
0 3 8 8 01 1 2 0 4 6 3 1 2 2 7 1 9 0 6 5 6 1 1 402 4 0 0 . 0 4 4 0 1 . 0 4 0 4 . 0 40 6 3 9 6 . 0 4 6 5 . 0 1 . 0 0 2 5 1 . 2 5 0 0 864 9
APPENDIX J
Formula Numbering System
Formulas were numbered as follows:
# A DISTANCE
MEASURE
WIDTH
MEASURE
1 A W
2 A WL
3 A WR
4 A W
5 A’ w
6 A' WL
7 A’ WR
8 A’ W1
9 D w
10 D WL
11 D WR
12 D W
13 D’ W
14 D' WL
15 D’ WR
16 D1 W’
17 I W
18 I WL
19 I WR
20 I W
# B FORMULA
0 LOG2(A/W)
20 LOG2(2A/W)
40 LOG2(A/W + 0.5)
60 LOG2(A /W + l)
80 LOG2(A/(W-)+0.5)
100 LOG2(A/(W-3) + 1)
120 Ln(A/W)
140 Ln(2A/W)
160 Ln(A/W + 0.5)
180 Ln(A/W + 1)
200 Ln(A/(W-3) + 0.5)
220 Ln(A/(W-3) + 1)
# A + #B = FORMULA NUMBER
Formula 241 is: MT = aLOG2(A') - bLOG2(W) + (b - a)LOG2(W'0)
Formula 242 is: MT = aLn(A’ ) - bLn(W’ ) + (b - a)Ln(W’ 0)
1 5 2
APPENDIX K
Comparison of Prominent Formulas
Y - I n t e r c e p t (a )
(WITHOUT SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 41 61 69 7 3
ALL SUBS 8 2 . 1 4 - 2 5 . 2 7 5 7 . 4 5 3 3 . 7 5 - 1 1 . 3 3 - 1 5 . 0 6
MALES 8 3 . 4 3 - 2 5 . 8 3 5 8 . 3 7 3 4 . 3 1 - 1 1 . 4 5 - 1 5 . 2 4
FEMALES 7 7 . 1 4 - 2 3 . 1 1 5 3 . 9 1 3 1 . 6 0 - 1 0 . 8 5 - 1 4 . 1 1
DECADE2 9 8 . 2 5 2 0 . 5 6 8 0 . 3 5 6 3 . 1 6 3 0 . 4 5 2 1 . 1 4
DECADE3 7 7 . 5 3 - 1 0 . 6 3 5 7 . 2 2 3 7 . 7 2 0 . 6 3 - 6 . 7 6
DECADE4 6 5 .4 2 - 3 6 . 1 1 4 2 . 0 3 1 9 . 5 7 - 2 3 . 1 5 - 2 6 . 2 4
DECADES 7 2 . 0 5 - 3 4 . 5 8 4 7 . 66 2 4 . 2 4 - 2 0 . 2 9 - 2 6 . 7 6
DECADE6 7 2 . 9 0 - 4 0 . 3 1 4 6 . 8 0 2 1 . 7 4 - 2 5 . 9 6 - 2 5 . 0 4
DECADE7 1 0 3 . 3 6 - 2 0 . 1 2 7 5 . 1 0 4 7 . 9 7 - 3 . 6 2 - 3 . 2 1
DECADE8 1 2 7 . 5 2 - 6 . 4 2 9 6 . 5 7 6 6 . 8 3 1 0 . 2 7 1 2 . 3 9
DECADE9 2 8 1 . 2 4 1 0 7 . 5 7 2 4 1 . 3 3 2 0 2 . 9 9 1 3 0 . 0 2 1 4 0 . 6 1
DECADE10 6 0 . 8 9 - 1 2 5 . 1 2 1 9 . 4 5 - 2 0 . 3 0 - 9 5 . 8 0 - 8 2 . 9 5
MDECADE2 1 1 1 . 4 6 3 6 . 6 9 9 4 . 3 0 7 7 . 8 2 4 6 . 4 9 3 7 . 7 8
MDECADE3 7 6 . 7 1 - 1 2 . 2 5 5 6 . 2 4 3 6 . 5 7 - 0 . 8 3 - 8 . 67
MDECADE4 6 4 .1 7 - 4 0 . 8 4 4 0 . 0 0 1 6 . 7 9 - 2 7 . 3 6 - 3 0 . 1 4
MDECADE5 7 0 . 8 8 - 3 7 . 3 4 4 6 . 1 8 2 2 . 4 6 - 2 2 . 6 5 - 2 9 . 5 1
MDECADE6 7 1 . 0 8 - 4 6 . 2 3 4 4 . 1 1 1 8 . 2 2 - 3 1 . 0 4 - 2 8 . 3 8
MDECADE7 1 1 1 . 5 4 - 1 4 . 1 5 8 2 . 9 0 5 5 . 4 2 3 . 1 7 3 . 6 7
MDECADE8 1 2 9 . 7 8 - 5 . 5 3 9 8 . 4 8 6 8 . 4 2 1 1 . 2 2 1 4 . 6 8
MDECADE9 3 0 6 . 6 3 1 3 9 . 4 3 2 6 8 . 2 2 2 3 1 . 3 2 1 6 1 . 0 9 1 6 7 . 5 4
MDECADEIO 6 0 . 8 9 - 1 2 5 . 1 2 1 9 . 4 5 - 2 0 . 3 0 - 9 5 . 8 0 - 8 2 . 9 5
FDECADE2 - 4 . 1 2 - 1 0 4 . 4 3 - 2 7 . 7 7 - 5 0 . 5 0 - 9 3 . 8 1 - 1 0 8 . 0 2
FDECADE3 8 0 . 9 5 - 3 . 8 4 6 1 . 3 6 4 2 . 5 4 6 . 7 3 1 . 2 7
FDECADE4 7 0 . 8 3 - 1 5 . 6 8 5 0 . 8 2 3 1 . 6 0 - 4 . 9 5 - 8 . 2 7
FDECADE5 7 8 . 3 8 - 1 9 . 5 6 5 5 . 7 3 3 3 . 9 8 - 7 . 4 0 - 1 1 . 6 8
FDECADE6 7 6 . 7 6 - 2 7 . 7 6 5 2 . 5 0 2 9 . 1 9 - 1 5 . 1 8 - 1 7 . 1 9
FDECADE7 7 8 . 0 4 - 3 8 . 5 9 5 0 . 9 5 2 4 . 9 2 - 2 4 . 6 2 - 2 4 . 2 6
FDECADE8 1 0 9 . 4 7 - 1 3 . 5 6 8 1 . 2 5 5 4 . 1 6 2 . 6 9 - 4 . 3 9
FDECADE9 1 5 4 . 3 1 - 5 1 . 7 3 1 0 6 . 9 0 6 1 . 3 6 - 2 5 . 3 1 1 1 . 6 6
153
S l o p e (b )
(WITHOUT SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 4 1 61 6 9 7 3
ALL SUBS 1 0 7 . 4 1 1 0 7 . 4 1 1 1 1 . 65 1 1 5 . 6 6 1 2 3 . 1 3 1 2 3 . 0 5
MALES 1 0 9 . 2 6 1 0 9 . 2 6 1 1 3 . 5 6 1 1 7 . 6 3 1 2 5 . 2 1 1 2 5 . 2 0
FEMALES 1 0 0 . 2 5 1 0 0 . 2 5 1 0 4 . 2 5 1 0 8 . 0 4 1 1 5 . 1 0 1 1 4 . 7 4
DECADE2 7 7 . 6 9 7 7 . 69 8 0 . 7 7 8 3 . 68 8 9 . 1 1 8 9 . 5 9
DECADE3 8 8 . 1 6 8 8 . 1 6 9 1 . 6 5 9 4 . 9 5 1 0 1 . 1 1 1 0 1 . 4 5
DECADE4 1 0 1 . 5 2 1 0 1 . 5 2 1 0 5 . 5 5 1 0 9 . 3 5 1 1 6 . 4 4 1 1 6 . 3 0
DECADES 1 0 6 . 6 3 1 0 6 . 6 3 1 1 0 . 8 1 1 1 4 . 7 6 1 2 2 . 1 3 1 2 2 . 6 8
DECADE6 1 1 3 . 2 1 1 1 3 . 2 1 1 1 7 . 7 0 1 2 1 . 9 5 1 2 9 . 8 7 1 2 9 . 1 5
DECADE7 1 2 3 . 4 7 1 2 3 . 4 7 1 2 8 . 3 2 1 3 2 . 9 0 1 4 1 . 4 4 1 4 0 . 6 6
DECADE8 1 3 3 . 9 4 1 3 3 . 9 4 1 3 9 . 2 8 1 4 4 . 3 2 1 5 3 . 7 2 1 5 2 . 7 1
DECADE9 1 7 3 . 6 8 1 7 3 . 6 8 1 8 0 . 5 3 1 8 7 . 0 2 1 9 9 . 1 2 1 9 6 . 2 9
DECADE1 0 1 8 6 . 0 2 1 8 6 . 0 2 1 9 3 . 0 4 1 9 9 . 6 7 2 1 2 . 0 2 2 1 0 . 1 8
MDECADE2 7 4 . 7 7 7 4 . 7 7 7 7 . 7 2 8 0 . 5 0 8 5 . 6 9 8 6 . 1 1
MDECADE3 8 8 . 9 6 8 8 . 9 6 9 2 . 4 8 9 5 . 8 1 1 0 2 . 0 2 1 0 2 . 4 6
MDECADE4 1 0 5 . 0 0 1 0 5 . 0 0 1 0 9 . 1 6 1 1 3 . 0 9 1 2 0 . 4 1 1 2 0 . 3 1
MDECADE5 1 0 8 . 2 2 1 0 8 . 2 2 1 1 2 . 4 5 1 1 6 . 4 5 1 2 3 . 9 1 1 2 4 . 5 3
MDECADE6 1 1 7 . 3 1 1 1 7 . 3 1 1 2 1 . 9 5 1 2 6 . 3 3 1 3 4 . 5 0 1 3 3 . 5 7
MDECADE7 1 2 5 . 6 8 1 2 5 . 6 8 1 3 0 . 5 8 1 3 5 . 2 1 1 4 3 . 8 5 1 4 3 . 1 6
MDECADE8 1 3 5 . 3 1 1 3 5 . 3 1 1 4 0 . 7 0 1 4 5 . 8 0 1 5 5 . 3 1 1 5 4 . 1 3
MDECADE9 1 6 7 . 2 0 1 6 7 . 2 0 1 7 3 . 8 0 1 8 0 . 0 5 1 9 1 . 6 9 1 8 9 . 5 3
MDECADE10 1 8 6 . 0 2 1 8 6 . 0 2 1 9 3 . 0 4 1 9 9 . 6 7 2 1 2 . 0 2 2 1 0 . 1 8
FDECADE2 1 0 0 . 3 0 1 0 0 . 3 0 1 0 4 . 4 1 1 0 8 . 3 0 1 1 5 . 5 6 1 1 6 . 6 2
FDECADE3 8 4 . 7 8 8 4 . 7 8 8 8 . 1 6 9 1 . 3 5 9 7 . 3 0 9 7 . 1 8
FDECADE4 8 6 . 5 0 8 6 . 5 0 8 9 . 9 5 9 3 . 2 1 9 9 . 2 9 9 8 . 8 1
FDECADE5 9 7 . 9 4 9 7 . 9 4 1 0 1 . 8 4 1 0 5 . 5 3 1 1 2 . 4 1 1 1 2 . 5 3
FDECADE6 1 0 4 . 5 2 1 0 4 . 5 2 1 0 8 . 7 1 1 1 2 . 6 7 1 2 0 . 0 6 1 1 9 . 6 8
FDECADE7 1 1 6 . 6 3 1 1 6 . 6 3 1 2 1 . 3 1 1 2 5 . 7 3 1 3 3 . 9 9 1 3 2 . 8 9
FDECADE8 1 2 3 . 0 3 1 2 3 . 0 3 1 2 7 . 8 8 1 3 2 . 4 6 1 4 0 . 9 8 1 4 1 . 0 9
FDECADE9 2 0 6 . 0 4 2 0 6 . 0 4 2 1 4 . 1 9 2 2 1 . 9 0 2 3 6 . 2 8 2 2 9 . 1 7
1 54
Coefficient of Determination(r^)
(WITHOUT SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 4 1 61 69 7 3
ALL SUBS 0 . 9 8 4 6 6 0 . 9 8 4 6 6 0 . 9 8 7 2 2 0 . 9 8 9 0 6 0 . 9 9 1 2 7 0 . 9 9 2 7 3
MALES 0 . 9 8 4 7 2 0 . 9 8 4 7 2 0 . 9 8 7 0 7 0 . 9 8 8 7 3 0 . 9 9 0 6 1 0 . 9 9 3 5 0
FEMALES 0 . 9 7 5 7 1 0 . 9 7 5 7 1 0 . 9 7 9 1 1 0 . 9 8 1 7 3 0 . 9 8 5 3 1 0 . 9 8 0 3 1
DECADE2 0 . 9 8 0 9 2 0 . 9 8 0 9 2 0 . 9 8 3 7 6 0 . 9 8 5 8 6 0 . 9 8 8 5 1 0 . 9 8 4 8 0
DECADE3 0 . 9 8 3 5 9 0 . 9 8 3 5 9 0 . 9 8 6 3 9 0 . 9 8 8 4 6 0 . 9 9 1 0 4 0 . 9 8 8 0 9
DECADE4 0 . 9 8 3 5 3 0 . 9 8 3 5 3 0 . 9 8 6 3 3 0 . 9 8 8 4 1 0 . 9 9 1 0 1 0 . 9 9 2 5 4
DECADES 0 . 9 8 3 4 5 0 . 9 8 3 4 5 0 . 9 8 5 5 0 0 . 9 8 6 9 0 0 . 9 8 8 3 2 0 . 9 9 3 4 0
DECADES 0 . 9 8 1 4 3 0 . 9 8 1 4 3 0 . 9 8 4 3 3 0 . 9 8 6 4 9 0 . 9 8 9 2 6 0 . 9 9 1 0 8
DECADE7 0 . 9 8 5 6 4 0 . 9 8 5 6 4 0 . 9 8 7 7 5 0 . 9 8 9 1 9 0 . 9 9 0 6 9 0 . 9 9 2 5 8
DECADE8 0 . 9 7 6 4 4 0 . 9 7 6 4 4 0 . 9 7 9 5 9 0 . 9 8 1 9 7 0 . 9 8 5 1 1 0 . 9 8 4 7 8
DECADE9 0 . 9 3 8 5 6 0 . 9 3 8 5 6 0 . 9 4 1 0 0 0 . 9 4 2 8 1 0 . 9 4 5 0 7 0 . 9 3 5 6 2
DECADE1 0 0 . 9 2 7 8 5 0 . 9 2 7 8 5 0 . 9 2 7 1 5 0 . 9 2 6 1 1 0 . 9 2 3 3 7 0 . 9 3 1 3 7
MDECADE2 0 . 9 8 1 2 3 0 . 9 8 1 2 3 0 . 9 8 3 6 3 0 . 9 8 5 3 5 0 . 9 8 7 3 0 0 . 9 8 2 9 9
MDECADE3 0 . 9 8 4 6 4 0 . 9 8 4 6 4 0 . 9 8 7 3 7 0 . 9 8 9 3 7 0 . 9 9 1 8 2 0 . 9 9 0 1 3
MDECADE4 0 . 9 8 1 4 0 0 . 9 8 1 4 0 0 . 9 8 4 1 2 0 . 9 8 6 1 2 0 . 9 8 8 5 9 0 . 9 9 1 1 6
MDECADE5 0 . 9 8 0 6 2 0 . 9 8 0 6 2 0 . 9 8 2 4 6 0 . 9 8 3 6 8 0 . 9 8 4 8 0 0 . 9 9 1 7 1
MDECADE6 0 . 9 8 3 1 0 0 . 9 8 3 1 0 0 . 9 8 5 7 0 0 . 9 8 7 5 8 0 . 9 8 9 8 4 0 . 9 9 2 3 1
MDECADE7 0 . 9 8 6 7 0 0 . 9 8 6 7 0 0 . 9 8 8 3 2 0 . 9 8 9 3 3 0 . 9 9 0 0 5 0 . 9 9 4 4 4
MDECADE8 0 . 9 7 5 8 8 0 . 9 7 5 8 8 0 . 9 7 9 1 2 0 . 9 8 1 5 9 0 . 9 8 4 8 9 0 . 9 8 4 8 1
MDECADE9 0 . 9 3 9 1 3 0 . 9 3 9 1 3 0 . 9 4 1 5 4 0 . 9 4 3 3 2 0 . 9 4 5 5 4 0 . 9 3 4 6 3
MDECADE10 0 . 9 2 7 8 5 0 . 9 2 7 8 5 0 . 9 2 7 1 5 0 . 9 2 6 1 1 0 . 9 2 3 3 7 0 . 9 3 1 3 7
FDECADE2 0 . 9 5 5 1 6 0 . 9 5 5 1 6 0 . 9 6 0 3 4 0 . 9 6 4 6 0 0 . 9 7 1 1 2 0 . 9 7 0 9 5
FDECADE3 0 . 9 7 2 6 1 0 . 9 7 2 6 1 0 . 9 7 5 7 1 0 . 9 7 8 0 7 0 . 9 8 1 2 1 0 . 9 7 2 7 7
FDECADE4 0 . 9 8 2 6 2 0 . 9 8 2 6 2 0 . 9 8 5 8 7 0 . 9 8 8 3 4 0 . 9 9 1 5 8 0 . 9 8 4 9 8
FDECADE5 0 . 9 8 2 9 8 0 . 9 8 2 9 8 0 . 9 8 6 2 1 0 . 9 8 8 6 6 0 . 9 9 1 9 1 0 . 9 8 5 8 6
FDECADE6 0 . 9 7 0 1 9 0 . 9 7 0 1 9 0 . 9 7 3 7 7 0 . 9 7 6 5 8 0 . 9 8 0 5 2 0 . 9 7 9 8 3
FDECADE7 0 . 9 6 7 8 7 0 . 9 6 7 8 7 0 . 9 7 1 5 3 0 . 9 7 4 3 9 0 . 9 7 8 4 1 0 . 9 7 2 3 2
FDECADE8 0 . 9 6 8 6 7 0 . 9 6 8 6 7 0 . 9 7 1 0 1 0 . 9 7 2 6 1 0 . 9 7 4 2 7 0 . 9 7 0 8 8
FDECADE9 0 . 9 2 0 3 9 0 . 9 2 0 3 9 0 . 9 2 2 9 0 0 . 9 2 4 7 8 0 . 9 2 7 1 7 0 . 9 2 4 0 5
155
Standard Error of Estimate(Se)
{WITHOUT SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 4 1 6 1 69 7 3
ALL SUBS 2 3 . 3 0 2 3 . 3 0 2 1 . 2 7 1 9 . 68 1 7 . 5 8 1 6 . 0 4
MALES 2 3 . 66 2 3 . 6 6 2 1 . 7 6 2 0 . 3 2 1 8 . 5 5 1 5 . 4 3
FEMALES 2 7 . 5 0 2 7 . 5 0 2 5 . 5 0 2 3 . 8 4 2 1 . 3 8 2 4 . 7 5
DECADE2 1 8 . 8 3 1 8 . 8 3 1 7 . 3 8 1 6 . 2 1 1 4 . 6 1 1 6 . 8 1
DECADE3 1 9 . 7 9 1 9 . 7 9 1 8 . 0 2 1 6 . 6 0 1 4 . 6 2 1 6 . 8 6
DECADE4 2 2 . 8 4 2 2 . 8 4 2 0 . 8 0 1 9 . 1 6 1 6 . 8 7 1 5 . 3 6
DECADES 2 4 . 0 4 2 4 . 0 4 2 2 . 5 0 2 1 . 3 9 2 0 . 2 0 1 5 . 1 8
DECADE6 2 7 . 0 7 2 7 . 0 7 2 4 . 8 7 2 3 . 0 8 2 0 . 5 8 1 8 . 7 6
DECADE7 2 5 . 9 1 2 5 . 9 1 2 3 . 9 3 2 2 . 4 7 2 0 . 8 6 1 8 . 6 2
DECADE8 3 6 . 1 7 3 6 . 1 7 3 3 . 6 6 3 1 . 6 4 2 8 . 7 6 2 9 . 0 7
DECADE9 7 7 . 2 4 7 7 . 2 4 7 5 . 69 7 4 . 5 2 7 3 . 0 4 7 9 . 0 7
DECADE1 0 9 0 . 1 7 9 0 . 1 7 9 0 . 6 0 9 1 . 2 5 9 2 . 9 2 8 7 . 9 4
MDECADE2 1 7 . 9 8 1 7 . 9 8 1 6 . 7 9 1 5 . 8 8 1 4 . 7 9 1 7 . 1 1
MDECADE3 1 9 . 3 1 1 9 . 3 1 17 .5 1 1 6 . 0 6 1 4 . 0 9 1 5 . 4 9
MDECADE4 2 5 . 1 3 2 5 . 1 3 2 3 . 2 2 2 1 . 7 1 1 9 . 6 8 1 7 . 3 2
MDECADE5 2 6 . 4 5 2 6 . 4 5 2 5 . 1 6 2 4 . 2 7 2 3 . 4 2 1 7 . 2 9
MDECADE6 2 6 . 7 4 2 6 . 7 4 2 4 . 5 9 2 2 . 9 2 2 0 . 7 3 1 8 . 0 3
MDECADE7 2 5 . 3 7 2 5 . 3 7 2 3 . 7 7 2 2 . 7 2 2 1 . 9 4 1 6 . 4 0
MDECADE8 3 6 . 9 8 3 6 . 98 3 4 . 4 0 3 2 . 3 0 2 9 . 2 7 2 9 . 3 4
MDECADE9 7 4 . 0 0 7 4 . 0 0 7 2 . 5 1 7 1 . 4 0 6 9 . 9 9 7 6 . 6 8
MDECADE10 9 0 . 1 7 9 0 . 1 7 9 0 . 6 0 9 1 . 2 5 9 2 . 9 2 8 7 . 9 4
FDECADE2 3 7 . 7 8 3 7 . 7 8 3 5 . 5 3 3 3 . 5 6 3 0 . 3 1 3 0 . 4 1
FDECADE3 2 4 . 7 3 2 4 . 7 3 2 3 . 2 9 2 2 . 1 3 2 0 . 4 8 2 4 . 6 6
FDECADE4 2 0 . 0 0 2 0 . 0 0 1 8 . 0 3 1 6 . 3 8 1 3 . 9 2 1 8 . 5 9
FDECADE5 2 2 . 4 0 2 2 . 4 0 2 0 . 1 7 1 8 . 2 8 1 5 . 4 4 2 0 . 4 2
FDECADE6 3 1 . 8 5 3 1 . 8 5 2 9 . 8 7 2 8 . 2 3 2 5 . 7 5 2 6 . 2 0
FDECADE7 3 6 . 9 4 3 6 . 9 4 3 4 . 7 7 3 2 . 9 8 3 0 . 2 8 3 4 . 2 9
FDECADE8 3 8 . 4 6 3 8 . 4 6 3 7 . 0 0 3 5 . 9 6 3 4 . 8 5 3 7 . 0 8
FDECADE9 1 0 5 . 3 3 1 0 5 . 3 3 1 0 3 . 6 6 1 0 2 . 3 9 1 0 0 . 7 5 1 0 2 . 8 8
1 5 6
Y-Intercept (a)
{WITH SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 4 1 61 6 9 7 3
ALL SUBS 1 4 5 . 0 5 5 1 . 4 6 1 0 3 . 3 9 6 7 . 7 3 5 . 8 8 2 0 . 9 3
MALES 1 4 5 . 6 3 5 0 . 0 4 1 0 3 . 2 1 6 6 . 8 9 3 . 9 4 1 8 . 9 0
FEMALES 1 4 2 . 8 0 5 6 . 9 8 1 0 4 . 1 1 7 0 . 9 5 1 3 . 4 0 2 8 . 9 1
DECADE2 1 4 4 . 2 3 7 6 . 6 4 1 1 4 . 0 9 8 8 . 2 8 4 3 . 5 1 4 9 . 5 4
DECADE3 1 3 4 . 1 0 5 8 . 3 6 1 0 0 . 0 9 7 0 . 9 6 2 0 . 4 4 2 9 . 8 8
DECADE4 1 2 8 . 2 2 4 0 . 4 9 8 8 . 9 5 5 5 . 3 2 - 3 . 0 0 1 2 . 7 2
DECADES 1 3 3 . 4 9 4 0 . 3 6 9 2 . 1 6 5 6 . 7 9 - 4 . 5 1 9 . 4 0
DECADE6 1 3 9 . 3 6 4 0 . 7 5 9 5 . 4 1 5 7 . 7 7 - 7 . 5 3 1 1 . 1 4
DECADE7 1 7 1 . 3 1 6 2 . 7 7 1 2 3 . 3 1 8 2 . 2 2 1 1 . 0 3 3 0 . 4 3
DECADE8 1 9 9 . 4 4 8 1 . 2 9 1 4 7 . 1 1 1 0 2 . 2 8 2 4 . 5 2 4 4 . 6 2
DECADE9 3 2 9 . 3 6 1 6 6 . 2 6 2 5 9 . 7 3 2 0 0 . 1 4 9 6 . 7 5 1 3 9 . 9 6
DECADE10 1 6 4 . 4 6 1 . 1 9 9 2 . 8 2 3 1 . 6 8 - 7 3 . 9 6 - 2 0 . 1 0
MDECADE2 1 5 2 . 2 9 8 6 . 4 8 1 2 3 . 1 7 9 8 . 2 5 5 5 . 0 5 6 1 .0 7
MDECADE3 1 3 2 . 7 1 5 6 . 0 5 9 8 . 3 5 6 8 . 9 3 1 7 . 9 1 2 6 . 5 6
MDECADE4 1 2 8 . 1 6 3 7 . 2 2 8 7 . 5 2 5 2 . 7 2 - 7 . 6 4 8 . 1 9
MDECADE5 1 3 2 . 8 9 3 8 . 2 9 9 0 . 9 5 5 5 . 0 7 - 7 . 1 1 6 . 5 8
MDECADE6 1 3 7 . 5 8 3 4 . 8 8 9 1 . 9 8 5 2 . 9 4 - 1 4 . 7 6 5 . 1 4
MDECADE7 1 7 6 . 2 7 6 4 . 8 1 1 2 7 . 2 9 8 5 . 3 9 1 2 . 8 3 3 3 . 0 5
MDECADE8 2 0 0 . 1 5 8 0 . 3 0 1 4 7 . 1 8 1 0 1 . 8 0 2 3 . 0 5 4 3 . 7 9
MDECADE9 3 4 0 . 8 9 1 8 1 . 2 1 2 7 3 . 3 5 2 1 5 . 5 5 1 1 5 . 2 8 1 5 7 . 2 8
MDECADE10 1 6 4 . 4 6 1 . 1 9 9 2 . 8 2 3 1 . 6 8 - 7 3 . 9 6 - 2 0 . 1 0
FDECADE2 8 1 . 7 6 0 . 3 2 4 3 . 67 1 0 . 9 5 - 4 5 . 9 6 - 4 0 . 5 7
FDECADE3 1 3 9 . 9 0 6 8 . 0 7 1 0 7 . 3 5 7 9 . 4 7 3 1 . 0 8 4 3 . 7 2
FDECADE4 1 2 8 . 4 5 5 4 . 6 1 9 5 . 1 2 6 6 . 5 7 1 7 . 0 2 3 2 . 5 5
FDECADE5 1 3 6 . 7 8 5 1 . 6 7 9 8 . 7 6 6 6 . 1 8 9 . 6 6 2 4 . 7 4
FDECADE6 1 4 3 . 1 3 5 3 . 1 8 1 0 2 . 6 7 6 7 . 9 9 7 . 7 8 2 4 . 2 9
FDECADE7 1 5 5 . 9 8 5 6 . 4 6 1 1 0 . 9 8 7 2 . 4 1 5 . 4 5 2 2 . 6 4
FDECADE8 1 9 3 . 7 4 8 9 . 2 1 1 4 6 . 5 6 1 0 6 . 1 8 3 6 . 2 1 5 2 . 4 7
FDECADE9 2 7 1 . 7 4 9 1 . 5 0 1 9 1 . 6 6 1 2 3 . 0 7 4 . 1 1 5 2 . 4 2
1 5 7
S l o p e (b )
(WITH SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 4 1 61 6 9 7 3
ALL SUBS 9 3 . 5 9 9 3 . 5 9 1 0 1 . 7 9 1 0 8 . 5 0 1 1 9 . 6 1 1 1 5 . 6 5
MALES 9 5 . 6 0 9 5 . 6 0 1 0 3 . 9 4 1 1 0 . 7 6 1 2 2 . 0 6 1 1 8 . 1 7
FEMALES 8 5 . 8 3 8 5 . 8 3 9 3 . 4 8 9 9 . 7 5 1 1 0 . 1 4 1 0 5 . 9 0
DECADE2 6 7 . 5 9 6 7 . 5 9 7 3 . 5 2 7 8 . 3 9 8 6 . 4 4 8 3 . 7 9
DECADE3 7 5 . 7 3 7 5 . 7 3 8 2 . 4 5 8 7 . 9 5 9 7 . 0 5 9 3 . 9 4
DECADE4 8 7 . 7 3 8 7 . 7 3 9 5 . 4 7 1 0 1 . 8 2 1 1 2 . 3 2 1 0 8 . 2 8
DECADES 9 3 . 1 3 9 3 . 1 3 1 0 1 . 2 5 1 0 7 . 9 0 1 1 8 . 9 0 1 1 5 . 2 3
DECADE6 9 8 . 6 1 9 8 . 61 1 0 7 . 2 7 1 1 4 . 3 6 1 2 6 . 0 9 1 2 1 . 7 0
DECADE7 1 0 8 . 5 4 1 0 8 . 5 4 1 1 7 . 9 7 1 2 5 . 6 8 1 3 8 . 4 4 1 3 3 . 7 3
DECADE8 1 1 8 . 1 5 1 1 8 . 1 5 1 2 8 . 4 3 1 3 6 . 8 5 1 5 0 . 8 0 1 4 6 . 0 8
DECADE9 1 6 3 . 1 1 1 6 3 . 1 1 1 7 6 . 5 8 1 8 7 . 6 2 2 0 5 . 9 3 1 9 6 . 4 3
DECADE10 1 6 3 . 2 7 1 6 3 . 2 7 1 7 7 . 2 9 1 8 8 . 7 2 2 0 7 . 5 5 1 9 7 . 0 7
MDECADE2 6 5 ..8 0 6 5 ..8 0 7 1 ,.5 2 7 6 ..2 0 8 3 ..9 4 8 1 .,3 5
MDECADE3 7 6 ..6 6 7 6 .. 6 6 8 3 ..4 4 8 9 .,0 0 9 8 ,.1 8 9 5 ..2 4
MDECADE4 9 0 ..9 4 9 0 ,.9 4 9 8 ..9 6 105.,52 116..37 112,.41
MDECADE5 9 4 ..6 0 9 4 ..6 0 102..84 109.,58 120,.73 117..11
MDECADE6 102..70 102..70 I l l , .67 11 9 ..01 131,.16 126..66
MDECADE7 111.,46 1 1 1 ..4 6 121..06 12 8 .,90 141..87 137,.11
MDECADE8 119.,85 119,.85 130,.25 13 8 ..77 15 2 ..89 148,.14
MDECADE9 159.,68 159.. 68 172..70 18 3 ..37 20 1 ..06 191,. 66
MDECADE10 163..27 163..27 17 7 .,29 18 8 .,72 207..55 197..07
FDECADE2 8 1 . 4 4 8 1 . 4 4 8 9 . 0 7 9 5 . 3 5 1 0 5 . 7 6 1 0 2 . 8 7
FDECADE3 7 1 . 8 3 7 1 . 8 3 7 8 . 2 8 8 3 . 5 7 9 2 . 3 2 8 8 . 4 8
FDECADE4 7 3 . 8 5 7 3 . 8 5 8 0 . 4 4 8 5 . 8 4 9 4 . 7 9 9 0 . 4 3
FDECADE5 8 5 . 1 1 8 5 . 1 1 9 2 . 6 1 9 8 . 7 5 1 0 8 . 9 2 1 0 5 . 0 2
FDECADE6 8 9 . 9 5 8 9 . 9 5 9 7 . 9 4 1 0 4 . 5 0 1 1 5 . 3 6 1 1 1 . 1 5
FDECADE7 9 9 . 5 1 9 9 . 5 1 1 0 8 . 4 2 1 1 5 . 7 3 1 2 7 . 8 3 1 2 3 . 2 6
FDECADE8 1 0 4 . 5 2 1 0 4 . 5 2 1 1 3 . 8 6 1 2 1 . 5 0 1 3 4 . 1 2 1 2 9 . 4 1
FDECADE9 1 8 0 . 2 4 1 8 0 . 2 4 1 9 5 . 9 9 2 0 8 . 8 9 2 3 0 . 2 6 2 2 0 . 7 7
158
Coefficient of Determination(r^)
(WITH SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 4 1 61 6 9 7 3
ALL SUBS 0 . 9 6 0 3 1 0 . 9 6 0 3 1 0 . 9 7 5 5 2 0 . 9 8 3 8 4 0 . 9 9 1 5 7 0 . 9 8 6 9 0
MALES 0 . 9 6 2 1 7 0 . 9 6 2 1 7 0 . 9 7 6 7 6 0 . 9 8 4 5 9 0 . 9 9 1 5 9 0 . 9 8 8 5 3
FEMALES 0 . 9 4 5 3 8 0 . 9 4 5 3 8 0 . 9 6 3 1 1 0 . 9 7 3 4 2 0 . 9 8 4 2 4 0 . 9 7 2 2 7
DECADE2 0 . 9 5 6 9 3 0 . 9 5 6 9 3 0 . 9 7 2 4 6 0 . 9 8 1 0 7 0 . 9 8 9 3 1 0 . 9 7 9 9 5
DECADE3 0 . 9 5 2 8 8 0 . 9 5 2 8 8 0 . 9 6 9 8 9 0 . 9 7 9 5 6 0 . 9 8 9 2 7 0 . 9 7 9 2 2
DECADE4 0 . 9 5 5 6 8 0 . 9 5 5 6 8 0 . 9 7 2 0 1 0 . 9 8 1 1 9 0 . 9 9 0 2 0 0 . 9 8 4 2 0
DECADES 0 . 9 6 0 5 0 0 . 9 6 0 5 0 0 . 9 7 5 0 7 0 . 9 8 2 8 6 0 . 9 8 9 7 2 0 . 9 8 7 3 6
DECADE6 0 .9 5 7 8 4 0 . 9 5 7 8 4 0 . 9 7 3 2 9 0 . 9 8 1 8 4 0 . 9 9 0 0 2 0 . 9 8 6 2 1
DECADE7 0 . 9 6 4 8 3 0 . 9 6 4 8 3 0 . 9 7 8 7 1 0 . 9 8 5 9 9 0 . 9 9 2 1 5 0 . 9 8 9 4 3
DECADE8 0 . 9 5 9 6 5 0 . 9 5 9 6 5 0 . 9 7 3 7 6 0 . 9 8 1 3 8 0 . 9 8 8 3 3 0 . 9 8 4 9 2
DECADE9 0 . 9 5 3 8 6 0 . 9 5 3 8 6 0 . 9 6 0 1 1 0 . 9 6 2 0 8 0 . 9 6 1 1 8 0 . 9 5 7 3 3
DECADE1 0 0 . 9 2 2 2 2 0 . 9 2 2 2 2 0 . 9 3 3 8 4 0 . 9 3 9 2 0 0 . 9 4 2 1 3 0 . 9 4 1 4 9
MDECADE2 0 . 9 6 2 1 3 0 . 9 6 2 1 3 0 . 9 7 6 0 4 0 . 9 8 3 4 0 0 . 9 8 9 7 6 0 . 9 8 1 3 5
MDECADE3 0 . 9 5 5 1 7 0 . 9 5 5 1 7 0 . 9 7 1 7 8 0 . 9 8 1 1 5 0 . 9 9 0 3 8 0 . 9 8 1 8 9
MDECADE4 0 . 9 5 5 2 2 0 . 9 5 5 2 2 0 . 9 7 1 2 0 0 . 9 8 0 1 1 0 . 9 8 8 7 5 0 . 9 8 4 1 4
MDECADE5 0 . 9 5 8 8 2 0 . 9 5 8 8 2 0 . 9 7 3 1 4 0 . 9 8 0 7 1 0 . 9 8 7 2 4 0 . 9 8 6 3 9
MDECADE6 0 . 9 6 1 2 8 0 . 9 6 1 2 8 0 . 9 7 5 9 4 0 . 9 8 3 8 7 0 . 9 9 1 0 8 0 . 9 8 8 5 9
MDECADE7 0 . 9 6 9 0 9 0 . 9 6 9 0 9 0 . 9 8 1 6 3 0 . 9 8 7 8 6 0 . 9 9 2 4 1 0 . 9 9 2 2 5
MDECADE8 0 . 9 6 0 9 5 0 . 9 6 0 9 5 0 . 9 7 4 6 2 0 . 9 8 1 9 5 0 . 9 8 8 5 2 0 . 9 8 5 8 1
MDECADE9 0 . 9 5 7 9 6 0 . 9 5 7 9 6 0 . 9 6 2 3 3 0 . 9 6 2 9 4 0 . 9 6 0 1 6 0 . 9 5 7 7 4
MDECADE10 0 .9 2 2 2 2 0 . 9 2 2 2 2 0 . 9 3 3 8 4 0 . 9 3 9 2 0 0 . 9 4 2 1 3 0 . 9 4 1 4 9
FDECADE2 0 . 8 9 7 9 8 0 . 8 9 7 9 8 0 . 9 2 2 5 7 0 . 9 3 8 3 0 0 . 9 5 7 4 3 0 . 9 4 3 9 4
FDECADE3 0 . 9 3 7 5 8 0 . 9 3 7 5 8 0 . 9 5 6 2 6 0 . 9 6 7 2 3 0 . 9 7 8 9 3 0 . 9 6 1 8 6
FDECADE4 0 . 9 4 9 0 0 0 . 9 4 9 0 0 0 . 9 6 7 0 3 0 . 9 7 7 5 2 0 . 9 8 8 4 7 0 . 9 7 3 2 8
FDECADE5 0 .9 5 7 9 1 0 . 9 5 7 9 1 0 . 9 7 3 8 6 0 . 9 8 2 8 3 0 . 9 9 1 6 5 0 . 9 8 0 1 9
FDECADE6 0 . 9 4 3 9 0 0 . 9 4 3 9 0 0 . 9 6 1 1 0 0 . 9 7 1 0 8 0 . 9 8 1 5 3 0 . 9 7 3 8 2
FDECADE7 0 . 9 3 7 8 3 0 . 9 3 7 8 3 0 . 9 5 6 0 3 0 . 9 6 6 7 5 0 . 9 7 8 2 6 0 . 9 6 7 2 4
FDECADE8 0 . 9 3 6 1 3 0 . 9 3 6 1 3 0 . 9 5 3 9 3 0 . 9 6 4 1 0 0 . 9 7 4 3 2 0 . 9 6 2 7 9
FDECADE9 0 . 9 1 5 1 3 0 . 9 1 5 1 3 0 . 9 2 9 2 4 0 . 9 3 6 9 3 0 . 9 4 4 0 9 0 . 9 4 0 3 3
1 5 9
Standard Error of Estimate(Se)
(WITH SW INCLUDED)
FORMULA FORMULA FORMULA FORMULA FORMULA FORMULA
GROUP 1 2 1 4 1 6 1 6 9 7 3
ALL SUBS 4 0 . 3 7 4 0 . 3 7 3 1 . 7 1 2 5 . 7 6 1 8 . 6 0 2 3 . 2 0
MALES 4 0 . 2 2 4 0 . 2 2 3 1 . 5 3 2 5 . 6 7 1 8 . 9 7 2 2 . 1 5
FEMALES 4 3 . 7 8 4 3 . 7 8 3 5 . 9 8 3 0 . 5 4 2 3 . 5 2 3 1 . 1 9
DECADE2 3 0 . 4 3 3 0 . 4 3 2 4 . 3 3 2 0 . 1 7 1 5 . 1 6 2 0 . 7 6
DECADE3 3 5 . 7 4 3 5 . 7 4 2 8 . 5 7 2 3 . 5 3 1 7 . 0 6 2 3 . 7 3
DECADE4 4 0 . 0 9 4 0 . 0 9 3 1 . 8 6 2 6 . 1 2 1 8 . 8 5 2 3 . 9 4
DECADES 4 0 . 0 8 4 0 . 0 8 3 1 . 8 4 2 6 . 4 0 2 0 . 4 4 2 2 . 6 7
DECADE6 4 3 . 9 0 4 3 . 9 0 3 4 . 9 4 2 8 . 8 1 2 1 . 3 6 2 5 . 1 0
DECADE7 4 3 . 9 7 4 3 . 9 7 3 4 . 2 1 2 7 . 7 6 2 0 . 7 8 2 4 . 1 1
DECADE8 5 1 . 4 1 5 1 . 4 1 4 1 . 4 6 3 4 . 9 2 2 7 . 6 5 3 1 . 4 3
DECADE9 7 6 . 1 2 7 6 . 1 2 7 0 . 7 8 6 9 . 0 1 6 9 . 8 2 7 3 . 2 0
DECADE10 1 0 0 . 6 2 1 0 0 . 6 2 9 2 . 7 9 8 8 . 9 6 8 6 . 7 9 8 7 . 2 6
MDECADE2 2 7 . 7 0 2 7 . 7 0 2 2 . 0 3 1 8 . 3 4 1 4 . 4 1 1 9 . 4 4
MDECADE3 3 5 . 2 4 3 5 . 2 4 2 7 . 9 6 2 2 . 8 5 1 6 . 3 2 2 2 . 4 0
MDECADE4 4 1 . 7 8 4 1 . 7 8 3 3 . 5 1 2 7 . 8 4 2 0 . 9 4 2 4 . 8 6
MDECADE5 4 1 . 6 0 4 1 . 60 3 3 . 6 0 2 8 . 4 7 2 3 . 1 6 2 3 . 9 2
MDECADE6 4 3 . 7 4 4 3 . 7 4 3 4 . 4 8 2 8 . 2 3 2 1 . 0 0 2 3 . 7 5
MDECADE7 4 2 . 2 4 4 2 . 2 4 3 2 . 5 6 2 6 . 4 7 2 0 . 9 3 2 1 . 1 5
MDECADE8 5 1 . 2 7 5 1 . 2 7 4 1 . 3 3 3 4 . 8 6 2 7 . 8 0 3 0 . 9 0
MDECADE9 7 0 . 9 8 7 0 . 9 8 6 7 . 1 9 6 6 . 6 5 6 9 . 1 0 7 1 . 1 7
MDECADE10 1 0 0 . 6 2 1 0 0 . 6 2 9 2 . 7 9 8 8 . 9 6 8 6 . 7 9 8 7 . 2 6
FDECADE2 5 8 . 2 5 5 8 . 2 5 5 0 . 7 4 4 5 . 3 0 3 7 . 6 2 4 3 . 1 8
FDECADE3 3 9 . 3 3 3 9 . 3 3 3 2 . 9 2 2 8 . 4 9 2 2 . 8 5 3 0 . 7 4
FDECADE4 3 6 . 3 3 3 6 . 3 3 2 9 . 2 1 2 4 . 1 2 1 7 . 2 7 2 6 . 2 9
FDECADES 3 7 . 8 6 3 7 . 8 6 2 9 . 8 3 2 4 . 1 8 1 6 . 8 6 2 5 . 9 7
FDECADE6 4 6 . 5 3 4 6 . 5 3 3 8 . 7 5 3 3 . 4 1 2 6 . 7 0 3 1 . 7 9
FDECADE7 5 4 . 3 7 5 4 . 3 7 4 5 . 7 3 3 9 . 7 6 3 2 . 1 5 3 9 . 4 7
FDECADE8 5 7 . 9 4 5 7 . 9 4 4 9 . 2 1 4 3 . 4 4 3 6 . 7 3 4 4 . 2 2
FDECADE9 1 1 6 . 4 8 1 1 6 . 4 8 1 0 6 . 3 6 1 0 0 . 4 1 9 4 . 5 4 9 7 . 6 6
160
A P P E N D IX L
M e a n s o f E a c h B a s ic M e a s u r e f o r E a c h G r o u p
MEASURES COMMON TO EVERY GROUP
TARGET A W D Z
SW 34 32 66 2
SI 44.5 11 55.5 33.5
SN 48 4 52 44
MW 126 32 158 94
MI 136.5 11 147.5 125.5
MN 140 4 144 136
LH 386 32 418 354
LI 396.5 11 407.5 385.5
LH 400 4 404 396
ALL
SUBJECTS N
MEAN
AGE A' D' WL WR W' MT
SW 1318 50.2 33.68323 51.91047 18.55387 17.90061 18.22724 217.7891
SI 1318 50.2 46.54818 59.33839 13.21624 12.36419 12.79021 322.8164
SN 1318 50.2 49.53187 57.75114 8.32549 8.11305 8.21927 479,2944
MW 1318 50.2 124.9879 150.5326 25.71169 25.37785 25.54477 297.9651
HI 1318 50.2 136.4473 152.3847 15.60926 16.26555 15.93741 440.5448
MN 1318 50.2 139.5565 149.2382 9.35205 10.01138 9.68172 611.6904
LW 1318 50.2 379.0231 410.2041 29.84294 32.51897 31.18096 460.3794
LI 1318 50.2 394.096 411.6457 16.22534 18.87405 17.5497 628.6343
IN 1318 50.2 397.92 408.865 9.8824 12.00759 10.94499 825.8968
MALES N
MEAN
AGE A' D' WL HR W' MT
SW 1047 49.9 33.6638 52.0745 18.80325 18.01815 18.4107 217.8166
SI 1047 49.9 46.41929 59.06017 13.00669 12.27507 12.64088 328.4928
SN 1047 49.9 49.61795 57.62369 8.09742 7.91404 8.00573 493.467
MW 1047 49.9 124.9279 150.5883 25.78892 25.532 25.66046 300.808
MI 1047 49.9 136.4255 152.1423 15.30755 16.12607 15.71681 448.4413
MN 1047 49.9 139.7139 148.9503 8.94174 9.53104 9.23639 626.2579
LH 1047 49.9 378.4246 409.6581 29.85291 32.61414 31.23352 463.3925
LI 1047 49.9 393.8458 411.0945 15.90735 18.59026 17.24881 637.8453
LN 1047 49.9 398.0521 408.4795 9.45845 11.39637 10.42741 837.6963
FEMALES N
MEAN
AGE A' D' WL WR W1 MT
SW 271 51.6 33.7583 51.27675 17.59041 17.4465 17.51845 217.6827
SI 271 51.6 47.04613 60.41328 14.02583 12.70849 13.36716 300.8856
SN 271 51.6 49.19926 58.24354 9.20664 8.88192 9.04428 424.5388
MW 271 51.6 125.2196 150.3173 25.41328 24.78229 25.09779 286.9815
MI 271 51.6 136.5314 153.321 16.77491 16.80443 16.78967 410.0369
MN 271 51.6 138.9483 150.3506 10.93727 11.86716 11.40221 555.4096
LW 271 51.6 381.3358 412.3137 29.80443 32.15129 30.97786 448.738
LI 271 51.6 395.0627 413.7749 17.45387 19.97048 18.71218 593.048
LN 271 51.6 397.4096 410.3542 11.5203 14.369 12.94465 780.3099
DECADE2 N
MEAN
AGE A' D' WL WR W MT
SW 35 21.7 34.18571 54.42857 19.97143 20.51429 20.24286 197.3143
SI 35 21.7 48 64.82858 17.37143 16.28572 16.82857 275.8286
SN 35 21.7 49.05714 60.94286 10.94286 12.82857 11.88571 371.8286
MW 35 21.7 125.2143 154.2571 29.37143 28.71428 29.04286 253.2
MI 35 21.7 135.9429 158.6 23.62857 21.68571 22.65714 355.2
MN 35 21.7 140.1143 154.6857 14.51429 14.62857 14.57143 476.2286
LW 35 21.7 371.9572 414.3143 43.14286 41.57143 42.35714 384.6857
LI 35 21.7 391.4429 420.4 28.31429 29.6 28.95714 497.8286
LN 35 21.7 396.9572 416.7143 19.62857 19.88571 19.75714 637.7143
1 6 1
MEAN
DECADE3 N AGE A' D'
SW 244 29.9 33.94262 53.28279
SI 244 29.9 47.00203 61.81967
SN 244 29.9 48.93443 59.55738
MW 244 29.9 125.3668 153.9303
HI 244 29.9 135.9836 155.1025
MN 244 29.9 139.1291 152.2582
LW 244 29.9 376.5861 414.0779
LI 244 29.9 393.3607 415.6803
LN 244 29.9 396.5451 411.6639
DECADE4 N
MEAN
AGE A' D’
SW 250 39.6 33.212 50.936
SI 250 39.6 46.576 59.3
SN 250 39.6 48.934 56.948
MW 250 39.6 125.06 150.528
HI 250 39.6 136.328 152.86
MN 250 39.6 139.806 149.444
LW 250 39.6 378.56 410.7
LI 250 39.6 394.944 412.5
LN 250 39.6 397.63 408.748
MEAN
DECADE5 N AGE A’ D'
SW 271 49.7 33.73616 51.48339
SI 271 49.7 47.00922 59.32472
SN 271 49.7 50.69373 58.43911
MW 271 49.7 126.2103 151.4207
MI 271 49.7 137.7214 153.1587
MN 271 49.7 139.8875 148.738
LW 271 49.7 378.7528 408.7306
LI 271 49.7 393.3303 410.0443
LN 271 49.7 396.5996 406.6605
MEAN
DECADE6 N AGE A' D'
SW 212 59.5 34.03066 51.45283
SI 212 59.5 46.29245 58.03773
SN 212 59.5 48.59434 55.68868
MW 212 59.5 124.25 148.5849
HI 212 59.5 135.908 150.1604
MN 212 59.5 138.8066 147.0472
LW 212 59.5 381.8773 409.6981
LI 212 59.5 395.7618 411.2028
LN 212 59.5 399.559 408.8207
MEAN
DECADE7 N AGE A1 D'
SW 217 69.6 33.53917 51.8894
SI 217 69.6 45.91014 57.6129
SN 217 69.6 50.98848 58.18894
MW 217 69.6 123.9977 147.553
MI 217 69.6 136.4516 150.0691
MN 217 69.6 139.8548 147.8249
LW 217 69.6 381.4931 408.9355
LI 217 69.6 394.9171 409.4101
LN 217 69.6 399 407.4562
WL WR W' MT
19.70492 18.97541 19.34016 198.7623
15.51639 14.11885 14.81762 274.4016
10.7582 10.48771 10.62295 390.0246
29.02459 28.10246 28,56352 257.6803
18.95082 19.28688 19.11885 372.5164
13.06148 13.19672 13.1291 504.4672
36.47951 38.5041 37.4918 396.9344
20.84836 23.79098 22.31967 534.3934
13.7582 16.47951 15.11885 688.7705
WL WR W' MT
18.252 17.196 17.724 200.328
13,14 12.308 12.724 293.088
8.052 7.976 8.014 441.768
25,76 25.176 25.468 271.68
16.14 16.924 16.532 404.736
9.208 10.068 9.638 572.688
30.756 33.524 32.14 418.416
16.168 18.944 17.556 573.648
10.048 12.188 11.118 770.64
WL WR W1 MT
17.99262 17.50184 17.74723 204.6863
12.70849 11.92251 12.3155 305.1144
8.02952 7.46125 7.74539 482.9225
25.39483 25.02583 25.21033 286.5388
15.00369 15.87085 15.43727 434.1033
8.38007 9.32103 8.85055 606.6863
28.53875 31.41698 29.97786 432.8192
15.20664 18.2214 16.71402 606.1771
9.05904 11.06273 10.06089 807.2767
WL WR W' MT
17.78773 17.0566 17.42217 216.1698
12.23585 11.25472 11.74528 329.8585
7.25 6.93868 7.09434 492.3396
24.28302 24.38679 24.33491 300.6793
13.98113 14.52359 14.25236 449.8585
7.99057 8.49057 8.24057 628.1321
26.24057 29.40094 27.82076 468.3962
14.04245 16.83962 15.44104 647.2642
8.08019 10.4434 9.26179 861.0283
WL WR W' MT
18.52074 18.17972 18.35023 250.5346
11.92627 11.47926 11.70276 382.2304
7.30876 7.09217 7.20046 558.1659
23.5576 23.553 23.5553 344.4332
13.05991 14.17512 13.61751 512.8755
7.58986 8.35023 7.97005 713.2258
26.18894 28.69585 27.4424 547.1613
13.35945 15.62673 14.49309 735.8986
7.58986 9.32258 8.45622 953.0046
162
DECADES N
MEAN
AGE A' D' WL WR W' MT
SW SI 78.3 33.78395 53.01234 19.76543 18.69136 19.2284 283.5555
SI 81 78.3 45.4321 58.02469 12.65432 12.53086 12.59259 433.7778
SN 81 78.3 48.25928 55.67901 7.32099 7.51852 7.41975 616.2963
MW 81 78.3 123.9136 148.9136 24.88889 25.11111 25 399.4074
MI 81 78.3 135.6852 149.8519 13.95062 14.38272 14.16667 560.5185
MN 81 78.3 139.8395 148.5309 8.2716 9.11111 8.69136 772.2963
LW 81 78.3 377.9691 405.679 25.7037 29.71605 27.70988 605.4074
LI 81 78.3 390.9074 406.0988 14.60494 15.77778 15.19136 826.4445
LN 81 78.3 400.5062 408.9259 7.45679 9.38272 8.41975 1058.667
DECADE9 N
MEAN
AGE A' D' WL WR W1 MT
SW 6 90.2 31.16667 46.33333 14.33333 16 15.16667 393
SI 6 90.2 45.75 56.66667 11.66667 10.16667 10.91667 646
SN 6 90.2 48.25 54.5 6.16667 6.33333 6.25 839
MW 6 90.2 126.5833 149.8333 21.5 25 23.25 647
MI 6 90.2 136.25 149.6667 11.16667 15.66667 13.41667 860
MN 6 90.2 140.5 148 6.16667 8.83333 7.5 1065
LW 6 90.2 377.5 404.5 23.16667 30.83333 27 1014
LI 6 90.2 394.4167 408 11.5 15.66667 13.58333 1189
LN 6 90.2 400.0833 408.1667 6.83333 9.33333 8.08333 1504
MEAN
DECADE10 N AGE A' D' WL WR W' MT
SW 2 98 27.25 43 15.5 16 15.75 285
SI 2 98 43.75 53.5 9.5 10 9.75 510
SN 2 98 44.75 53.5 11.5 6 8.75 882
MW 2 98 124.5 148.5 25.5 22.5 24 345
MI 2 98 132.25 145.5 13 13.5 13.25 630
MN 2 98 138.75 145.5 5 8.5 6.75 993
LW 2 98 371.25 395 16 31.5 23.75 705
LI 2 98 390.5 401.5 8 14 11 1026
LN 2 98 395.5 400.5 4.5 5.5 5 1302
MEAN
MDECADE2 N AGE A’ D' WL WR W' MT
SW 31 21.5 33.77419 54.12903 20.41936 20.29032 20.35484 199.9355
SI 31 21.5 47.91935 64.83871 17.51613 16.32258 16.91936 282.9677
SN 31 21.5 48.70968 61.09678 11.29032 13.48387 12.3871 373.3548
MW 31 21.5 124.4355 153.7419 29.77419 28.83871 29.30645 257.4193
MI 31 21.5 135.7097 159 24.45161 22.12903 23.29032 358.4516
MN 31 21.5 139.9194 154.6774 14.70968 14.80645 14.75806 474.9677
LW 31 21.5 369.9355 413.0968 43.51613 42.80645 43.16129 390.3871
LI 31 21.5 391.2258 420.2581 28.29032 29.77419 29.03226 501.2903
LN 31 21.5 396.6452 416.4516 19.54839 20.06452 19.80645 626.7097
MDECADE3 N
MEAN
AGE A' D1 WL WR W< MT
SW 197 29.7 34.2868 53.83249 20.09645 18.99492 19.54568 196.8731
SI 197 29.7 46.83249 61.60914 15.44162 14.11168 14.77665 276.3046
SN 197 29.7 48.79696 59.50761 10.84264 10.57868 10.71066 395.5736
MW 197 29.7 125.6117 154.5533 29.26396 28.61929 28.94162 257.3909
MI 197 29.7 135.8858 154.9492 18.71066 19.41624 19.06345 373.2487
MN 197 29.7 139.4949 152.4264 12.88832 12.97462 12.93147 510.3655
LW 197 29.7 375.8274 413.7107 36.71574 39.05076 37.88325 395.3604
LI 197 29.7 393.1396 415.4112 20.74619 23.79696 22.27157 538.2031
LN 197 29.7 395.8959 411.0203 13.76142 16.48731 15.12437 691.7969
163
MEAN
MDECADE4 N AGE A1 D'
SW 203 39.6 33.36424 51.31527
SI 203 39.6 46.50492 59.02956
SN 203 39.6 48.86207 56.42857
MW 203 39.6 124.9532 150.1478
HI 203 39.6 136.2537 152.2414
MN 203 39.6 139.7759 148.7389
LW 203 39.6 378.367 409.9901
LI 203 39.6 394.9261 412.0345
LN 203 39.6 397.3448 407.4975
MEAN
MDECADES N AGE A' D'
SW 229 49.6 33.77729 51.65502
SI 229 49.6 46.99345 59.22707
SN 229 49.6 50.97161 58.49782
MW 229 49.6 126.4039 151,7467
HI 229 49.6 137.8297 153.1834
MN 229 49.6 139.7249 148.2838
LW 229 49.6 378.2249 408.4585
LI 229 49.6 392.9651 409.4149
LN 229 49.6 398.5087 408,2271
MEAN
MDECADES N AGE A1 D'
SW 144 59.5 33.72222 51.55556
SI 144 59.5 45.9375 57.31944
SN 144 59.5 48.22569 54.85417
MW 144 59.5 123.6528 148.2847
MI 144 59.5 135.6667 149.5556
MN 144 59.5 139.6076 146.9306
LW 144 59.5 381.691 408.993
LI 144 59.5 395.4861 410.3611
LN 144 59.5 399.6424 407.757
MEAN
MDECADE7 N AGE A' D'
SW 164 69.6 33.08537 51.42683
SI 164 69.6 45.72256 57.0061
SN 164 69.6 51.76829 58.5
MW 164 69.6 123.6281 147.0366
MI 164 69.6 136.5244 149.5366
MN 164 69.6 139.8567 147.0244
LW 164 69.6 381.061 408.5732
LX 164 69.6 395.1281 408.7439
LN 164 69.6 398.6403 406.1768
MDECADES N
MEAN
AGE A' D'
SW 72 78.3 33.90278 53.11111
SI 72 78.3 45.23611 57.56944
SN 72 78.3 48.19444 55.40278
MW 72 78.3 123.8472 148.6111
MI 72 78.3 135.6806 149.3333
MN 72 78.3 139.8889 148.2361
LW 72 78.3 377.8264 404.5833
LI 72 78.3 390.5972 405.4028
LN 72 78.3 400.5208 408.5278
WL WR W' MT
18.46798 17.39409 17.93103 201.7832
12.94089 12.10837 12.52463 300.3251
7.62069 7.51232 7.5665 459.5764
25.62069 24.76847 25.19458 275.734
15.41379 16.56158 15.98769 414.3547
8.5468 9.37931 8.96305 591.5764
30.21675 33.02956 31.62315 426
15.62562 18.59113 17.10837 585.8423
9.07389 11.23153 10.15271 793.6552
WL HR W' MT
18.15284 17.60262 17.87773 204.786
12.57205 11.8952 12.23362 306.6026
7.78166 7.27074 7.5262 495.4323
25.51092 25.17467 25.34279 287.2402
14.87336 15.83406 15.35371 438.8908
8.11354 9.00437 8.55895 615.3537
28.65502 31.81223 30.23362 432.1048
15.04367 17.8559 16.44978 611.4498
8.71616 10.72052 9.71834 815.8428
WL WR W' MT
18.29861 17.36806 17.83333 214.7917
11.60417 11.15972 11.38194 336.75
6.82639 6.43056 6.62847 512.125
24.46528 24.79861 24.63194 305.2083
13.59028 14.1875 13.88889 462.9583
7.20833 7.4375 7.32292 656.1667
25.41667 29.1875 27.30208 472.8333
13.42361 16.32639 14.875 664.9583
7.25694 8.97222 8.11458 882.2083
WL WR W' MT
18.4878 18.19512 18.34146 252.439
11.4878 11.07927 11.28354 397.2439
6.78659 6.67683 6.73171 583.1342
23.26829 23.54878 23.40854 350.0854
12.40244 13.62195 13.0122 530.6342
6.82317 7.5122 7.16768 740.7805
26.84756 28.17683 27.5122 556.1342
12.39024 14.84146 13.61585 754.8658
6.92683 8.14634 7.53659 969.7317
WL WR W' MI
19.81944 18.59722 19.20833 282.8333
12.36111 12.30556 12.33333 439.6667
7.09722 7.31944 7.20833 625.1667
24.55556 24.97222 24.76389 404.3333
13.48611 13.81944 13.65278 569
7.95833 8.73611 8.34722 780.5
24.54167 28.97222 26.75694 611.5
14.36111 15.25 14.80556 830.1667
7.20833 8.80556 8.00694 1073.833
16 4
MEAN
MDECADE9 N AGE
SW 5 90.2
SI 5 90.2
SN 5 90.2
MW 5 90.2
MI 5 90.2
MN 5 90.2
LW 5 90.2
LI 5 90.2
LN 5 90.2
A' D' WL
31 45 12.8
45.9 57.6 12.6
48.3 55 6.6
127.5 151.8 22.4
135.8 150.4 12
140.3 148.6 6.8
375.8 403.8 23.2
393.2 407 11.8
399.9 409.2 7.8
WR W' MT
15.2 14 390
10.8 11.7 646.8
6.8 6.7 850.8
26.2 24.3 668.4
17.2 14.6 867.6
9.8 8.3 1052.4
32.8 28 1004.4
15.8 13.8 1186.8
10.8 9.3 1484.4
MEAN
MDECADE10 N AGE A’ D1 WL WR W MT
SW 2 98 27.25 43 15.5 16 15.75 285
SI 2 98 43.75 53.5 9.5 10 9.75 510
SN 2 98 44.75 53.5 11.5 6 8.75 882
MW 2 98 124.5 148.5 25.5 22.5 24 345
MI 2 98 132.25 145.5 13 13.5 13.25 630
MN 2 98 138.75 145.5 5 8.5 6.75 993
LW 2 98 371.25 395 16 31.5 23.75 705
LI 2 98 390.5 401.5 8 14 11 1026
LN 2 98 395.5 400.5 4.5 5.5 5 1302
FDECADE2 N
MEAN
AGE A' D' WL WR W' MT
SW 4 23.8 37.375 56.75 16.5 22.25 19.375 177
SI 4 23.8 48.625 64.75 16.25 16 16.125 220.5
SN 4 23.8 51.75 59.75 8.25 7.75 8 360
MW 4 23.8 131.25 15S.25 26.25 27.75 27 220.5
MI 4 23.8 137.75 155.5 17.25 18.25 17.75 330
MN 4 23.8 141.625 154.75 13 13.25 13.125 486
LW 4 23.8 387.625 423.75 40.25 32 36.125 340.5
LI 4 23.8 393.125 421.5 28.5 28.25 28.375 471
LN 4 23.8 399.375 418.75 20.25 18.5 19.375 723
FDECADE3 N
MEAN
AGE A’ D 1 WL WR W' MT
SW 47 30.6 32.5 50.97872 18.06383 18.89362 18.47872 206.6808
SI 47 30.6 47.71276 62.70213 15.82979 14.14894 14.98936 266.4255
SN 47 30.6 49.51064 59.76596 10.40425 10.10638 10.25532 366.766
MW 47 30.6 124.3404 151.3192 28.02128 25.93617 26.97872 258.8936
MX 47 30.6 136.3936 155.7447 19.95745 18.74468 19.35106 369.4468
MN 47 30.6 137.5957 151.5532 13.78723 14.12766 13.95745 479.7447
LW 47 30.6 379.766 415.617 35.48936 36.21276 35.85106 403.5319
LI 47 30.6 394.2872 416.8085 21.2766 23.76596 22.52128 518.4255
LN 47 30.6 399.266 414.3617 13.74468 16.44681 15.09575 676.0851
FDECADE4
SW
S I
SN
MW
MI
MN
LW
LI
LN
N
47
47
47
47
47
47
47
47
47
MEAN
AGE
39.5
39.5
39.5
39.5
39.5
39.5
39.5
39.5
39.5
A'
32.46809
46.88298
49.24468
125.5213
136,6489
139.9362
379.3936
395.0213
398.8617
D'
49.29787
60.46809
59.19149
152.1702
155.5319
152.4894
413.766
414.5107
414.1489
WL
17.31915
14
9.91489
26.3617
19.2766
12.06383
33.08511
18.51064
14.25532
WR
16.34043
13.17021
9.97872
26.93617
18.48936
13.04255
35.65957
20.46808
16.31915
W'
16.82979 194
13.58511 261
9.94681 364
26.64894 254
18.88298 363
12.55319 491
34.37234 385
19.48936 520
15.28723 671
MT
.0426
.8298
.8511
,1702
.1915
.1064
.6596
9787
2341
1 65
FDECADE5 »
MEAN
AGE A' D‘ WL WR W MT
SW 42 50 33.51191 50.54762 17.11905 16.95238 17.03572 204.1429
SI 42 50 47.09524 59.85714 13.45238 12.07143 12.7619 297
SN 42 50 49.17857 58.11905 9.38095 8.5 8.94048 414.7143
MW 42 50 125.1548 149.6429 24.76191 24.21428 24.48809 282.7143
MI 42 50 137.131 153.0238 15.71429 16.07143 15.89286 408
MN 42 50 140.7738 151.2143 9.83333 11.04762 10.44048 559.4286
LW 42 50 381.631 410.2143 27.90476 29.26191 28.58333 436.7143
LI 42 50 395.3214 413.4762 16.09524 20.21428 18.15476 577.4286
LN 42 50 386.1905 398.119 10.92857 12.92857 11.92857 760.5714
FDECADE6 N
MEAN
AGE A* D' WL WR W ‘ MT
SW 68 59.4 34.68382 51.23529 16.70588 16.39706 16.55147 219.0882
SI 68 59.4 47.04412 59.55882 13.57353 11.45588 12.51471 315.2647
SN 68 59.4 49.375 57.45588 8.14706 8.01471 8.08088 450.4412
MW 68 59.4 125.5147 149.2206 23.89706 23.51471 23.70588 291.0882
MI 68 59.4 136.4191 151.4412 14.80882 15.23529 15.02206 422.1176
MN 68 59.4 137.1103 147.2941 9.64706 10.72059 10.18382 568.7647
LW 68 59.4 382.2721 411.1912 27.98529 29.85294 28.91912 459
LI 68 59.4 396.3456 412.9853 15.35294 17.92647 16.63971 609.7941
LN 68 59.4 399.3824 411.0735 9.82353 13.55882 11.69118 816.1765
FDECADE7 N
MEAN
AGE A' D' WL WR W' MT
SW S3 68.9 34.9434 53.32076 18.62264 18.13208 18.37736 244.6415
SI 53 68.9 46.49057 59.49057 13.28302 12.71698 13 335.7736
SN 53 68.9 48.57547 57.22641 8.92453 8.37736 8.65094 480.9057
MW 53 68.9 125.1415 149.1509 24.45283 23.56604 24.00943 326.9434
MI 53 68.9 136.2264 151.717 15.09434 15.88679 15.49057 457.9245
MN 53 68.9 139.8491 150.3019 9.96226 10.9434 10.45283 627.9623
LW 53 68.9 382.8302 410.0566 24.15094 30.30189 27.22642 519.3962
LI 53 68.9 394.2642 411.4717 16.35849 18.0566 17.20755 677.2075
LN 53 68.9 400.1132 411.4151 9.64151 12.96226 11.30189 901.2453
FPECADE8 H
MEAN
AGE A' D1 WL WR W> MT
SW 9 78.1 32.83333 52.22222 19.33333 19.44444 19.38889 289.3333
SI 9 78.1 47 61.66667 15 14.33333 14.66667 386.6667
SN 9 78.1 48.77778 57.88889 9.11111 9.11111 9.11111 545.3333
MW 9 78.1 124.4444 151.3333 27.55556 26.22222 26.88889 360
MI 9 78.1 135.7222 154 17.66667 18.88889 18.27778 492.6667
MN 9 78.1 139.4444 150.8889 10.7777S 12.11111 11.44444 706.6667
LW 9 78.1 379.1111 414.4445 35 35.66667 35.33333 556.6667
LI 9 78.1 393.3889 411.6667 16.55556 20 18.27778 796.6667
LN 9 78.1 400.3889 412.1111 9.44444 14 11.72222 937.3333
MEAN
FDECADE9 N AGE A1 D1 WL WR W' MT
SW 1 94 32 53 22 20 21 408
SI 1 94 45 52 7 7 7 642
SN 1 94 48 52 4 4 4 780
MW 1 94 122 140 17 19 18 540
MI 1 94 138.5 146 7 8 7.5 822
MN 1 94 141.5 145 3 4 3.5 1128
LW 1 94 386 408 23 21 22 1062
LI 1 94 400.5 413 10 15 12.5 1200
LN 1 94 401 403 2 2 2 1602
166
A P P E N D IX M
D e ta ile d D e s c r ip tiv e S ta tis tic s
ALL SUBJECTS COMBINED (N=1318)
AGE
MEAN SD MEDIAN SKEWNESS KURTOSIS
5 0 . 2 4 3 5 5 1 6 . 2 2 9 1 1 50 0 . 1 7 - 0 . 9
MT
TARGET MEAN SD
SW 2 1 7 . 7 8 9 1 6 5 . 9 6 9 1
S I 3 2 2 . 8 1 6 4 1 0 3 . 6 3 0 5
SN 4 7 9 . 2 9 4 4 1 9 1 . 6 3 2 6
MW 2 9 7 . 9 6 5 1 1 1 2 . 3 2 4 6
MI 4 4 0 . 5 4 4 8 1 6 7 . 1 4 4 7
MN 6 1 1 . 6 9 0 4 1 8 1 . 7 6 3 8
LW 4 6 0 . 3 7 9 4 1 3 6 . 5 3 7 7
LI 6 2 8 . 6 3 4 3 1 6 9 . 4 5 1 7
LN 8 2 5 . 8 9 6 8 2 4 1 . 3 8 0 5
TARGET MEAN SD
SW 1 8 . 5 5 3 8 7 5 . 9 8 3 1
S I 1 3 . 2 1 6 2 4 5 . 0 3 9 1
SN 8 . 3 2 5 4 9 4 . 9 3 1 1
MW 2 5 . 7 1 1 6 9 8 . 2 0 7 2
MI 1 5 . 6 0 9 2 6 7 . 6 7 6 5
MN 9 . 3 5 2 0 5 7 . 0 2 3
LW 2 9 . 8 4 2 9 4 1 3 . 6 4 3
LI 1 6 . 2 2 5 3 4 1 0 . 9 0 4 8
LN 9 . 8 8 2 4 1 0 . 1 6 3 6
TARGET MEAN SD
SW 1 7 . 9 0 0 6 1 5 . 8 0 5 5
S I 1 2 . 3 6 4 1 9 4 . 4 1 8 3
SN 8 . 1 1 3 0 5 5 . 0 2 5 1
MW 2 5 . 3 7 7 8 5 8 . 0 5 1 9
MI 1 6 . 2 6 5 5 5 7 . 0 7 5 3
MN 1 0 . 0 1 1 3 8 7 . 2 3 2 3
LW 3 2 . 5 1 8 9 7 1 2 . 3 6 8 5
LI 1 8 . 8 7 4 0 5 1 1 . 3 8 9 9
LN 1 2 . 0 0 7 5 9 1 1 . 3 6 0 9
MEDIAN SKEWNESS KURTOSIS
1 9 8 4 . 2 4 3 3 . 8 8
3 0 0 2 . 4 4 1 2 . 6 1
4 68 9 . 2 5 1 9 7 . 8 6
2 8 2 9 . 2 4 1 6 2 . 8 6
4 2 0 1 2 . 4 7 2 9 6 . 7 2
603 1 . 0 1 5 . 4 6
432 3 . 0 7 2 0 . 7 8
618 1 . 5 7 9 . 1 5
8 2 2 0 . 6 2 2 . 6
WL
MEDIAN SKEWNESS KURTOSIS
18 0 . 5 8 0 . 0 7
12 1 . 6 1 5 . 2
7 2 . 2 7 , 7 9
2 5 0 . 9 5 2 . 2 3
14 1 . 9 7 7 . 7 3
7 2 . 3 6
2 6 1 . 4 2 . 7
13 2 . 8 6 1 0 . 5 1
7 4 . 1 2 2 2 . 9
WR
MEDIAN SKEWNESS KURTOSIS
17 0 . 6 6 1 . 2 9
12 1 . 6 1 5 . 0 3
7 3 . 8 9 3 3 . 3 7
24 1 . 2 9 3 . 5 2
15 1 . 9 4 8 . 1 4
7 2 . 3 5 6 . 9 5
30 1 . 1 1 1 . 5 8
15 2 . 4 9 7 . 7 2
8 3 . 1 8 1 3 . 3
D'
TARGET MEAN SD MEDIAN SKEWNESS KURTOSIS
SW 5 1 . 9 1 0 4 7 8 . 0 2 4 9 52 - 0 . 4 3 1 . 2 4
S I 5 9 . 3 3 8 3 9 6 . 3 8 6 4 58 4 . 1 2 5 9 . 3 8
SN 5 7 . 7 5 1 1 4 2 2 . 5 5 2 3 55 2 3 . 7 4 5 9 5 . 9 6
MW 1 5 0 . 5 3 2 6 1 3 . 9 9 5 5 1 5 0 1 2 . 6 3 3 0 . 9 9
MI 1 5 2 . 3 8 4 7 1 2 . 7 6 3 1 50 2 1 . 5 3 6 4 3 . 2 5
MN 1 4 9 . 2 3 8 2 8 . 2 9 0 8 147 - 2 . 9 2 5 8 . 0 6
LW 4 1 0 . 2 0 4 1 2 2 . 3 8 1 4 4 1 0 - 9 . 9 1 1 3 2 . 9 1
LI 4 1 1 . 6 4 5 7 1 4 . 0 1 3 2 4 10 - 1 1 . 9 6 2 5 1 . 6 2
LN 4 0 8 . 8 6 5 1 8 . 9 8 8 9 407 - 1 2 . 7 2 2 1 3 . 7 6
1 6 7
MALES (N =1047)
AGE
MEAN SD MEDIAN SKEWNESS KURTOSIS
4 9 . 8 9 6 8 5 1 6 . 5 1 1 0 5 49 0 . 2 3 - 0 . 8 7
MT
TARGET MEAN SD MEDIAN SKEWNESS KURTOSIS
SW 2 1 7 . 8 1 6 6 6 8 . 6 7 4 9 1 9 8 4 . 4 2 3 5 . 2 5
S I 3 2 8 . 4 9 2 8 1 0 7 . 5 5 5 3 1 2 2 . 5 6 1 3 . 0 5
SN 4 9 3 . 4 6 7 2 0 1 . 3 9 2 7 4 8 0 9 . 8 7 2 0 1 . 2 9
MW 3 0 0 . 8 0 8 1 2 0 . 0 9 2 6 2 8 2 9 . 3 8 1 5 5 . 6 8
MI 4 4 8 . 4 4 1 3 1 7 8 . 7 3 5 7 4 3 2 1 2 . 6 9 2 8 3 . 1
MN 6 2 6 . 2 5 7 9 1 8 2 . 8 8 4 7 6 1 8 1 . 1 2 6 . 3 4
LW 4 6 3 . 3 9 2 5 1 3 9 . 6 2 6 6 4 3 8 3 . 2 8 2 2 . 8 8
LI 6 3 7 . 8 4 5 3 1 7 0 . 9 618 1 . 7 3 1 0 . 5 8
LN 8 3 7 . 6 9 6 3 2 4 1 . 0 1 5 7 8 4 0 0 . 6 2 2 . 9 6
WL
TARGET MEAN SD MEDIAN SKEWNESS KURTOSIS
SW 1 8 . 8 0 3 2 5 5 . 9 5 2 18 0 . 5 4 - 0 . 1 7
S I 1 3 . 0 0 6 6 9 4 . 8 4 5 5 12 1 . 5 6 3 . 8 4
SN 8 . 0 9 7 4 2 4 . 8 8 2 8 7 2 . 4 4 9 . 5 8
MW 2 5 . 7 8 8 9 2 8 . 3 7 3 4 2 5 0 . 9 7 2 . 2 8
MI 1 5 . 3 0 7 5 5 7 . 4 9 9 2 13 2 . 0 6 8 . 2 3
MN 8 . 9 4 1 7 4 6 . 8 4 4 7 7 2 .5 7 7 . 7 4
LW 2 9 . 8 5 2 9 1 1 3 . 8 5 9 2 6 1 . 5 3 . 0 3
LI 1 5 . 9 0 7 3 5 1 0 . 5 9 1 3 12 3 1 1 . 6 8
LN 9 . 4 5 8 4 5 9 . 5 9 4 1 7 4 . 3 2 2 6 . 2 5
WR
TARGET MEAN SD MEDIAN SKEWNESS KURTOSIS
SW 1 8 . 0 1 8 1 5 5 . 7 4 6 6 17 0 . 5 2 0 . 2
S I 1 2 . 2 7 5 0 7 4 . 3 8 7 6 11 1 . 8 1 6 . 2 8
SN 7 . 9 1 4 0 4 5 . 1 3 7 3 6 4 . 3 3 3 8 . 3 4
MW 2 5 . 5 3 2 8 . 2 6 4 9 2 4 1 . 4 3 . 8 8
MI 1 6 . 1 2 6 0 7 7 . 1 7 1 6 14 2 . 0 9 9 . 0 9
MN 9 . 5 3 1 0 4 6 . 9 7 0 5 7 2 . 5 4 8 . 0 7
LW 3 2 . 6 1 4 1 4 1 2 . 3 5 0 4 3 1 1 . 1 1 . 5 5
L I 1 8 . 5 9 0 2 6 1 1 . 4 3 7 15 2 . 6 1 8 . 3 5
LN 1 1 . 3 9 6 3 7 1 0 . 9 8 1 9 8 3 . 3 7 1 4 . 8 8
TARGET MEAN SD
D '
MEDIAN SKEWNESS KURTOSIS
SW 5 2 . 0 7 4 5 7 . 9 6 2 4 52 - 0 . 3 8 1 . 1 9
S I 5 9 . 0 6 0 1 7 6 . 3 6 9 5 5 8 4 . 9 7 5 . 3 3
SN 5 7 . 6 2 3 6 9 2 5 . 1 5 0 6 5 5 2 1 . 5 6 4 8 4 . 8 9
MW 1 5 0 . 5 8 8 3 1 5 . 0 2 3 2 1 5 0 1 2 . 7 8 3 1 3 . 3 5
MI 1 5 2 . 1 4 2 3 1 3 . 8 3 5 1 1 5 0 2 1 . 2 7 5 8 7 . 5 1
MN 1 4 8 . 9 5 0 3 6 . 4 9 6 2 1 4 7 3 . 1 1 5 . 9 5
LW 4 0 9 . 6 5 8 1 2 4 . 4 8 1 1 4 1 0 - 9 . 5 1 1 1 5 . 5 9
L I 4 1 1 . 0 9 4 5 1 5 . 1 0 4 3 4 1 0 - 1 2 . 0 4 2 3 2 . 3 6
LN 4 0 8 . 4 7 9 5 1 6 . 5 4 2 6 4 0 7 - 1 4 . 0 7 2 9 0 . 1 1
168
FEMALES (N=271)
AGE
MEAN SD MEDIAN SKEWNESS KURTOSIS
5 1 . 5 8 3 0 3 1 5 . 0 4 4 3 6 53 - 0 . 0 5 - 0 . 9 9
MT
TARGET MEAN SD MEDIAN SKEWNESS K U R TO SIS
SW 2 1 7 . 6 8 2 7 5 4 . 3 7 4 9 2 1 0 2 . 3 9 9 . 5 6
S I 3 0 0 . 8 8 5 6 8 3 . 4 2 9 9 2 8 8 1 . 0 6 1 . 2
SN 4 2 4 . 5 3 8 8 1 3 4 . 9 4 3 9 4 02 0 . 7 2 0 . 6 8
MW 2 8 6 . 9 8 1 5 7 4 . 2 7 5 3 2 7 0 1 . 4 8 3 . 4 2
MI 4 1 0 . 0 3 6 9 1 0 6 . 4 5 7 3 4 0 2 1 . 0 8 3 . 3 6
MN 5 5 5 . 4 0 9 6 1 6 6 . 0 5 7 2 5 5 2 0 . 4 3 0 . 5 8
LW 4 4 8 . 7 3 8 1 2 3 . 4 3 2 6 432 1 . 7 8 5 . 2 3
LI 5 9 3 . 0 4 8 1 5 9 . 0 9 2 5 5 8 2 0 . 8 3 1 . 6 1
LN 7 8 0 . 3 0 9 9 2 3 7 . 7 7 3 3 7 68 0 . 6 6 1 . 3 4
WL
TARGET MEAN SD MEDIAN SKEWNESS K U R TO SIS
SW 1 7 . 5 9 0 4 1 6 . 0 1 6 5 17 0 . 7 6 1 . 0 8
S I 1 4 . 0 2 5 8 3 5 . 6 6 3 13 1 . 6 3 7 . 3 1
SN 9 . 2 0 6 6 4 5 . 0 2 6 8 1 . 4 2 2 . 6 7
MW 2 5 . 4 1 3 2 8 7 . 5 3 8 25 0 . 8 2 1 . 5 9
MI 1 6 . 7 7 4 9 1 8 . 2 3 7 5 15 1 . 6 6 6 . 3 4
MN 1 0 . 9 3 7 2 7 7 . 4 7 7 4 8 1 . 5 4 1 . 9 6
LW 2 9 . 8 0 4 4 3 1 2 . 7 9 8 5 2 7 0 . 9 1 0 . 7 3
L I 1 7 . 4 5 3 8 7 1 1 . 9 8 1 3 14 2 . 4 7 . 2 2
LN 1 1 . 5 2 0 3 1 1 . 9 9 5 3 8 3 . 4 9 1 4 . 8 6
WR
TARGET MEAN SD MEDIAN SKEWNESS K U R TO SIS
SW 1 7 . 4 4 6 5 6 . 0 1 6 9 17 1 . 1 5 4 . 9 7
S I . 1 2 . 7 0 8 4 9 4 . 5 2 6 5 12 0 . 8 8 0 . 9 7
SN 8 . 8 8 1 9 2 4 . 4 9 2 1 8 1 . 6 2 3 . 8 6
MW 2 4 . 7 8 2 2 9 7 . 1 5 2 9 2 4 0 . 5 3 - 0 . 0 8
MI 1 6 . 8 0 4 4 3 6 . 6 7 5 7 16 1 . 2 3 3 . 5 4
MN 1 1 . 8 6 7 1 6 7 . 9 0 9 9 1 . 8 5 4 . 5 4
LW 3 2 . 1 5 1 2 9 1 2 . 4 5 4 2 3 0 1 . 1 4 1 . 6 8
L I 1 9 . 9 7 0 4 8 1 1 . 1 5 9 1 17 2 . 0 4 5 . 4
LN 1 4 . 3 6 9 1 2 . 4 6 2 3 10 2 . 6 5 9 . 6
TARGET MEAN SD
D*
MEDIAN SKEWNESS K U R TO SIS
SW 5 1 . 2 7 6 7 5 8 . 2 4 6 3 5 2 - 0 . 5 6 1 . 2 9
S I 6 0 . 4 1 3 2 8 6 . 3 4 9 5 9 1 . 2 9 3 . 3 2
SN 5 8 . 2 4 3 5 4 5 . 4 7 7 2 57 1 . 2 3 1 . 1 8
MW 1 5 0 . 3 1 7 3 9 . 0 0 0 1 1 5 0 0 . 6 2 0 . 9 3
MI 1 5 3 . 3 2 1 7 . 2 0 5 2 1 5 2 1 . 4 5 4 . 2 5
MN 1 5 0 . 3 5 0 6 1 3 . 0 4 7 4 1 4 9 - 5 . 3 2 4 2 . 8 1
LW 4 1 2 . 3 1 3 7 1 0 . 7 6 9 4 11 1 . 2 8 4 . 0 2
LI 4 1 3 . 7 7 4 9 8 . 2 6 3 5 4 1 2 2 . 2 4 9 . 0 6
LN 4 1 0 . 3 5 4 2 2 6 . 3 7 8 9 4 1 0 - 9 . 7 7 1 0 6 . 3 3
1 6 9
APPENDIX N
M o v e m e n t T im e A N O V A T a b l e w ith B o n f e r o n i C r itic a l V a lu e s f o r
C r o s s - S e c tio n a l D a ta
MT ANOVA Table
SUM OF MEAN
SQUARES D . F . SQUARE F
P
MEAN 3 6 9 1 0 8 4 2 1 1
* * * * * * * * *
3 4 3 1 . 5 5 0 . 0 0 0 0
SEX 2 7 7 3 9 3 1 2 7 7 3 9 3 2 . 5 8 0 . 1 0 8 3
AGE 2 8 6 3 6 5 7 3 7 4 0 9 0 9 3 9 3 8 . 0 3 0 . 0 0 0 0
SA 7 8 0 8 4 2 7 1 1 1 5 4 9 1 . 0 4 0 . 4 0 3 0
ERROR 1 1 4 0 0 4 7 4 5 6 1 3 0 2 1 0 7 5 6 3
TARGET 5 0 8 5 2 9 8 0 8 6 3 5 6 6 2 2 7 0 7 . 6 0 0 . 0 0 0 0
TARGET X SEX 1 3 3 2 4 9 8 1 6 6 5 6 1 . 8 5 0 . 0 6 2 5
TARGET X AGE 4 6 3 2 1 7 4 56 8 2 7 1 7 9 . 2 1 0 . 0 0 0 0
TARGET X SEX X AGE 4 5 2 8 9 6 5 6 8 0 8 7 0 . 90 0 . 6 8 5 1
ERROR 2 9 3 5 7 0 8 6 2 1 0 4 1 6 8 9 8 3
Calculation of Bonferoni Critical Difference Values
alpha
k
alpha/k
df error
ms error
ave. # obs/mean
t
t*sqrt(2*ms/n)=
critical distance
TARGET
0 . 0 5
9
0 . 0 0 5 5 5 6
1 0 4 1 6
8 9 8 3
1 3 1 8
2 . 8 9
10.68
AGE
0 . 0 5
8
0 . 0 0 6 2 5 0
1 3 0 2
1 0 7 5 6 3
1 4 8 2 . 7 5
2 . 8 4
3 4 . 2 6
TA
0 . 0 5
72
0 . 0 0 0 6 9 4
1 0 4 1 6
8 9 8 3
1 6 4 . 7 5
3 . 3 0
3 4 . 4 6
TS
0 . 0 5
18
0 . 0 0 2 7 7 8
1 0 4 1 6
8 9 8 3
6 5 9
3 . 0 0
1 5 . 6 6
170
A P P E N D I X O
Y - I n t e r c e p t a n d S lo p e A N O V A s w ith B o n f e r o n i C o m p a r is o n T a b le s
Formula 73 - Y-Intercept ANOVA Table
ANALYSIS OF VARIANCE
SOURCE SUM OF SQUARES
SEX 23668.1020
AGE 105174.3120
INTERACTION 180380.9058
ERROR 21281845.0738
DF
1
7
7
1302
MEAN SQUARE
23668.1020
15024.9017
25768.7008
16345.5031
TAIL
F VALUE PROBABILITY
1.45 0.2289
0.92 0.4904
1.58 0.1382
ANALYSIS OF VARIANCE; VARIANCES ARE NOT ASSUMED TO BE EQUAL
WELCH 15, 109 2.08 0.0161
BROWN-FORSYTHE
SEX 1, 8 0.77 0.4056
AGE 7, 7 0.33 0.9174
INTERACTION 7, 7 0.43 0.8537
LEVENE’S TEST FOR EQUALITY OF VARIANCES
SEX 1,1302 13.36 0.0003
AGE 7,1302 1.81 0.0822
INTERACTION 7,1302 2.69 0.0090
All. GROUPS COMBINED
(EXCEPT CASES WITH UNUSED VALUES
FOR VARIABLES SEX AND AGE
MEAN -13.301
STD. DEV. 129.146
S. E. M.I 3.557
MAXIMUM 1.3E+3
MINIMUM -1.5E+3
CASES EXCLUDED ( 0)
CASES INCLUDED 1318
ROBUST S.D. 111.330
F o rm u la 73 - Y - I n t e r c e p t BONFERRONI TEST
SIGNIFICANCE AT H
1% LEVEL **
A
L
5% LEVEL ^ E
10% LEVEL - U
>10% LEVEL H 7 7
FOR 120 TESTS D 5 5
E T T
R 0 0
2 3 4
GROUP SAMPLE 5 4 4
HO. LABEL MEAN SIZE
F
E
M
A
O LU O
T 5 Z 7 V EN 2 3 J 5 ¥ 7 V
s 5 5 s E D 5 S 5 5 5 5 E
T T r T R E T T T T T T R
0 O 0 O 8 R 0 O 0 0 0 0 8
5 6 7 8 4 2 3 4 5 6 7 8 4
4 4 4 4 5 4 4 4 4 4 4
MALE
1 UNDER25 44.15 31
*
2 25T034 -4.49 197
3 35T044 -26.41 203
4 —45T054 -43.15 229
*
5 ~55T064 -26.40 144
6 65T074 10.15 164
**
7 ~75T084 20.16 72
*
8 OVERS4 93.83 7
FEM&IS
9 UNDER25 -98.39 4
10 25T034 4.74 47
11 35T044 -5.46 47
12 45T054 -9.10 42
13 55T064 -13.33 68
14 65T074 -19.18 53
15 ~75T084 -2.35 9
16 OVERS4 11.66 1
F o rm u la 7 3 - S lo p e ANOVA T a b le
I ANALYSIS OF VARIANCE
j SOURCE SUM OF SQUARES
I SEX 134.1538
I AGE 196121.2732
| INTERACTION 13939.1802
I ERROR 2337299.6408
DF
1
7
7
1302
MEAN SQUARE
134.1538
28017.3247
1991.3115
1795.1610
F VALUE
0.07
15.61
1.11
TAIL
PROBABILITY
0.7846
0.0000
0.3545
| ANALYSIS OF VARIANCE; VARIANCES ARE NOT ASSUMED TO BE EQUAL
I WELCH 15, 109 13.94 0.0000
| BROHN-FORSYTHE
j SEX 1, 11 1.50 0.2470
I AGE 7, 9 6.59 0.0058
I INTERACTION
7, 9 0.63 0.7202
I LEVENE'S TEST FOR EQUALITY OF VARIANCES
1 SEX 1,1302 4.68 0.0305
[ AGE 7,1302 0.87 0.5335
| INTERACTION 7,1302 1.96 0.0579
u >
ALL GROUPS COMBINED
(EXCEPT CASES WITH UNUSED VALUES
FOR VARIABLES SEX AMD AGE
MEAN 122.996
STD. DEV. 45.617
S. E. M.I 1.257
MAXIMUM 669.558
MINIMUM -50.564
CASES EXCLUDED ( 0)
CASES INCLUDED 1318
ROBUST S.D. 40.869
F o rm u la 73 - S lo p e BONFEKRONI TEST
SIGNIFICANCE AT
1% LEVEL **
5% LEVEL *
10% LEVEL -
>10% LEVEL
FOR 120 TESTS
GROUP SAMPLE
NO. LABEL MEAN SIZE
MALE
1 ONDER25 85.10 31
2 25T034 101.88 197
3 ~35T044 119.68 203
4 “45T054 127.78 229
5 55T064 133.25 144
6 “65T074 142.12 164
7 75TOS4 153.13 72
8 OVER84 196.28 7
FEMALE
9 UNDER25 115.70 4
10 25T034 96.65 47
11 35T044 98.45 47
12 45T054 112.41 42
13 55T064 119.12 68
14 65T074 132.09 53
15 75T084 140.64 9
16 OVER84 229.17 1
M
A
L
E
O O
N 5 7 7 * 7 7 V
D 5 5 5 5 5 5 E
E T T T T T T R
R O O O O O O 8
2 3 4 5 6 7 8 4
5 4 4 4 4 4 4
* * * * kk * * kk * *
* * * * kk * * * *
* * kk * * * * kk
* * * * kk * *
kk A * *
kk * * * *
kk * * * * * *
kk * * * * kk *
_ kk * * kk * * * *
* * * * kk i t * * *
kk * * * *
* k * * * *
* * * * *
F
E
M
A
LU 0
EN 5 3 7 S s 7 V
□ 5 5 5 5 5 5 E
E T T T T T T R
R 0 O O o o O 8
2 3 4 5 6 7 8 4
5 4 4 4 4 4 4
* **
kk
** kk
** kk
** kk ** ★
k* ** **
kk ** kk ±* k
* *
* * * *
F o rm u la 6 9 - Y - I n t e r c e p t ANOVA T a b le
| ANALYSIS OF VARIANCE
| SOURCE SUH OF SQUARES
| SEX 31135.8062
I AGE 80901.2077
[ INTERACTION 151688.2298
| ERROR 31092295.9224
DF
1
7
7
1302
MEAN SQUARE
31135.8062
11557.3154
21669.7471
23880.4116
F VALUE
1.30
0.48
0.91
TAIL
PROBABILITY
0.2535
0.8468
0.4997
I ANALYSIS OF VARIANCE; VARIANCES ARE NOT ASSUMED TO BE EQUAL
I WELCH 15, 109 1.60 0.0857
| BROWN-FORSYTBE
I SEX
1, 8 0.86 0.3811
I AGE 7, 7 0.21 0.9710
| INTERACTION
7, 7 0.44 0.8474
| LEVENE'S TEST FOR EQUALITY OF VARIANCES
1 SEX 1,1302 6.95 0.0084
I AGE 7,1302 1.04 0.4009
I INTERACTION 7,1302 1.33 0.2320
ALL GROUPS COMBINED
{EXCEPT CASES WITH UNUSED VALUES
FOR VARIABLES SEX AND AGE
MEAN -11.330
STD. DEV. 154.783
S. E. M.I 4.263
MAXIMUM 3.4E+3
MINIMUM -4.8E+2
CASES EXCLUDED { 0}
CASES INCLUDED 1318
ROBUST S.D. 112.875
F o rm u la 69 - Y - I n t e r c e p t BONFERRONI TEST
SIGNIFICANCE AT H
1% LEVEL ** L
5% LEVEL * E
10% LEVEL - U
>10% LEVEL N
FOR 120 TESTS D
E
R
2
GROUP SAMPLE 5
NO. LABEL MEAN SIZE
MALE
1 0NDER25 46.49 31
2 25T034 -0.83 197
3 35T044 -27.36 203
4 45T054 -22.65 229
5 55T064 -31.04 144
6 6ST074 3.17 164
7 751084 11.22 72
8 OVER84 87.69 7
FEMALE
9 DNDER25 -93.81 4
10 251034 6.73 47
11 35T044 -4.95 47
12 45T054 -7.40 42
13 55T064 -15.18 68
14 —65T074 -24.62 53
15 751084 2.68 9
16 OVER84 -25.31 1
o LU
2 3 7 S 7 7 V EN
5 5 5 5 5 5 E D
T T T I T T R E
0 0 0 0 0 0 8 R
3 4 5 6 7 8 4 2
4 4 4 4 4 4 5
5 7 7 5 7 7
0
V
5 5 5 5 5 5 E
T T T T T T R
O 0 0 0 O 0 8
3 4 5 6 7 8 4
4 4 4 4 4 4
F o rm u la 69 - S lo p e ANOVA T a b le
| ANALYSIS OF VARIANCE
j SOURCE SUM OF SQUARES
I SEX 32.0562
I AGE 209431.8497
| INTERACTION 14121.3666
| ERROR 2283642.2012
DF
1
7
7
1302
MEAN SQUARE
32.0562
29918.8357
2017.3381
1753.9495
TAIL
F VALUE PROBABILITY
0.02 0.8925
17.06 0.0000
1.15 0.3289
I ANALYSIS OF VARIANCE; VARIANCES ARE NOT ASSUMED TO BE EQUAL
| WELCH 15, 109 14.51 0.0000
| BROWN-FORSYTHE
i SEX
1, 11 1.33 0.2733
I AGE 7, 9 7.01 0.0047
[ INTERACTION 7, 9 0.59 0.7472
| LEVENE'S TEST FOR EQUALITY OF VARIANCES
I SEX 1,1302 4.84 0.0278
| AGE 7,1302 0.87 0.5305
| INTERACTION 7,1302 2.01 0.0506
o
' O
ALL GROUPS COMBINED
(EXCEPT CASES WITH UNUSED VALUES
FOR VARIABLES SEX AMD AGE
MEAN 123.133
STD. DEV. 45.316
S. E. M.X 1.248
MAXIMUM 442.786
MINIMUM -3.6E+2
CASES EXCLUDED { 0)
CASES INCLUDED 1318
ROBUST S.D. 41.051
F o rm u la 69 - S lo p e BONFERRONI TEST
SIGNIFICANCE AT K
1% LEVEL ** L
5% LEVEL * E
10% LEVEL - U O
>10% LEVEL N 2 3 T 3 S 7 V
FOR 120 TESTS D 5 5 5 5 5 5 E
E T T T T T T R
R 0 o 0 O 0 0 8
2 3 4 5 6 7 8 4
GROUP SAMPLE 5 4 4 4 4 4 4
NO. LABEL MEAN SIZE
HALE
1 0NDER25 85.69 31
** ** ** ** ** **
2 25T034 102.02 197
** ** ** ** ** **
3 35T044 120.41 203
*• itir **■ **
4 45TOS4 123.91 229
** ■** ** **
5 ~55T064 134.50 144
** ** - *
6 6ST074 143.85 164
★ * ** ** **
7 —75T084 155.31 72
** ** ** ** -
8 OVERS4 197.50 7
** ** ** ** *
FEMALE
9 0NDER25 115*56 4
10 2ST034 97.30 47
- * * * * itir **
11 35T044 99*29 47
it itir * ★ ** * *
12 ^451054 112.41 42
** ** ★ it
13 “55T064 120.06 68
* * itir **
14 65T074 133*99 53
★ * * * *
15 75T084 140.98 9
-
16 OVER84 236.28 1
*
oo
LD O
EN 7 7 s F 6 7 V
D 5 5 5 5 5 5 E
E T T r T T T R
R 0 0 o O O O 8
2 3 4 5 6 7 8 4
5 4 4 4 4 4 4
it ** *
**
** *
** **
** ** ** *
** ** ** **
** ** ** ** *
★ * * *
APPENDIX P
Predicted and Actual MT Using Formulas 73A, 73B, 69A, and 69B
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
H I PREDICTED M X PREDICTED MX PREDICTED H I PREDICTED
A ll,
BASED ON DISTANCE BASED ON DISTANCE BASED OH DISTANCE BASED OH DISTANCE
SUBJECTS N MEAN AGE H I MEAN DATA FRj CU MEAN EACH V IS IT FRCU MEAN MEAN DAIA FRCH MEAN EACH V IS IT FRCH MEAN
SW 1 318 5 0 .2 2 1 7 .7 8 9 1 1 6 7 .7 6 2 5 5 8 7 2 -5 0 .0 2 6 5 4 1 1 6 6 .8 6 4 3 - 5 0 .9 2 4 8 1 3 2 .7 6 6 1 5 8 7 2 - 8 5 .0 2 2 9 4 1 1 5 5 .5 5 6 2 -6 2 .2 3 2 9
S I 1 318 5 0 .2 3 2 2 .8 1 6 4 3 2 7 .5 1 3 1 8 7 6 4 .6 9 6 7 8 7 7 9 3 2 6 .4 4 6 4 3 .6 3 2 9 2 .5 1 6 7 8 7 8 - 3 0 .2 9 9 6 1 2 3 1 5 .1 3 8 4 - 7 .6 7 8
SB 1 3 1 8 5 0 .2 4 7 9 .2 9 4 4 4 8 5 .4 6 9 4 B 6 6 .1 7 5 0 8 5 9 9 4 8 2 .6 6 4 1 3 .3 6 9 7 4 5 0 .4 7 3 0 8 6 -2 8 .8 2 1 3 1 4 4 7 1 .3 5 5 9 - 7 .9 3 8 5
HH 1 3 1 8 5 0 .2 2 9 7 .9 6 5 1 3 0 7 .0 4 1 9 2 4 3 8 9 .0 7 6 8 2 4 3 8 3 0 6 .5 0 0 1 8 .5 3 5 2 7 2 .0 4 5 5 2 4 3 8 -2 5 .9 1 9 5 7 5 2 9 5 .1 9 2 5 - 2 .7 7 2 6
H I 1 3 1 B 5 0 .2 4 4 0 .5 4 4 8 4 7 8 .5 5 0 8 7 8 6 3 3 8 .0 0 6 0 7 8 6 4 7 8 .1 0 9 3 3 7 .5 6 4 5 4 4 3 .5 5 4 4 7 8 6 3 3 .0 0 9 6 7 8 6 2 4 6 6 .8 0 1 5 2 6 .2 5 6 7
M N 1318 5 0 .2 6 1 1 .6 9 0 4 6 4 8 .3 5 1 5 0 8 6 9 3 6 .6 6 1 1 0 8 6 6 4 8 .0 0 0 5 3 6 .3 1 0 1 6 1 3 .3 5 5 1 0 8 6 9 1 .6 6 4 7 0 8 6 B 6 3 6 .6 9 1 9 2 5 .0 0 1 5
LW 1318 5 0 .2 4 6 0 .3 7 9 4 4 6 5 .6 1 5 9 9 0 4 1 5 .2 3 6 5 9 0 4 0 4 6 5 .3 0 7 6 4 .9 2 8 2 4 3 0 .6 1 9 5 9 0 4 1 -2 9 .7 5 9 8 0 9 4 5 3 .9 9 9 3 - 6 .3 8 0 1
L I 1318 5 0 .2 6 2 8 .6 3 4 3 6 4 8 .8 7 8 3 4 6 6 8 2 0 .2 4 4 0 4 6 6 6 4 8 .8 0 0 9 2 0 .1 6 6 6 6 1 3 .8 8 1 9 4 6 6 8 -1 4 .7 5 2 3 5 3 6 3 7 .4 9 2 6 8 .8 5 8 3
IB 1 3 1 8 5 0 .2 8 2 5 .8 9 6 8 8 2 5 .9 7 2 9 5 B 3 8 0 .0 7 6 1 5 8 3 7 8 2 5 .8 5 3 8 - 0 .0 4 3 7 9 0 .9 7 6 5 5 8 3 8 -3 4 .9 2 0 2 4 1 8 1 4 .5 4 5 9 - 1 1 .3 5 0 9
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
MX PREDICTED MI PREDICTED MT PREDICTED H I PREDICTED
BASED ON DISTANCE BASED ON DISTANCE BASED 09) DISTANCE BASED ON DISTANCE
HALES N MEAN AGE H I mean d ata FROM MEAN EACH V IS IT FROM MEAN MEAN DATA FROM MEAN EACH V IS IT FROM MEAN
SW 1047 4 9 .9 2 1 7 .8 1 6 6 1 6 7 .6 5 2 6 5 6 6 1 - 5 0 .1 6 3 9 4 3 1 6 6 .6 2 2 3 - 5 1 .1 9 4 3 1 3 2 .6 5 3 5 5 6 6 1 - B 5 .163043 1 5 6 .1 3 5 1 - 6 1 .6 8 1 5
S I 1047 4 9 .9 3 2 8 .4 9 2 8 3 2 5 .9 2 1 4 5 9 6 6 - 2 .5 7 1 3 4 0 3 3 2 4 .6 7 1 4 - 3 .8 2 1 4 2 9 0 .9 2 2 3 5 9 6 6 -3 7 .5 7 0 4 4 0 3 1 4 .1 8 4 2 - 1 4 ,3 0 8 6
SN 1047 4 9 .9 4 9 3 .4 6 7 4 8 3 .7 9 7 2 3 7 3 6 -9 .6 6 9 7 6 2 6 4 8 0 .2 8 1 8 - 1 3 .1 8 5 2 4 4 8 .7 9 B 1 3 7 3 6 -4 4 .6 6 8 8 6 2 4 6 9 .7 9 4 8 - 2 3 .6 7 2 2
M W 1 0 4 7 4 9 .9 3 0 0 .8 0 8 3 0 6 .2 6 7 4 9 3 9 6 5 .4 5 9 4 9 3 9 5 3 0 5 .5 2 1 2 4 .7 1 3 2 2 7 1 .2 6 B 3 9 3 9 6 -2 9 .5 3 9 6 0 6 2 9 5 .0 3 4 1 - 5 .7 7 3 9
H I 1047 4 9 .9 4 4 8 .4 4 1 3 4 7 7 .0 0 0 9 1 6 9 2 8 .5 5 9 6 1 6 9 4 7 6 .2 9 9 6 2 7 .8 5 8 3 4 4 2 .0 0 1 8 1 6 9 - 6 .4 3 9 4 8 3 0 4 6 5 .8 1 2 7 1 7 .3 7 1 4
MN 10 4 7 4 9 .9 6 2 6 .2 5 7 9 6 4 6 .2 7 9 7 1 0 5 7 2 0 .0 2 1 8 1 0 5 6 4 5 .8 2 2 4 1 9 .5 6 4 5 6 1 1 .2 8 0 6 1 0 5 7 - 1 4 .9 7 7 2 8 9 6 3 5 .3 3 4 9 9 .0 7 7
LW 10 4 7 4 9 .9 4 6 3 .3 9 2 5 4 6 4 .1 4 4 9 3 7 4 3 0 .7 5 2 4 3 7 4 2 4 6 3 .5 5 1 8 0 .1 5 9 3 4 2 9 .1 4 5 8 3 7 4 3 - 3 4 .2 4 6 6 6 2 4 5 3 .0 6 4 6 - 1 0 .3 2 7 9
L I 10 4 7 4 9 .9 6 3 7 .8 4 5 3 6 4 6 .9 0 8 0 1 5 6 7 9 .0 6 2 7 1 5 6 6 6 4 6 .5 0 6 5 8 .6 6 1 2 6 1 1 .9 0 8 9 1 5 6 7 -2 5 .9 3 6 3 B 4 6 3 6 .0 1 9 2 - 1 .8 2 6 1
I B 10 4 7 4 9 .9 8 3 7 .6 9 6 3 8 2 3 .5 9 8 4 4 7 9 7 -1 4 .0 9 7 8 5 2 8 2 3 .2 1 6 6 - 1 4 .4 7 9 7 7 8 8 .5 9 9 3 4 7 9 7 -4 9 .0 9 6 9 5 2 8 1 2 .7 2 9 7 - 2 4 .9 6 6 6
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
MX PREDICTED MX PREDICTED MX PREDICTED MT PREDICTED
BASED ON DISTANCE BASED ON DISTANCE BASED OB DISTANCE BASED CM DISTANCE
FEMALES H MEAN AGE MI MEAN DATA FROM MEAN EACH V IS IT FRCH MEAN MEAN DATA FR£M MEAN EACH V IS IT FRCH MEAN
SW 271 5 1 . e 2 1 7 .6 8 2 7 1 6 8 .5 2 8 9 1 2 4 8 - 4 9 .1 5 3 7 8 7 1 6 7 .7 9 9 2 - 4 9 .8 8 3 5 1 3 3 .7 5 9 3 1 2 4 8 - B 3 .923387 1 5 3 .3 1 9 5 - 6 4 .3 6 3 2
S I 271 5 1 .6 3 0 0 .8 8 5 6 3 3 4 .3 8 7 1 1 0 8 8 3 3 .5 0 1 5 1 0 8 3 3 3 .3 0 5 1 3 2 .4 1 9 5 2 9 9 .6 1 7 5 1 0 8 8 -1 .2 6 8 0 8 9 1 3 1 8 .8 2 5 4 1 7 .9 3 9 8
SH 2 7 1 5 1 .6 4 2 4 .5 3 8 8 4 9 2 .9 9 1 0 1 3 7 4 6 8 .4 5 2 2 1 3 7 4 9 1 .8 6 7 1 6 7 .3 2 8 3 4 5 8 .2 2 1 4 1 3 7 4 3 3 .6 8 2 6 1 3 7 4 7 7 .3 8 7 5 5 2 .8 4 8 7
M W 2 7 1 5 1 .6 2 8 6 .9 8 1 5 3 1 0 .6 9 6 2 9 0 6 2 3 .7 1 4 7 9 0 6 3 1 0 .2 8 3 5 2 3 .3 0 2 2 7 5 .9 2 6 6 9 0 6 - 1 1 .0 5 4 8 0 9 2 9 5 .8 0 3 7 6 .8 2 2 2
H I 27 1 5 1 .6 4 1 0 .0 3 6 9 4 8 5 .5 8 2 3 9 5 2 7 5 .5 4 5 4 9 5 2 4 8 5 .1 0 0 7 7 5 .0 6 3 8 4 5 0 .8 1 2 7 9 5 2 4 0 .7 7 5 8 9 5 2 4 7 0 .6 2 1 1 6 0 .5 8 4 2
MN 27 1 5 1 .6 5 5 5 .4 0 9 6 6 5 7 .7 6 3 6 6 1 2 4 1 0 2 .3 5 4 0 6 1 6 5 6 .4 1 4 5 1 0 1 .0 0 4 9 6 2 2 .9 9 4 0 6 1 2 4 6 7 .5 8 4 4 6 1 2 6 4 1 .9 3 4 9 8 6 .5 2 5 3
LW 27 1 5 1 .6 4 4 8 .7 3 8 4 7 2 .3 1 3 8 8 2 4 6 2 3 .5 7 5 8 8 2 4 4 7 2 .0 8 9 5 2 3 .3 5 1 5 4 3 7 .5 4 4 2 8 2 4 6 -1 1 .1 9 3 7 1 7 4 5 7 .6 0 9 8 8 .8 7 1 8
L I 271 5 1 .6 5 9 3 .0 4 8 6 5 7 .8 9 6 4 3 9 9 6 4 .8 4 B 4 3 9 8 6 5 7 .6 6 5 1 6 4 .6 1 7 1 6 2 3 .1 2 6 8 3 9 9 3 0 .0 7 8 8 3 9 8 6 4 3 .1 8 5 4 5 0 .1 3 7 4
IB 271 5 1 .6 7 8 0 .3 0 9 9 8 3 6 .9 2 8 0 7 9 7 5 6 .6 1 8 1 7 9 7 8 3 6 .0 4 0 4 5 5 .7 3 0 5 8 0 2 .1 5 8 4 7 9 7 2 1 .8 4 8 5 7 9 7 8 2 1 .5 6 0 6 4 1 .2 5 0 7
DECADE2 N MEAN ACE MT
FORMULA 73A
MT PREDICTED
b a s e d ON
KEAN DATA
DISTANCE
FROM MEAN
SW 35 2 1 .7 1 9 7 .3 1 4 3 1 2 8 .1 2 3 2 3 7 1 9 - 6 9 .1 9 1 0 6 2
S I 35 2 1 .7 2 7 5 .8 2 8 6 2 5 3 .6 6 5 0 7 0 0 4 - 2 2 .1 6 3 5 2 9
SN 35 2 1 .7 3 7 1 ,8 2 8 6 3 6 8 .4 3 9 4 6 5 5 5 - 3 .3 8 9 1 3 4 4
M W 35 2 1 .7 2 5 3 .2 2 3 0 .9 9 6 7 5 0 1 1 - 2 2 .2 0 3 2 4 9
H I 35 2 1 .7 3 5 5 .2 3 6 1 .5 1 7 0 9 6 0 2 6 .3 1 7 0 9 6 0 2
MN 35 2 1 .7 4 7 6 .2 2 8 6 4 8 8 .1 4 2 3 2 9 6 1 1 1 .9 1 3 7 2 9 6
IN 35 2 1 .7 3 8 4 .6 8 5 7 3 4 8 .0 8 3 9 5 9 4 8 - 3 6 .6 0 1 7 4 0
L I 3 5 2 1 .7 4 9 7 .8 2 8 6 4 6 6 .6 0 2 7 7 0 9 3 -1 1 .2 2 5 8 2 9
I S 3 5 2 1 .7 6 3 7 .7 1 4 3 6 1 8 .7 7 9 6 5 4 6 3 -1 8 .9 3 4 6 4 5
DECADE3 H MEAN ACE HT
FORMULA 73A
HT PREDICTED
BASED ON
MEAN DATA
DISTANCE
FROM KEAN
SW 244 2 9 . 9 1 9 8 .7 6 2 3 1 3 9 .0 9 1 0 7 8 4 7 -5 9 .6 7 1 2 2 1
S I 244 2 9 .9 2 7 4 .4 0 1 6 2 7 2 .8 3 6 1 6 6 5 6 - 1 .5 6 5 4 3 3 4
SN 244 2 9 .9 3 9 0 .0 2 4 6 4 0 1 .5 3 9 8 5 1 7 6 1 1 .5 1 5 2 5 1 7
M W 244 2 9 .9 2 5 7 .6 8 0 3 2 5 3 .6 5 9 7 9 6 8 8 - 4 .0 2 0 5 0 3 1
MI 244 2 9 .9 3 7 2 .5 1 6 4 3 9 4 .0 5 2 0 1 7 7 5 2 1 .5 3 5 6 1 7 7
MN 244 2 9 .9 5 0 4 .4 6 7 2 5 3 3 .7 7 2 7 2 8 5 1 2 9 .3 0 5 5 2 6 5
LN 244 2 9 .9 3 9 6 .9 3 4 4 3 8 2 .2 9 9 3 6 3 4 6 -1 4 .6 3 5 0 3 6
L I 24 4 2 9 .9 5 3 4 .3 9 3 4 5 3 2 .7 3 2 6 3 3 6 8 - 1 .6 6 0 7 6 6 3
IN 244 2 9 . 9 6 8 8 .7 7 0 5 6 7 7 .5 8 8 9 9 1 8 5 - 1 1 .1 8 1 5 0 8
DECADE4 N MEAN ACE HE
FORMULA 73A
HE PREDICTED
BASED ON
KEAN DATA
DISTANCE
FRCM MEAN
SW 250 3 9 . 6 2 0 0 .3 2 8 1 4 9 .6 4 9 1 7 3 9 -5 0 .6 7 8 8 2 6
S I 250 3 9 . 6 2 9 3 .0 8 8 2 9 6 .2 1 2 9 4 2 3 9 3 .1 2 4 9 4 2 3 9
SN 250 3 9 . 6 4 4 1 .7 6 8 4 3 7 .3 0 5 3 0 5 0 7 - 4 .4 6 2 6 9 4 9
m 250 3 9 . 6 2 7 1 .6 8 2 7 7 .7 4 7 7 9 1 3 9 6 .0 6 7 7 9 1 3 8
m 250 3 9 . 6 4 0 4 .7 3 6 4 3 3 .6 3 3 7 4 6 0 4 2 8 .8 9 7 7 4 6 0
M N 250 3 9 . 6 5 7 2 .6 8 8 5 B 7 .24214182 1 4 .5 5 4 1 4 1 8
LW 250 3 9 .6 4 1 8 .4 1 6 4 2 1 .6 2 3 2 8 6 9 9 3 .2 0 7 2 8 6 ^ 9
L I 250 3 9 .6 5 7 3 .6 4 8 5 8 7 .8 2 9 4 9 3 0 2 1 4 .1 8 1 4 9 3 0
I S 2 50 3 9 . 6 7 7 0 .6 4 7 4 7 .9 2 7 0 5 6 1 5 - 2 2 .7 1 2 9 4 3
DECADE5 N MEAN AGE t a
FORMULA 73A
HT PREDICTED
BASED ON
MEAN DATA
DISTANCE
FROM MEAN
SW 271 4 9 .7 2 0 4 .6 8 6 3 1 6 6 .0 8 7 2 1 5 0 1 - 3 8 .5 9 9 0 8 4
S I 271 4 9 .7 3 0 5 .1 1 4 4 3 2 6 .0 0 6 2 6 4 7 1 2 0 .8 9 1 8 6 4 7
SN 271 4 9 .7 4 8 2 .9 2 2 5 4 8 5 .2 7 4 6 3 5 7 1 2 .3 5 2 1 3 5 7 1
M W 271 4 9 .7 2 8 6 .5 3 8 8 3 0 6 .5 2 6 2 9 4 8 8 1 9 .9 8 7 4 9 4 8
MI 2 7 1 4 9 .7 4 3 4 .1 0 3 3 4 7 7 .2 5 3 1 1 6 B 4 3 .1 4 9 B 1 6 7
M N 2 71 4 9 .7 6 0 6 .6 8 6 3 6 4 4 .8 7 5 3 6 6 2 3 8 .1 8 9 0 6 6 2
LW 271 4 9 .7 4 3 2 .8 1 9 2 4 6 2 .9 3 6 7 6 5 2 2 3 0 .1 1 7 5 6 5 2
L I 271 4 9 .7 6 0 6 .1 7 7 1 6 4 5 .3 0 5 9 0 8 1 4 3 9 .1 2 8 8 0 8 1
I S 271 4 9 .7 8 0 7 .2 7 6 7 8 2 1 .3 3 8 4 9 9 8 4 1 4 .0 6 1 7 9 9 8
00
o
FORMULA 73A
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FROM KEAN
1 2 7 .5 3 6 7 - 6 9 .7 7 7 6
2 5 2 .9 7 7 - 2 2 .8 5 1 6
3 6 7 .7 8 1 1 - 4 .0 4 7 5
2 3 0 .9 3 1 7 - 2 2 .2 6 8 3
3 6 1 .3 6 8 3 6 .1 6 8 3
4 8 8 .0 3 9 5 1 1 .8 1 0 9
3 4 6 .9 2 6 8 - 3 7 .7 5 8 9
4 8 6 .6 3 4 4 - 1 1 .1 9 4 2
6 1 8 .8 3 0 7 - 1 8 .8 8 3 6
FORMULA 73A
HT PREDICTED
BASED OH DISTANCE
EACH V IS IT FROM MEAN
1 3 8 .2 7 0 S - 6 0 .4 9 1 5
2 7 2 .0 5 0 5 - 2 .3 5 1 1
4 0 0 .7 0 8 9 1 0 .6 8 4 3
2 5 3 .1 9 2 5 - 4 .4 8 7 8
3 9 3 .6 9 4 2 2 1 .1 7 7 8
5 3 3 .0 3 9 4 2 8 .5 7 2 2
3 8 1 .2 9 5 4 - 1 5 .6 3 9
5 3 2 .3 8 5 9 - 2 .0 0 7 5
6 7 6 .4 7 7 5 - 1 2 .2 9 3
FORMULA 73A
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FROM KEAN
1 4 8 .8 1 3 8 - 5 1 .5 1 4 2
2 9 5 .6 2 9 6 2 .5 4 1 6
4 3 6 .6 2 6 8 - 5 .1 4 1 2
2 7 7 .3 8 0 8 5 .7 0 0 8
4 3 3 .3 5 5 5 2 B .6 1 9 5
5 8 6 .9 1 4 1 1 4 .2 2 6 1
4 2 1 .2 5 7 2 .8 4 1
5 8 7 .6 3 0 2 1 3 .9 8 2 2
7 4 7 .4 2 9 - 2 3 .2 1 1
FORMULA 73A
H i PREDICTED
BASED ON DISTANCE
EACH V IS IT FROM MEAN
1 6 5 .2 4 7 1 - 3 9 .4 3 9 2
3 2 5 .2 4 6 5 2 0 .1 3 2 1
4 8 0 .6 4 3 3 - 2 .2 7 9 2
3 0 5 .7 6 6 1 1 9 .2 2 7 3
4 7 6 .3 7 9 1 4 2 .2 7 5 B
6 4 4 .7 5 9 3 3 8 .0 7 3
4 6 2 .6 8 5 2 9 .8 6 5 8
6 4 5 .0 5 0 5 3 8 .8 7 3 4
8 2 0 .6 6 2 9 1 3 .3 8 6 2
FORMULA 73B
MT PREDICTED
BASED O S DISTANCE
MEAN DATA FRCH KEAN
1 6 5 .2 0 3 3 3 7 1 9 - 3 2 .1 1 0 9 6 2
2 9 0 .7 4 5 1 7 0 0 4 1 4 .9 1 6 5 7 0 0
4 0 5 .5 1 9 5 6 5 5 5 3 3 .6 9 0 9 6 5 5
2 6 8 .0 7 6 8 5 0 1 1 1 4 .8 7 6 8 5 0 1
3 9 8 .5 9 7 1 9 6 0 2 4 3 .3 9 7 1 9 6 0
5 2 5 .2 2 2 4 2 9 6 1 4 8 .9 9 3 8 2 9 6
3 8 5 .1 6 4 0 5 9 4 8 0 .4 7 8 3 5 9 4 7
5 2 3 .6 8 2 8 7 0 9 3 2 5 .8 5 4 2 7 0 9
6 5 5 .8 5 9 7 5 4 6 3 1 8 .1 4 5 4 5 4 6
FORMULA 73B
HT PREDICTED
BASED ON DISTANCE
MEAN DATA FROM MEAN
1 4 0 .4 5 1 9 7 8 4 7 - 5 8 .3 1 0 3 2 1
2 7 4 .1 9 7 0 6 6 5 6 -0 .2 0 4 5 3 3 4
4 0 2 .9 0 0 7 5 1 7 6 1 2 .8 7 6 1 5 1 7
2 5 5 .0 2 0 6 9 6 8 8 -2 .6 5 9 6 0 3 1
3 9 3 .4 1 2 9 1 7 7 5 2 2 .8 9 6 5 1 7 7
5 3 5 .1 3 3 6 2 8 5 1 3 0 .6 6 6 4 2 8 5
3 8 3 .6 6 0 2 6 3 4 6 -1 3 .2 7 4 1 3 6
5 3 4 .0 9 3 5 3 3 6 8 -0 .2 9 9 8 6 6 3
6 7 8 .9 4 9 B 9 1 8 5 -9 .8 2 0 6 0 8 1
FORMULA 73B
MT PREDICTED
BASED ON DISTANCE
KEAN DATA FROM KEAN
1 2 4 .3 8 3 5 7 3 B 9 6 - 7 5 .9 4 4 4 2 6
2 7 0 .9 4 7 3 4 2 3 9 -2 2 .1 4 0 6 5 7
4 1 2 .0 3 9 7 0 5 0 7 -2 9 .7 2 8 2 9 4
2 5 2 .4 8 2 1 9 1 3 9 -1 9 .1 9 7 8 0 B
4 0 8 .3 6 8 1 4 6 0 4 3 .6 3 2 1 4 6 0 4
5 6 1 .9 7 6 5 4 1 8 2 - 1 0 .7 1 1 4 5 8
3 9 6 .3 5 7 6 B 6 9 9 -2 2 .0 5 B 3 1 3
5 6 2 .5 6 3 8 9 3 0 2 - 1 1 .0 8 4 1 0 6
7 2 2 .6 6 1 4 5 6 1 5 -4 7 .9 7 8 5 4 3
FORMULA 73B
HT PREDICTED
BASED ON DISTANCE
MEAN DATA FRCH MEAN
1 3 1 .0 9 5 3 1 5 0 1 -7 3 .5 9 0 9 8 4
2 9 1 .0 1 4 3 6 4 7 1 - 1 4 .1 0 0 0 3 5
4 5 0 .2 B 2 7 3 5 7 1 -3 2 .6 3 9 7 6 4
2 7 1 .5 3 4 3 9 4 S B -1 5 .0 0 4 4 0 5
4 4 2 .2 6 1 2 1 6 8 8 .1 5 7 9 1 6 7 9
6 0 9 .8 8 3 4 6 6 2 3 .1 9 7 1 6 6 2
4 2 7 .9 4 4 8 6 5 2 2 - 4 .8 7 4 3 3 4 7
6 1 0 .3 1 4 0 0 8 1 4 4 .1 3 6 9 0 8 1 3
7 8 6 .3 4 6 5 9 9 8 4 - 2 0 .9 3 0 1 0 0
FORMULA 73B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FROM KEAN
1 6 4 .9 8 9 3 - 3 2 .3 2 5
2 9 0 .4 2 9 6 1 4 .6 0 1
4 0 5 .2 3 3 6 3 3 .4 0 5
2 6 8 .3 8 4 2 1 5 .1 8 4 2
3 9 8 .8 2 0 9 4 3 .6 2 0 9
5 2 5 .4 9 2 4 9 .2 6 3 4
3 8 4 .3 7 9 3 - 0 .3 0 6 4
5 2 4 .0 8 6 9 2 6 .2 5 8 3
6 5 6 .2 8 3 4 1 8 .5 6 9 1
FORMULA 73B
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH KEAN
1 4 0 .4 5 8 5 - 5 8 .3 0 3 8
2 7 4 .2 3 8 3 - 0 .1 6 3 3
4 0 2 .8 9 6 5 1 2 .8 7 1 9
2 5 5 .3 8 0 2 - 2 .3 0 0 1
3 9 5 .8 8 1 7 2 3 .3 6 5 3
5 3 5 .2 2 7 4 3 0 .7 6 0 2
3 8 3 .4 8 3 - 1 3 .4 5 1 4
5 3 4 .5 7 3 7 0 .1 8 0 3
6 7 8 .6 6 5 1 - 1 0 .1 0 5 4
FORMULA 73B
HT PREDICTED
BASED 0 8 DISTANCE
EACH V IS IT FROM KEAN
1 2 4 .3 5 8 5 - 7 5 .9 6 9 5
2 7 1 .1 7 4 4 - 2 1 .9 1 3 6
4 1 2 .1 7 1 6 - 2 9 .5 9 6 4
2 5 2 .9 2 5 5 - I B . 754 5
4 0 8 .9 0 0 1 4 .1 6 4 1
5 6 2 .4 5 8 9 - 1 0 .2 2 9 1
3 9 6 .8 0 1 6 - 2 1 .6 1 4 4
5 6 3 .1 7 4 6 - 1 0 .4 7 3 4
7 2 2 .9 7 4 - 4 7 .6 6 6
FORMULA 73B
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCM KEAN
1 3 1 .0 0 2 - 7 3 .6 8 4 3
2 9 1 .0 0 1 3 - 1 4 .1 1 3 1
4 4 6 .3 9 8 2 - 3 6 .5 2 4 3
2 7 1 .5 2 0 9 - 1 5 .0 1 7 9
4 4 2 .1 3 3 8 a . 0305
6 1 0 .5 1 4 5 3 .8 2 8 2
4 2 8 .4 4 - 4 .3 7 9 2
6 1 0 .8 0 5 4 4 .6 2 8 3
7 8 6 .4 1 7 9 - 2 0 .8 5 8 8
rOKHCTLA. 73A FORMULA 73A FORKOLA 73B rOKKOLA 73B
MT PREDICTED HT PREDICTED JO PREDICTED
HT PREDICTED
BAB ED CM DIBXAHCE BASED CM DISTANCE BASED OB DISTANCE BASED OH DISTANCE
DECADE6 H MEAN ACE MT H U B DAIA FRCH MEAN EACH V IS IT HICK MEAN MEAN DATA FRCH MEAN EACH V IS IT FRCH MEAN
s n 212 5 9 .5 2 1 6 .1 6 9 8 1 8 0 .9 2 9 4 3 5 3 4 -3 5 .2 4 0 3 6 4 1 8 0 .1 8 1 4 - 3 5 .9 8 8 4 1 5 4 .0 5 1 9 3 5 3 4 - 6 2 .1 1 7 8 6 4 1 5 4 .0 5 4 1 - 6 2 .1 1 5 7
a z 212 5 9 .5 3 2 9 .8 5 8 5 3 5 1 .2 7 6 5 6 8 3 4 21.41B 06B 3 3 5 0 .9 2 3 B 2 1 .0 6 5 3 3 2 4 .3 9 9 0 6 8 3 4 - 5 .4 5 9 4 3 1 6 3 2 4 .7 9 6 5 - 5 . 0 6 2
SB 2 1 2 5 9 .5 4 9 2 .3 3 9 6 5 1 9 .2 7 2 3 7 2 9 7 2 6 .9 3 2 7 7 2 9 5 1 8 .9 6 1 5 2 6 .6 2 1 9 4 9 2 .3 9 4 B 7 2 9 7 0 .0 5 5 2 7 2 9 7 4 9 2 .8 3 4 2 0 .4 9 4 6
M9 2 12 5 9 .5 3 0 0 .6 7 9 3 3 3 0 .6 5 B 9 2 2 8 3 2 9 .9 7 9 6 2 2 8 3 3 0 ,4 5 6 3 2 9 .7 7 7 3 0 3 .7 8 1 4 2 2 8 3 3 .1 0 2 1 2 2 8 2 3 0 4 .3 2 8 9 3 .6 4 9 6
M l 2 12 5 9 .5 4 4 9 .8 5 8 5 5 1 5 .7 1 4 3 4 4 4 1 6 5 .8 5 5 8 4 4 4 5 1 5 .7 0 4 4 6 5 .8 4 5 9 4 8 8 .8 3 6 8 4 4 4 1 3 8 .9 7 8 3 4 4 4 4 8 9 .5 7 7 3 9 .7 1 B 5
M S 2 12 5 9 .5 6 2 8 .1 3 2 1 6 9 9 .3 6 4 1 3 9 5 2 7 1 .2 3 2 0 3 9 5 6 9 8 .5 9 9 4 7 0 .4 6 7 3 6 7 2 .4 8 6 6 3 9 5 2 4 4 .3 5 4 5 3 9 5 6 7 2 .4 7 2 2 4 4 .3 4 0 1
LW 2 12 5 9 .5 4 6 8 .3 9 6 2 5 0 4 .1 5 0 9 6 5 9 5 3 5 .7 5 4 7 6 5 9 5 0 4 .2 2 4 9 3 5 .8 2 8 7 4 7 7 .2 7 3 4 6 5 9 5 8 .8 7 7 2 6 5 9 5 4 7 8 .0 9 7 5 9 .7 0 1 3
L I 2 12 5 9 .5 6 4 7 .2 6 4 2 7 0 2 .5 2 4 3 9 8 4 9 5 5 .2 6 0 1 9 8 4 7 0 2 .6 6 4 5 5 .3 9 9 8 6 7 5 .6 4 6 8 9 B 4 9 2 8 .3 8 2 6 9 8 4 6 7 6 .5 3 7 2 9 .2 7 2 8
X* 21 2 5 9 .5 8 6 1 .0 2 8 3 8 9 4 .3 8 5 9 9 8 6 3 3 .3 5 7 6 9 8 6 8 9 4 .5 7 1 5 3 3 .5 4 3 2 8 6 7 .5 0 8 4 9 8 6 6 .4 8 0 1 9 3 6 0 8 6 8 .4 4 4 2 7 .4 1 5 9
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
MT PREDICTED JO PREDICTED HT PREDICTED HT PREDICTED
BASED C M DISTANCE BASED OB DISTANCE BASED ON DISTANCE BASED OH DISTANCE
DECADE? H K tlH AGE h t MEAN DATA FRCH MEAN EACH V IS IT FRCH MEAN MEAN DAXA FRCH KEAN EACH V IS IT FRCH MEAN
A W 217 6 9 .6 2 5 0 .5 3 4 6 1 9 7 .3 8 9 0 4 3 6 - 5 3 .1 4 5 5 5 6 1 9 6 .5 0 5 - 5 4 .0 2 9 6 1 9 6 .9 6 3 4 4 3 6 -5 3 .5 7 1 1 5 6 1 9 6 .9 2 9 4 - 5 3 .6 0 5 2
S I 217 6 9 .6 3 8 2 .2 3 0 4 3 7 9 .4 2 0 5 1 3 3 - 2 .8 0 9 8 8 6 6 3 7 8 .9 3 4 3 - 3 .2 9 6 1 3 7 8 .9 9 4 9 1 3 3 - 3 .2 3 5 4 8 6 6 3 7 9 .3 5 8 8 - 2 .8 7 1 6
SB 217 6 9 .6 5 5 8 .1 6 5 9 5 7 1 .2 1 1 7 9 5 8 9 1 3 .0 4 5 8 9 5 8 5 6 3 .5 0 5 9 5 .3 4 5 7 0 .7 8 6 1 9 5 8 9 1 2 .6 2 0 2 9 5 8 5 6 3 .9 2 9 9 5 .7 6 4
HT 217 6 9 .6 3 4 4 .4 3 3 2 3 5 7 .1 9 1 9 9 1 3 6 1 2 .7 5 8 7 9 1 3 3 5 7 .0 7 7 9 1 2 .6 4 4 7 3 5 6 .7 6 6 3 9 1 3 6 1 2 .3 3 3 1 9 1 3 3 5 7 .5 0 2 3 1 3 .0 6 9 1
H I 217 6 9 .6 5 1 2 .8 7 5 5 5 5 8 .6 2 3 5 0 4 9 1 4 5 .7 4 8 0 0 4 9 5 5 8 .6 1 7 3 4 5 .7 4 1 8 5 5 8 .1 9 7 9 0 4 9 1 4 5 .3 2 2 4 0 4 9 5 5 9 .0 4 1 6 4 6 .1 6 6 1
M f 2 17 6 9 .6 7 1 3 .2 2 5 8 7 5 8 .6 4 6 2 7 6 4 5 4 5 .4 2 0 4 7 6 4 7 5 8 .7 2 4 7 4 5 .4 9 8 9 7 5 8 .2 2 0 6 7 6 4 5 4 4 .9 9 4 8 7 6 4 7 5 9 .1 4 8 7 4 5 .9 2 2 9
LH 2 17 6 9 .6 5 4 7 .1 6 1 3 5 4 5 .8 6 0 7 3 1 7 8 -1 .3 0 0 5 6 8 2 5 4 5 .9 6 9 7 - 1 .1 9 1 6 5 4 5 .4 3 5 1 3 1 7 8 - 1 .7 2 6 1 6 8 2 5 4 6 .3 9 4 - 0 .7 6 7 3
L I 2 17 6 9 .6 7 3 5 .8 9 8 6 7 6 0 .0 9 5 6 5 9 8 2 2 4 .1 9 7 0 5 9 8 7 6 0 .3 0 1 6 2 4 .4 0 3 7 5 9 .6 7 0 0 5 9 8 2 2 3 .7 7 1 4 5 9 8 7 6 0 .7 2 6 2 4 .8 2 7 4
LN 217 6 9 .6 9 5 3 .0 0 4 6 9 6 8 .0 0 9 6 5 5 7 7 1 5 .0 0 5 0 5 5 7 9 6 8 .2 4 0 5 1 5 .2 3 5 9 9 6 7 .5 8 4 0 5 5 7 7 1 4 .5 7 9 4 5 5 7 9 6 8 .6 6 5 5 1 5 .6 6 0 9
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
FfC PREDICTED HT PREDICTED MT PREDICTED HT PREDICTED
BASED OH DISTANCE BASED OB DISTANCE BASED ON DISTANCE BASED ON DISTANCE
DECADES N H U B AGE KT H U B DATA FRCM MEAN EACH V IS IT FRCH MEAN MEAN DAXA FRCH MEAN BACH V IS IT FRCM MEAN
SW B1 7 8 .3 2 8 3 .5 5 5 5 2 1 3 .6 7 1 3 0 4 8 3 - 6 9 .8 8 4 1 9 5 2 1 2 .7 7 1 3 - 7 0 .7 8 4 2 2 5 0 .7 5 1 4 0 4 8 3 -3 2 .8 0 4 0 9 5 2 5 0 .8 2 0 2 - 3 2 .7 3 5 3
S I 6 1 7 8 .3 4 3 3 .7 7 7 8 4 0 6 .0 3 3 8 4 1 0 2 -2 7 .7 4 3 9 5 8 4 0 5 .5 0 1 B - 2 8 .2 7 6 4 4 3 .1 1 3 9 4 1 0 2 9 .3 3 6 1 4 1 0 2 4 4 3 .5 5 0 6 9 .7 7 2 8
SN 8 1 7 8 .3 6 1 6 .2 9 6 3 5 9 9 .8 7 5 4 0 2 9 4 -1 6 .4 2 0 8 9 7 5 9 9 .6 2 9 4 - 1 6 .6 6 6 9 6 3 6 .9 5 5 5 0 2 9 4 2 0 .6 5 9 2 0 2 9 6 3 7 .6 7 8 2 2 1 .3 8 1 9
M N 8 1 7 8 .3 3 9 9 .4 0 7 4 3 8 2 .6 9 4 2 3 3 9 4 -1 6 .7 1 3 1 6 6 3 8 2 .5 5 6 4 - 1 6 .8 5 1 4 1 9 .7 7 4 3 3 3 9 4 2 0 .3 6 6 9 3 3 9 4 2 0 .6 0 5 4 2 1 .1 9 8
H I a i 7 8 .3 5 6 0 .5 1 8 5 5 9 5 .3 7 7 5 4 0 5 3 4 .8 5 9 0 4 0 4 5 9 5 .4 9 4 3 3 4 .9 7 5 8 6 3 2 .4 5 7 6 4 0 5 7 1 ,9 3 9 1 4 0 4 6 3 3 .5 4 3 1 7 3 .0 2 4 6
MN 81 7 8 .3 7 7 2 .2 9 6 3 8 0 9 .8 9 1 3 3 2 0 3 3 7 .5 9 5 0 3 2 0 8 1 0 .0 4 8 9 3 7 .7 5 2 6 8 4 6 .9 7 1 4 3 2 0 3 7 4 .6 7 5 1 3 2 0 8 4 8 .0 9 7 8 7 5 .8 0 1 5
117 81 7 8 .3 6 0 5 .4 0 7 4 5 8 0 .4 1 8 6 3 4 7 4 - 2 4 .9 8 8 7 6 5 5 7 9 .4 7 6 5 - 2 5 .9 3 0 9 6 1 7 .4 9 8 7 3 4 7 4 1 2 .0 9 1 3 3 4 7 6 1 7 .5 2 5 3 1 2 .1 1 7 9
U 81 7 8 .3 8 2 6 .4 4 4 5 8 0 8 .6 2 7 9 5 4 3 6 - 1 7 .8 1 6 5 4 5 8 0 7 .5 3 7 7 - 1 8 .9 0 6 8 8 4 5 .7 0 8 0 5 4 3 6 1 9 .2 6 3 5 5 4 3 8 4 5 .5 8 6 6 1 9 .1 4 2 1
LN 81 7 8 .3 1 0 5 8 .6 6 7 1 0 3 2 .7 7 9 2 2 6 8 - 2 5 .8 8 7 7 7 3 1 0 3 3 .0 6 1 - 2 5 .6 0 6 1 0 6 9 .8 5 9 3 2 6B 1 1 .1 9 2 3 2 6 8 1 0 7 1 .1 1 1 2 .4 4 3
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
MT PREDICTED MT PREDICTED H I PREDICTED HT PREDICTED
BASED CM DISTANCE BASED OH DISTANCE BASED OH DISTANCE BASED ON DISTANCE
DECADES H MEAN AGE HZ H U B DAXA FRCH MEAN EACH V IS IT FRCH MEAN MEAN DATA FRCH MEAN EACH V IS IT FRCM MEAN
S B e 9 0 .2 3 9 3 2 1 2 .2 6 5 2 7 8 5 5 - 1 B 0 .73472 2 0 6 .8 3 8 3 - 1 8 6 .1 6 1 7 3 2 2 .7 0 8 8 7 8 5 5 -7 0 .2 9 1 1 2 1 3 1 7 .6 8 3 3 - 7 5 .3 1 6 7
S I € 9 0 .2 646 4 3 5 .8 9 4 8 4 1 1 9 -2 1 0 .1 0 5 1 5 4 3 5 .1 3 4 9 - 2 1 0 .8 6 5 1 5 4 6 .3 3 8 4 4 1 1 9 -9 9 .6 6 1 5 5 8 5 4 5 .9 7 9 8 - 1 0 0 .0 2 0 2
SN 6 9 0 .2 8 3 9 6 4 6 .0 7 2 7 5 3 1 3 - 1 9 2 .9 2 7 2 4 6 4 5 .7 3 5 4 - 1 9 3 .2 6 4 6 7 5 6 .5 1 6 3 5 3 1 3 -8 2 .4 8 3 6 4 6 7 5 6 .5 8 0 4 - 8 2 .4 1 9 6
MT S 9 0 .2 647 4 1 6 .6 3 8 8 2 4 3 3 -2 3 0 .3 6 1 1 7 4 1 6 .0 2 7 8 - 2 3 0 .9 7 2 2 5 2 7 .0 8 2 4 2 4 3 3 -1 1 9 .9 1 7 5 7 5 2 6 .8 7 2 9 - 1 2 0 .1 2 7 1
H I 6 9 0 .2 8 60 6 4 5 .7 5 8 3 1 5 7 3 -2 1 4 .2 4 1 6 8 6 4 5 .4 5 8 4 - 2 1 4 .5 4 1 6 7 5 6 .2 0 1 9 1 5 7 3 -1 0 3 .7 9 8 0 8 7 5 6 .3 0 3 5 - 1 0 3 .6 9 6 5
MN 6 9 0 .2 1065 8 7 7 .8 0 6 3 6 6 3 1 -1 8 7 .1 9 3 6 3 8 7 7 .5 0 9 9 - 1 8 7 .4 9 0 1 9 B 8 .2 4 9 9 6 6 3 1 -7 6 .7 5 0 0 3 3 9 8 8 .3 5 5 - 7 6 .6 4 5
L E T 6 9 0 .2 1014 6 2 9 .1 6 2 1 2 2 0 6 -3 8 4 .8 3 7 8 7 6 2 9 .0 1 2 3 - 3 8 4 .9 8 7 7 7 3 9 .6 0 5 7 2 2 0 6 -2 7 4 .3 9 4 2 7 7 3 9 .8 5 7 4 - 2 7 4 .1 4 2 6
LX 6 9 0 .2 118 9 8 7 8 .3 8 6 2 7 1 3 9 -3 1 0 .6 1 3 7 2 8 7 8 .2 0 6 2 - 3 1 0 .7 9 3 8 9 8 8 .8 2 9 8 7 1 3 9 -2 0 0 .1 7 0 1 2 9 8 9 .0 5 1 2 -1 9 9 .9 4 8 8
LN 6 9 0 .2 1504 1 1 1 9 .9 0 1 2 9 4 1 -3 8 4 .0 9 8 7 0 1 1 1 9 .6 5 1 -3 8 4 .3 4 9 1 2 3 0 .3 4 4 8 9 4 1 - 2 7 3 .6 5 5 1 0 1 2 3 0 .4 9 6 - 2 7 3 .5 0 4
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
H I PREDICTED MT PREDICTED MT PREDICTED MT PREDICTED
BASED CN DISTANCE BASED ON DISTANCE BASED OS DISTANCE BASED ON DISTANCE
DECADE10 K MIAS ACE MX MEAN DAXA FRCM MEAN EACH V IS IT FRCM MEAN KEAN DAXA FRCH MEAN EACH V IS IT FROM KEAN
SW 2 98 28 5 2 1 2 .2 5 5 1 4 4 4 8 -7 2 ,7 4 4 8 5 5 2 1 2 .1 9 0 1 - 7 2 .8 0 9 9 3 8 4 .6 1 5 1 4 4 4 8 9 9 .6 1 5 1 4 4 4 3 8 4 .9 1 0 2 9 9 .9 1 0 2
S I 2 98 51 0 446.15746B 5B -6 3 .8 4 2 5 3 1 4 4 6 .0 1 4 6 - 6 3 .9 8 5 4 6 1 8 .5 1 7 4 6 8 5 8 1 0 8 .5 1 7 4 6 8 6 1 8 .7 3 4 7 1 0 8 .7 3 4 7
SB 2 98 88 2 6 7 4 .8 8 2 6 4 1 0 1 -2 0 7 .1 1 7 3 5 6 7 4 .8 4 5 3 - 2 0 7 .1 5 4 7 8 4 7 .2 4 2 6 4 1 0 1 -3 4 .7 5 7 3 5 8 8 4 7 .5 6 5 4 - 3 4 .4 3 4 6
M W 2 98 345 4 3 6 .2 6 7 1 6 8 7 5 9 1 .2 6 7 1 6 8 7 4 3 6 .2 3 2 9 1 .2 3 2 6 0 8 .6 2 7 1 6 8 7 5 2 6 3 .6 2 7 1 6 8 6 0 8 .9 5 2 2 6 3 .9 5 2
H I 2 98 630 6 7 2 .2 4 7 8 2 1 9 6 4 2 .2 4 7 8 2 1 9 6 7 2 .2 5 6 6 4 2 .2 5 6 6 8 4 4 .6 0 7 8 2 1 9 6 2 1 4 .6 0 7 8 2 1 8 4 4 .9 7 6 7 2 1 4 .9 7 6 7
y d 2 98 993 9 1 8 .6 0 3 4 9 6 - 7 4 .3 9 6 5 0 4 9 1 8 .5 5 8 8 - 7 4 .4 4 1 2 1 0 9 0 .9 6 3 4 9 6 9 7 .9 6 3 4 9 5 9 1 0 9 1 .2 7 9 9 8 .2 7 9
LW 2 98 705 6 5 5 .8 9 4 7 1 1 5 -4 9 .1 0 5 2 8 8 6 5 5 .9 1 3 2 - 4 9 .0 8 6 8 B 2 8 .2547 1 1 5 1 2 3 .2 5 4 7 1 1 8 2 8 .6 3 3 3 1 2 3 .6 3 3 3
L I 2 98 1 0 2 6 9 1 9 .4 5 5 1 4 4 4 8 -1 0 6 .5 4 4 8 5 9 1 9 .4 5 1 1 - 1 0 6 .5 4 8 9 1 0 9 1 .8 1 5 1 4 4 5 6 5 .8 1 5 1 4 4 4 1 0 9 2 .1 7 1 6 6 .1 7 1
IN 2 98 13 0 2 1 1 7 2 .4 8 7 2 7 3 8 - 1 2 9 .5 1 2 7 2 1 1 7 2 .4 9 7 - 1 2 9 .5 0 3 1 3 4 4 .8 4 7 2 7 3 8 4 2 .8 4 7 2 7 3 7 1 3 4 5 .2 1 7 4 3 .2 1 7
FORMULA 73A FORHDIA 73A FORMULA 73B FORMULA 73B
NX PREDICTED HT PREDICTED HT PREDICTED HE PREDICTED
BASED ON DISTANCE BASED OH DISTANCE BASED ON DISTANCE BASED ON DISTANCE
MDECADE2 N MEAN ACE HT MEAN DAXA FROM MEAN EACH V IS IT FRCM KEAN KEAN DATA FRCH MEAN EACH V IS IT FROM MEAN
SW 3 1 2 1 .5 1 9 9 .9 3 5 5 1 2 7 .3 4 3 8 2 4 4 - 7 2 .5 9 1 6 7 5 1 2 6 .6 3 5 7 - 7 3 .2 9 9 8 1 6 5 .4 4 6 3 2 4 4 - 3 4 .4 B 9 1 7 5 1 6 5 .4 3 2 B - 3 4 .5 0 2 7
S I 3 1 2 1 .5 2 8 2 .9 6 7 7 2 5 3 .0 7 0 1 7 2 9 6 -2 9 .8 9 7 5 2 7 2 5 2 .1 9 1 3 - 3 0 .7 7 6 4 2 9 1 .1 7 2 6 7 2 9 6 8 .2 0 4 9 7 2 9 5 2 9 0 .9 8 8 4 8 .0 2 0 7
SN 3 1 2 1 .5 3 7 3 .3 5 4 8 3 6 7 .8 7 1 2 4 7 8 -5 .4 8 3 5 5 2 1 3 6 7 .0 0 4 5 - 6 .3 5 0 3 4 0 5 .9 7 3 7 4 7 8 3 2 .6 1 8 9 4 7 8 4 0 5 .8 0 1 6 3 2 .4 4 6 8
M W 3 1 2 1 .5 2 5 7 .4 1 9 3 2 3 0 .0 6 7 4 5 5 9 2 -2 7 .3 5 1 8 4 4 2 2 9 .8 3 2 1 - 2 7 .5 8 7 2 2 6 8 .1 6 9 9 5 5 9 2 1 0 .7 5 0 6 5 5 9 2 6 8 .6 2 9 2 1 1 .2 0 9 9
H I 3 1 2 1 .5 3 5 8 .4 5 1 6 3 6 0 .9 6 3 7 3 0 7 7 2 .5 1 2 1 3 0 7 6 3 6 0 .5 4 9 5 2 .0 9 7 9 3 9 9 .0 6 6 2 3 0 7 7 4 0 .6 1 4 6 3 0 7 3 9 9 .3 4 6 5 4 0 .8 9 4 9
MN 3 1 2 1 .5 4 7 4 .9 6 7 7 4 8 6 .9 6 7 1 3 1 8 6 1 1 .9 9 9 4 3 1 8 4 8 6 .5 2 6 8 1 1 .5 5 9 1 5 2 5 .0 6 9 6 3 1 8 6 5 0 .1 0 1 9 3 1 8 5 2 5 .3 2 3 9 5 0 .3 5 6 2
LW 3 1 2 1 .5 3 9 0 .3 8 7 1 3 4 6 .8 8 2 4 1 3 2 5 - 4 3 .5 0 4 6 8 6 3 4 5 .3 1 1 9 - 4 5 .0 7 5 2 3 8 4 .9 8 4 9 1 3 2 5 - 5 .4 0 2 1 8 6 7 3 B 4 .1 0 B 9 - 6 .2 7 8 2
L I 3 1 2 1 .5 5 0 1 .2 9 0 3 4 8 5 .3 9 4 2 3 8 -1 5 .8 9 6 0 6 1 4 8 5 .0 7 0 2 - 1 6 .2 2 0 1 5 2 3 .4 9 6 7 3 8 2 2 .2 0 6 4 3 8 0 5 2 3 .8 6 7 2 2 2 .5 7 6 9
LN 3 1 2 1 .5 6 2 6 .7 0 9 7 6 1 7 .2 1 8 4 9 2 4 5 -9 .4 9 1 2 0 7 5 6 1 6 .8 1 0 9 - 9 .8 9 8 8 6 5 5 .3 2 0 9 9 2 4 5 2 8 .6 1 1 2 9 2 4 6 5 5 .6 0 8 1 2 8 .8 9 8 4
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
H I PREDICTED HT PREDICTED HT PREDICTED HE PREDICTED
BASED ON DISTANCE BASED CN DISTANCE BASED ON DISTANCE BASED CN DISTANCE
MDECADES H MEAN ACE HT MEAN DAXA FRCH KEAN EACH V IS IT FRCM MEAN MEAN DAXA FRCM MEAN EACH V IS IT FRCM MEAN
SW 1 9 7 2 9 .7 1 9 6 .8 7 3 1 1 3 9 .7 2 2 3 5 9 4 - 5 7 .1 5 0 7 4 0 1 3 9 .0 1 4 6 - 5 7 .8 5 8 5 1 4 1 .8 1 0 4 5 9 4 - 5 5 .0 6 2 6 4 0 1 4 1 .8 5 8 - 5 5 .0 1 5 1
S I 1 9 7 2 9 .7 2 7 6 .3 0 4 6 2 7 1 .8 1 1 5 8 5 7 2 -4 .4 9 3 0 1 4 2 2 7 1 .0 4 5 5 - 5 .2 5 9 1 2 7 3 .8 9 9 6 8 5 7 2 -2 .4 0 4 9 1 4 2 2 7 3 .8 8 9 1 - 2 .4 1 5 5
SN 19 7 2 9 .7 3 9 5 .5 7 3 6 4 0 0 .5 4 7 1 4 9 4 1 4 .9 7 3 5 4 9 4 0 3 9 9 .7 6 6 8 4 .1 9 3 2 4 0 2 .6 3 5 2 4 9 4 1 7 .0 6 1 6 4 9 4 0 4 0 2 .6 1 7 .0 3 6 4
M W 1 9 7 2 9 .7 2 5 7 .3 9 0 9 2 5 3 .5 9 1 9 5 8 6 4 -3 .7 9 B 9 4 1 3 2 5 3 .1 3 3 8 - 4 .2 5 7 1 2 5 5 .6 8 0 0 5 8 6 4 - 1 .7 1 0 8 4 1 3 2 5 5 .9 7 7 2 - 1 .4 1 3 7
H I 19 7 2 9 .7 3 7 3 .2 4 8 7 3 9 3 .0 5 4 9 5 2 2 1 9 .8 0 6 2 5 2 2 3 9 2 .7 7 3 4 1 9 .5 2 4 7 3 9 5 .1 4 3 0 5 2 2 2 1 .8 9 4 3 5 2 2 3 9 5 .6 1 6 8 2 2 .3 6 8 1
HH 1 9 7 2 9 .7 5 1 0 .3 6 5 5 5 3 2 .7 6 7 2 1 8 7 3 2 2 .4 0 1 7 1 8 7 5 3 2 .3 7 1 2 2 .0 0 5 5 5 3 4 .8 5 5 3 1 8 7 3 2 4 .4 8 9 8 1 8 7 5 3 5 .2 1 4 5 2 4 .8 4 9
IK 1 9 7 2 9 .7 3 9 5 .3 6 0 4 3 8 1 .3 4 2 3 1 8 0 6 - 1 4 .0 1 B 0 8 1 3 8 0 .2 3 - 1 5 .1 3 0 4 3 8 3 .4 3 0 4 1 8 0 6 - 1 1 .9 2 9 9 8 1 3 8 3 .0 7 3 5 - 1 2 .2 8 6 9
£ 1 1 9 7 2 9 . 7 5 3 8 .2 0 3 1 5 3 1 .4 7 9 0 2 9 0 5 - 6 .7 2 4 0 7 0 9 5 3 1 .2 2 8 2 - 6 .9 7 4 9 5 3 3 .5 6 7 1 2 9 0 5 - 4 .6 3 5 9 7 0 9 5 3 4 .0 7 1 6 - 4 .1 3 1 5
I S 19 7 2 9 .7 6 9 1 .7 9 6 9 6 7 5 .8 8 7 8 6 3 1 1 -1 5 .9 0 9 0 3 6 6 7 4 .7 3 1 4 - 1 7 .0 6 5 5 6 7 7 .9 7 5 9 6 3 1 1 - 1 3 .8 2 0 9 3 6 6 7 7 .5 7 4 8 - 1 4 .2 2 2 1
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
HT PREDICTED HT PREDICTED H I PREDICTED H I PREDICTED
BASED ON DISTANCE BASED ON DISTANCE BASED ON DISTANCE BASED ON DISTANCE
MDECADE4 N KEEN ACE HT MEAN DAXA FRCM MEAN EACH V IS IT FRCM MEAN KEAN DAXA FRCH MEAN EACH V IS IT FRCM KEAN
SW 203 3 9 . 6 2 0 1 .7 B 3 2 1 5 0 .3 9 0 0 9 6 5 8 -5 1 .3 9 3 1 0 3 1 4 9 .6 3 9 8 - 5 2 .1 4 3 4 1 2 5 .1 2 4 4 9 6 5 8 2 -7 6 .6 5 8 7 0 3 1 2 5 .2 5 6 1 - 7 6 .6 2 7 1
S I 203 3 9 . 6 3 0 0 .3 2 5 1 2 9 5 .5 8 7 0 3 3 7 9 -4 .7 3 8 0 6 6 2 2 9 5 .1 4 6 4 - 5 .1 7 8 7 2 7 0 .3 2 1 4 3 3 7 9 - 3 0 .0 0 3 6 6 6 2 7 0 .6 6 2 7 - 2 9 .6 6 2 4
SN 203 3 9 . 6 4 5 9 .5 7 6 4 4 3 5 .9 1 5 4 0 5 4 4 -2 3 .6 6 0 9 9 4 4 3 5 .3 9 2 7 - 2 4 .1 8 3 7 4 1 0 .6 4 9 8 0 5 4 4 -4 8 .9 2 6 5 9 4 4 1 0 .9 0 8 9 -4 B .6 6 7 5
M M 203 3 9 .6 2 7 5 .7 3 4 2 7 7 .4 0 9 1 8 5 9 4 1 .6 7 5 1 8 5 9 3 2 7 7 .1 1 9 4 1 .3 8 5 4 2 5 2 .1 4 3 5 8 5 9 4 -2 3 .5 9 0 4 1 4 2 5 2 .6 3 5 6 - 2 3 .0 9 8 4
H I 20 3 3 9 . 6 4 1 4 .3 5 4 7 4 3 3 .0 1 9 5 3 6 3 7 1 8 .6 6 4 8 3 6 3 4 3 2 .8 5 3 5 1 8 .4 9 8 8 4 0 7 .7 5 3 9 3 6 3 7 -6 .6 0 0 7 6 3 6 4 0 8 .3 6 9 7 - 5 .9 8 5
MN 2 0 3 3 9 .6 5 9 1 .5 7 6 4 5 8 6 .4 9 4 2 1 4 8 9 -5 .0 8 2 1 8 5 1 5 8 6 .3 1 9 8 - 5 .2 5 6 6 5 6 1 .2 2 8 6 1 4 8 9 -3 0 .3 4 7 7 8 5 5 6 1 .8 3 6 1 - 2 9 .7 4 0 3
IK 20 3 3 9 .6 42 6 4 2 1 .3 6 2 6 7 4 8 1 -4 .6 3 7 3 2 5 1 4 2 1 .0 5 0 7 - 4 .9 4 9 3 3 9 6 .0 9 7 0 7 4 8 1 -2 9 .9 0 2 9 2 5 3 9 6 .5 6 6 8 - 2 9 .4 3 3 2
L I 2 0 3 3 9 .6 5 8 5 .8 4 2 3 5 8 7 .6 5 0 9 0 0 3 3 1 .8 0 8 6 0 0 3 2 5 8 7 .5 8 7 5 1 .7 4 5 2 5 6 2 .3 8 5 3 0 0 3 3 - 2 3 .4 5 6 9 9 9 5 6 3 .1 0 3 7 - 2 2 .7 3 8 6
IN 203 3 9 . 6 7 9 3 .6 5 5 2 7 4 7 .4 3 4 3 1 8 1 4 -4 6 .2 2 0 8 8 1 7 4 7 .0 6 3 2 - 4 6 .5 9 2 7 2 2 .1 6 B 7 1 8 1 4 -7 1 .4 8 6 4 8 1 7 2 2 .5 7 9 7 - 7 1 .0 7 5 5
FORMULA 73A FORMULA 73A
HT PREDICTED HT PREDICTED
BASED OH D ISTM CE BASED m
MDCCADE5 N MZAH AGE m H EM DAIA ntO H H E M EACH V IS IT
SW 22 9 4 9 .6 2 0 4 .7 8 6 1 6 6 .3 0 1 1 3 8 9 3 - 3 B . 4 8 4 8 6 1 1 6 5 .5 1 1 5
s x 2 2 9 4 9 .6 3 0 6 .6 0 2 6 3 2 5 .4 6 4 1 5 0 9 5 1 8 .8 6 1 5 5 0 9 3 2 4 .7 5 2
SH 2 2 9 4 9 .6 4 9 5 .4 3 2 3 4 8 5 .0 0 6 0 8 8 4 2 -1 0 .4 2 6 2 1 1 4 7 9 .8 0 3 7
W* 2 2 9 4 9 .6 2 8 7 .2 4 0 2 3 0 6 .5 6 5 7 4 8 9 1 1 9 .3 2 5 5 4 8 9 3 0 5 .8 0 2 6
H I 2 2 9 4 9 .6 4 3 8 .8 9 0 8 4 7 6 .8 5 0 9 8 9 6 9 3 7 .9 6 0 1 8 9 6 4 7 6 .0 1 1 9
HH 2 2 9 4 9 . 6 6 1 5 .3 5 3 7 6 4 3 .7 6 6 4 4 2 3 2 8 .4 1 2 7 4 2 2 6 4 3 .8 9 2 8
LH 2 2 9 4 9 , 6 4 3 2 .1 0 4 8 462.410463B B 3 0 .3 0 5 6 6 3 8 4 6 2 .2 8 4 2
L I 229 4 9 .6 6 1 1 .4 4 9 8 6 4 4 .4 6 0 8 1 3 2 6 3 3 .0 1 1 0 1 3 2 6 4 4 .3 9 9 4
X JT 229 4 9 .6 8 1 5 .8 4 2 8 8 2 1 .2 8 2 2 3 7 0 7 5 .4 3 9 4 3 7 0 7 8 2 1 .5 5 5 6
TOKMULA 73A FORMULA 73A
HT PREDICTED XT PREDICTED
BASED CM D ISTM CE BASED OH
HDECAKfi H MEAH AGE m H EM DAIA FRCM H E M EACH V IS IT
SW 1 4 4 5 9 .5 2 1 4 .7 9 1 7 1 8 0 .9 7 4 9 7 2 5 3 -3 3 .8 1 6 7 2 7 1 8 0 .5 7 1 1
SX 1 44 5 9 .5 3 3 6 .7 5 3 4 8 .6 5 4 7 3 4 9 1 1 .9 0 4 7 3 4 8 3 4 9 .1 4 4 2
SN 1 44 5 9 .5 5 1 2 .1 2 5 5 1 5 .5 5 0 0 2 5 7 3 .4 2 5 0 2 5 7 0 5 1 6 .6 6 0 4
HH 1 44 5 9 .5 3 0 5 .2 0 8 3 3 2 9 .7 8 8 0 8 0 2 6 2 4 .5 7 9 7 8 0 2 3 3 0 .2 6 7 9
M X 1 44 5 9 .5 4 6 2 .9 5 8 3 5 1 3 .9 9 7 4 4 7 2 8 5 1 .0 3 9 1 4 7 2 5 1 5 .2 7 0 8
HH 144 5 9 .5 6 5 6 .1 6 6 7 6 9 7 .7 8 8 2 7 0 1 4 4 1 .6 2 1 5 7 0 1 6 9 9 .7 1 7
I X 1 4 4 5 9 .5 4 7 2 .8 3 3 3 5 0 2 .8 8 0 0 0 0 2 4 3 0 .0 4 6 7 0 0 2 5 0 4 .1 9 7 9
XX 14 4 5 9 .5 6 6 4 .9 5 8 3 7 0 0 .7 0 4 2 8 0 6 9 3 5 .7 4 5 9 8 0 6 7 0 2 .6 7 2 5
LN 1 4 4 5 9 .5 8 8 2 .2 0 8 3 8 9 1 .9 9 6 1 4 9 4 9 9 .7 8 7 8 4 9 4 8 8 9 4 .5 7 6 5
FORMULA 73A FORMULA 73A
HT PREDICTED HP PREDICTED
BASED OH D ISTM CE BASED ON
MDKGADZ7 N H U H ACT HP HEM DATA FECK H E M EACH V IS IT
SH 16 4 6 9 .6 2 5 2 .4 3 9 1 9 6 .0 3 5 5 1 6 2 8 -5 6 .4 0 3 4 8 3 1 9 5 .6 9 3 2
SX 16 4 6 9 .6 3 9 7 .2 4 3 9 3 7 6 .9 6 4 0 5 0 6 3 - 2 0 .2 7 9 8 4 9 3 7 7 .9 1 6 6
SH 164 6 9 .6 5 8 3 .1 3 4 2 5 7 1 .2 4 0 5 0 9 5 -1 1 .8 9 3 6 9 0 5 6 3 .2 9 9
M W 164 6 9 .6 3 5 0 .0 8 5 4 3 5 6 .0 4 2 2 4 2 9 9 5 .9 5 6 8 4 2 9 9 3 5 7 .1 2 1
M X 164 6 9 .6 5 3 0 .6 3 4 2 5 5 6 .9 4 0 5 4 7 2 5 2 6 .3 0 6 3 4 7 2 5 5 8 .9 2 2 4
HH 164 6 9 .6 7 4 0 .7 8 0 5 7 5 6 .1 0 9 7 6 0 5 7 1 5 .3 2 9 2 6 0 5 7 5 8 .9 6 2 3
U f 164 6 9 .6 5 5 6 .1 3 4 2 5 4 4 .7 2 7 4 7 6 7 4 -1 1 .4 0 6 7 2 3 5 4 6 .7 4 9 1
L I 164 6 9 .6 7 5 4 .8 6 5 B 7 5 8 .3 3 1 3 6 4 0 3 3 .4 6 5 5 6 4 0 2 7 6 1 .2 7 7 1
121 1 6 4 6 9 .6 9 6 9 .7 3 1 7 9 6 5 .4 6 8 0 2 6 6 3 - 4 .2 6 3 6 7 3 3 9 6 9 .2 5 1 4
FORMULA 73A FORMULA 73A
HT PREDICTED HT PREDICTED
BASED OH D IST M C E BASED OH
MDECADES N H E M ACT XT H E M DATA FROM H E M EACH V IS IT
SH 72 7 8 .3 2 8 2 .8 3 3 3 2 1 3 .9 3 1 1 7 7 8 8 -6 8 .9 0 2 1 2 2 2 1 3 .0 5 0 3
SX 72 7 8 .3 4 3 9 .6 6 6 7 4 0 4 .5 5 2 8 5 1 5 9 - 3 5 .1 1 3 8 4 8 4 0 4 .2 4 2 2
SH 72 7 8 .3 6 2 5 .1 6 6 7 5 9 8 .8 3 7 0 9 3 9 9 -2 6 .3 2 9 6 0 6 5 9 8 .7 6 7
M9 7 2 7 8 .3 4 0 4 .3 3 3 3 3 8 2 .3 1 9 7 0 2 8 8 -2 2 .0 1 3 5 9 7 3 8 2 .2 6 2 1
K I 7 2 7 8 .3 5 6 9 5 9 4 .6 5 4 8 0 7 8 2 2 5 .6 5 4 8 0 7 8 5 9 4 .9 0 8 6
HH 72 7 8 .3 7 8 0 .5 8 0 9 .4 5 8 3 5 9 8 4 2 8 .9 5 8 3 5 9 8 8 0 9 .7 9 5 3
TM 72 7 8 .3 6 1 1 .5 5 7 9 .8 5 7 6 5 0 7 6 -3 1 .6 4 2 3 4 9 5 7 8 .9 1 6 7
XX 72 7 8 .3 8 3 0 .1 6 6 7 8 0 8 .2 5 4 1 8 5 4 - 2 1 .9 1 2 5 1 4 8 0 7 .1 7 1 1
i n 72 7 8 .3 1 0 7 3 .8 3 3 1 0 3 2 .5 6 3 3 5 3 1 - 4 1 .2 6 9 6 4 6 1 0 3 3 .0 5 7
FORMULA 73B FORMULA 7 3 8
HT PREDICTED XT PREDICTED
DISTM CE BASED ON DISTM CE BASED ON D ISTM CE
FROM MEM H E M DATA FRCM H E M EACH V IB IT FRCH M EM
- 3 9 .2 7 4 5 1 3 1 .3 1 5 5 3 8 9 3 - 7 3 .4 7 0 4 6 1 1 3 1 .2 5 7 4 - 7 3 .5 2 8 6
1 8 .1 4 9 4 2 9 0 .4 7 8 5 5 0 9 5 - 1 6 .1 2 4 0 4 9 2 9 0 .4 9 8 - 1 6 .1 0 4 6
- 1 5 .6 2 8 6 4 5 0 .0 2 0 4 8 8 4 2 -4 5 .4 1 1 8 1 1 4 4 5 .5 4 9 7 - 4 9 .8 8 2 6
1 8 .5 6 2 4 2 7 1 .5 8 0 1 4 8 9 1 -1 5 .6 6 0 0 5 1 2 7 1 .5 4 8 5 - 1 5 .6 9 1 7
3 7 .1 2 1 1 4 4 1 .8 6 5 3 8 9 6 9 2 .9 7 4 5 8 9 6 9 4 4 1 .7 5 7 6 2 .8 6 6 8
2 8 .5 3 9 1 6 0 8 .7 8 0 8 4 2 3 - 6 .5 7 2 8 5 7 7 6 0 9 .6 3 9 - 5 .7 1 4 7
3 0 .1 7 9 4 4 2 7 .4 2 4 8 6 3 8 8 - 4 .6 7 9 9 3 6 1 4 2 8 .0 3 0 2 - 4 .0 7 4 6
3 2 .9 4 9 6 6 0 9 .4 7 5 2 1 3 2 6 - 1 .9 7 4 5 8 6 7 6 1 0 .1 4 5 1 - 1 .3 0 4 7
5 .7 1 2 8 7 8 6 .2 9 6 6 3 7 0 7 - 2 9 .5 4 6 1 6 2 7 8 7 .3 0 1 5 - 2 8 .5 4 1 3
FORMULA 73B FORKUXA 73B
HT PREDICTED HT PREDICTED
DISTM CE BASED ON DISTM CE BASED ON DISTM CE
FRCH H E M H E M DATA FRCH H EM EACH V IS IT FRCH H E M
- 3 4 .2 2 0 6 1 5 5 .0 1 2 2 2 8 7 8 -5 9 .7 7 9 4 7 1 1 5 4 .5 6 2 4 - 6 0 .2 2 9 3
1 2 .3 9 4 2 3 2 2 .6 9 1 9 9 1 1 5 -1 4 .0 5 8 0 0 8 3 2 3 ,1 3 5 5 - 1 3 .6 1 4 5
4 .5 3 5 4 4 8 9 .5 8 7 2 8 1 9 5 -2 2 .5 3 7 7 1 8 4 9 0 .6 5 1 7 - 2 1 .4 7 3 3
2 5 .0 5 9 6 3 0 3 .8 2 5 3 3 6 5 1 -1 .3 8 2 9 6 3 4 3 0 4 .2 5 9 1 - 0 .9 4 9 2
5 2 .3 1 2 5 4 8 8 .0 3 4 7 0 3 5 3 2 5 .0 7 6 4 0 3 5 4 8 9 .2 6 1 9 2 6 .3 0 3 6
4 3 .5 5 0 3 6 7 1 .8 2 5 5 2 6 3 9 1 5 .6 5 8 8 2 6 3 6 7 3 .7 0 8 3 1 7 .5 4 1 6
3 1 .3 6 4 6 4 7 6 .9 1 7 2 5 6 4 9 4 .0 8 3 9 5 6 4 9 4 7 8 .1 8 9 5 .3 5 5 7
3 7 .7 1 4 2 6 7 4 .7 4 1 5 3 6 9 4 9 .7 8 3 2 3 6 9 4 6 7 6 .6 6 4 1 1 .7 0 5 7
1 2 .3 6 B 2 8 6 6 .0 3 3 4 0 5 7 4 -1 6 .1 7 4 B 9 4 8 6 8 .5 6 8 1 - 1 3 .6 4 0 2
FORMULA 73B FORMULA 73B
XT PREDICTED HP PREDICTED
D ISTM CE BASED ON DISTM CE BASED ON DISTM CE
FRCH H E M H E M DATA FRCH H EM EACH V IB IT FRCH H E M
- 5 6 .7 4 5 8 1 9 8 .3 3 7 9 0 0 2 8 - 5 4 .1 0 1 0 9 9 1 9 6 .8 7 5 5 - 5 5 .5 6 3 5
- 1 9 .3 2 7 3 3 7 9 .2 6 6 4 3 4 6 3 -1 7 .9 7 7 4 6 5 3 7 9 .0 9 8 9 - 1 8 .1 4 5
- 1 9 .8 3 5 2 5 7 3 .5 4 2 8 9 3 5 -9 .5 9 1 3 0 6 4 5 6 4 .4 8 1 1 - 1 8 .6 5 3 1
7 .0 3 5 6 3 5 8 .3 4 4 6 2 6 9 9 8 .2 5 9 2 2 6 9 9 3 5 8 .3 0 3 3 8 .2 1 7 9
2 8 .2 8 8 2 5 5 9 .2 4 2 9 3 1 2 5 2 8 .6 0 8 7 3 1 2 5 6 0 .1 0 4 5 2 9 .4 7 0 3
1 8 .1 8 1 8 7 5 8 .4 1 2 1 4 4 5 7 1 7 .6 3 1 6 4 4 5 7 6 0 .1 4 4 4 1 9 .3 6 3 9
- 9 .3 8 5 1 5 4 7 .0 2 9 8 6 0 7 4 - 9 .1 0 4 3 3 9 2 5 4 7 .9 3 1 3 -B .2 0 2 9
6 .4 1 1 3 7 6 0 .6 3 3 7 4 8 0 3 5 .7 6 7 9 4 8 0 2 7 6 2 .4 5 9 2 7 .5 9 3 4
- 0 .4 8 0 3 9 6 7 .7 7 0 4 1 0 6 3 - 1 .9 6 1 2 8 9 3 9 7 0 .4 3 4 3 0 .7 0 2 6
FORMULA 73B FORMULA 73B
HT PREDICTED HT PREDICTED
D ISTM C E BASED ON D ISTM C E BASED OH D ISTM C E
FRCM H EM H E M DATA FRCH H EM EACH V IS IT FRCH H E M
- 6 9 .7 8 3 2 5 1 .0 1 1 2 7 7 8 8 - 3 1 .8 2 2 0 2 2 2 5 1 .2 6 6 5 - 3 1 .5 6 6 8
- 3 5 .4 2 4 5 4 4 1 .6 3 2 9 5 1 5 9 1 .9 6 6 2 5 1 5 9 4 4 2 .4 5 8 4 2 .7 9 1 7
- 2 6 .3 9 9 7 6 3 5 .9 1 7 1 9 3 9 9 1 0 .7 5 0 4 9 3 9 6 3 6 .9 8 3 2 1 1 .8 1 6 5
- 2 2 .0 7 1 2 4 1 9 .3 9 9 8 0 2 8 8 1 5 .0 6 6 5 0 2 8 4 2 0 .4 7 8 5 1 6 .1 4 5 2
2 5 .9 0 8 6 6 3 1 .7 3 4 9 0 7 8 2 6 2 .7 3 4 9 0 7 8 6 3 3 .1 2 4 8 6 4 .1 2 4 8
2 9 .2 9 5 3 8 4 6 .5 3 8 4 5 9 8 4 6 6 .0 3 8 4 5 9 8 8 4 8 .0 1 1 6 6 7 .5 1 1 6
- 3 2 .5 8 3 3 6 1 6 .9 3 7 7 5 0 7 6 5 .4 3 7 7 5 0 7 5 6 1 7 .1 3 2 8 5 .6 3 2 8
- 2 2 .9 9 5 6 8 4 5 .3 3 4 2 8 5 4 1 5 .1 6 7 5 8 5 3 8 4 5 .3 8 7 3 1 5 .2 2 0 6
- 4 0 .7 7 6 1 0 6 9 .6 4 3 4 5 3 1 - 4 .1 8 9 5 4 6 9 1 0 7 1 .2 7 3 - 2 . 5 6
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
MT PREDICTED I ts PREDICTED MI PREDICTED HT PREDICTED
BASED CM DISTANCE BASED OH DISTANCE BASED OH DISTANCE BASED CH DISTANCE
KDECME9 H H U H ASS MT U A H DATA FROC MEAN EACH V IS IT FROM HEAH MEAN DATA TR O f MEAN EACH V IS IT FRCH MEAN
SH 5 9 0 .2 3 9 0 2 0 8 .0 9 8 8 3 1 8 8 -1 8 1 .9 0 1 1 6 2 0 0 .6 1 0 2 - 1 8 9 .3 8 9 8 3 1 8 .5 4 2 4 3 1 8 8 -7 1 ,4 5 7 5 6 8 3 0 5 .7 7 6 2 - 8 4 .2 2 3 8
S I 5 9 0 .2 6 4 6 .8 4 3 9 .2 1 9 4 0 3 9 6 - 2 0 7 .5 8 0 5 9 4 3 6 .3 4 6 4 - 2 1 0 .4 5 3 6 5 4 9 .6 6 3 0 0 3 9 6 - 9 7 .1 3 6 9 9 6 5 4 1 .5 1 2 4 - 1 0 5 .2 8 7 6
SH 5 9 0 .2 8 5 0 .8 6 4 8 .1 3 8 2 1 3 7 6 -2 0 2 .6 6 1 7 8 6 4 4 .6 0 4 9 - 2 0 6 .1 9 5 1 7 5 8 .5 8 1 8 1 3 7 6 - 9 2 .2 1 8 1 8 6 7 4 9 .7 7 0 9 - 1 0 1 .0 2 9 1
US 5 9 0 .2 6 6 8 .4 4 1 9 .2 4 9 6 5 5 1 3 -2 4 9 .1 5 0 3 4 4 1 6 .5 7 5 8 - 2 5 1 .8 2 4 2 5 2 9 .6 9 3 2 5 5 1 3 - 1 3 8 .7 0 6 7 4 5 2 1 .7 4 1 8 - 1 4 6 .6 5 8 2
H I 5 9 0 .2 8 6 7 .6 6 4 6 .8 6 3 4 5 9 4 9 -2 2 0 .7 3 6 5 4 6 4 3 .3 1 2 9 - 2 2 4 .2 8 7 1 7 5 7 .3 0 7 0 5 9 4 9 - 1 1 0 .2 9 2 9 4 7 4 8 .4 7 8 9 - 1 1 9 .1 2 1 1
HH 5 9 0 .2 1 0 5 2 .4 8 7 8 .7 6 2 4 6 7 9 8 -1 7 3 .6 3 7 5 3 6 7 4 .0 5 5 - 1 7 8 .3 4 5 9 8 9 .2 0 6 0 6 7 9 8 -6 3 .1 9 3 9 3 2 9 7 9 .2 2 1 1 - 7 3 .1 7 8 9
LH 5 9 0 .2 1 0 0 4 .4 6 2 8 .7 7 2 6 1 5 8 1 - 3 7 5 .6 2 7 3 8 6 2 5 .4 3 3 5 - 3 7 8 .9 6 6 5 7 3 9 .2 1 6 2 1 5 8 1 -2 6 5 .1 8 3 7 8 7 3 0 .5 9 9 6 - 2 7 3 .8 0 0 4
I I 5 9 0 .2 1 1 8 6 .8 8 7 7 .8 0 6 3 6 6 3 1 - 3 0 8 .9 9 3 6 3 8 7 3 .1 8 9 9 - 3 1 3 .6 1 0 1 9 8 8 .2 4 9 9 6 6 3 1 -1 9 8 .5 5 0 0 3 9 7 8 .3 5 6 - 2 0 8 .4 4 4
XH S 9 0 .2 1 4 8 4 .4 1 1 2 0 .5 0 8 9 5 5 8 -3 6 3 .8 9 1 0 4 1 1 1 4 .6 3 9 - 3 6 9 .7 6 1 1 2 3 0 .9 5 2 5 5 5 8 -2 5 3 .4 4 7 4 4 1 2 1 9 .8 0 5 - 2 6 4 .5 9 5
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
MT PREDICTED MT PREDICTED ME PREDICTED MT PREDICTED
BASED ON DISTANCE BASED OH DISTANCE BASED O S DISTANCE BASED OH DISTANCE
HDECADE10 H MUM ACT MT HEAH DATA FROM MEAN EACH V IS IT FRCH MEAN HEAH DATA FRCK MEAN EACH V IS IT FRCH MEAN
s tr 2 98 2 85 2 1 2 .2 5 5 1 4 4 4 8 -7 2 .7 4 4 8 5 5 2 1 2 .1 9 0 1 - 7 2 .8 0 9 9 3 8 4 .6 1 5 1 4 4 4 8 9 9 .6 1 5 1 4 4 4 3 8 4 .9 1 0 2 9 9 .9 1 0 2
S I 2 98 51 0 4 4 6 .1 5 7 4 6 8 5 8 -6 3 .8 4 2 5 3 1 4 4 6 .0 1 4 6 -6 3 .9 B 5 4 6 1 8 .5 1 7 4 6 8 5 8 1 0 8 .5 1 7 4 6 8 6 1 8 .7 3 4 7 1 0 8 .7 3 4 7
SH 2 98 88 2 6 7 4 .8 8 2 6 4 1 0 1 - 2 0 7 .1 1 7 3 5 6 7 4 .8 4 5 3 - 2 0 7 .1 5 4 7 8 4 7 .2 4 2 6 4 1 0 1 -3 4 .7 5 7 3 5 8 8 4 7 .5 6 5 4 - 3 4 .4 3 4 6
HH 2 98 3 4 5 4 3 6 .2 6 7 1 6 8 7 5 9 1 .2 6 7 1 6 8 7 4 3 6 .2 3 2 9 1 .2 3 2 6 0 8 .6 2 7 1 6 8 7 5 2 6 3 .6 2 7 1 6 8 6 0 8 .9 5 2 2 6 3 .9 5 2
H I 2 98 630 6 7 2 .2 4 7 8 2 1 9 6 4 2 .2 4 7 8 2 1 9 6 7 2 .2 5 6 6 4 2 .2 5 6 6 8 4 4 .6 0 7 8 2 1 9 6 2 1 4 .6 0 7 8 2 1 8 4 4 .9 7 6 7 2 1 4 .9 7 6 7
HH 2 98 993 9 1 8 .6 0 3 4 9 6 -7 4 .3 9 6 5 0 4 9 1 8 .5 5 8 8 - 7 4 .4 4 1 2 1 0 9 0 .9 6 3 4 9 6 9 7 .9 6 3 4 9 5 9 1 0 9 1 .2 7 9 9 8 .2 7 9
LR 2 98 705 6 5 5 .8 9 4 7 1 1 5 -4 9 .1 0 5 2 8 8 6 5 5 .9 1 3 2 - 4 9 .0 8 6 8 8 2 8 .2 5 4 7 1 1 5 1 2 3 .2 5 4 7 1 1 8 2 8 .6 3 3 3 1 2 3 .6 3 3 3
L I 2 98 1 0 2 6 9 1 9 .4 5 5 1 4 4 4 8 -1 0 6 .5 4 4 8 5 9 1 9 .4 5 1 1 - 1 0 6 .5 4 8 9 1 0 9 1 .8 1 5 1 4 4 5 6 5 .8 1 5 1 4 4 4 1 0 9 2 .1 7 1 6 6 ,1 7 1
LN 2 98 130 2 1 1 7 2 .4 8 7 2 7 3 8 - 1 2 9 .5 1 2 7 2 1 1 7 2 .4 9 7 - 1 2 9 .5 0 3 1 3 4 4 .8 4 7 2 7 3 8 4 2 .8 4 7 2 7 3 7 1 3 4 5 .2 1 7 4 3 .2 1 7
FORKOLA 73A FORMULA 73A FORMULA 73B FORMULA 73B
HT PREDICTED HT PREDICTED HT PREDICTED MT PREDICTED
BASED OH DISTANCE BASED ON DISTANCE BASED OH DXSTAHCE BASED OH DISTANCE
FDECADZ2 H MEAN ACT MT U A H DATA FRCH HEAH EACH V IS IT FRCM HEAH MEAN DATA FRCM HEAH EACH V IS IT FRCM MEAN
SH 4 2 3 .8 1 77 1 3 5 .0 7 4 0 4 6 9 1 -4 1 .9 2 5 9 5 3 1 3 4 .5 1 9 1 - 4 2 .4 8 0 9 1 6 1 .8 5 3 6 4 6 9 1 - 1 5 .1 4 6 3 5 3 1 6 1 .5 5 1 6 - 1 5 .4 4 8 4
S I 4 2 3 .8 2 2 0 .5 2 5 9 .9 5 6 5 9 8 2 9 3 9 .4 5 6 5 9 8 2 2 5 9 .0 6 6 1 3 8 .5 6 6 1 2 8 6 .7 3 6 1 9 8 2 9 6 6 .2 3 6 1 9 8 2 2 8 6 .0 9 8 6 6 5 .5 9 B 6
SH 4 2 3 .8 360 3 7 5 .1 8 2 5 6 0 1 2 1 5 .1 8 2 5 6 0 1 3 7 3 .7 9 9 2 1 3 .7 9 9 2 4 0 1 .9 6 2 1 6 0 1 2 4 1 .9 6 2 1 6 0 1 4 0 0 .8 3 1 6 4 0 .8 3 1 6
M 4 2 3 .8 2 2 0 .5 2 3 9 .7 7 9 4 1 6 6 1 1 9 .2 7 9 4 1 6 6 2 3 9 .4 5 3 1 1 8 .9 5 3 1 2 6 6 .5 5 9 0 1 6 6 1 4 6 .0 5 9 0 1 6 6 2 6 6 .4 B 5 6 4 5 .9 8 5 6
MI 4 2 3 .8 3 3 0 3 6 8 .1 0 0 5 3 1 5 2 3 8 .1 0 0 5 3 1 5 3 6 7 .7 1 4 8 3 7 .7 1 4 8 3 9 4 .8 8 0 1 3 1 5 2 6 4 .8 8 0 1 3 1 5 3 9 4 .7 4 7 3 6 4 .7 4 7 3
HH 4 2 3 .8 4 8 6 5 0 0 .4 6 4 1 2 4 5 6 1 4 .4 6 4 1 2 4 5 4 9 9 .7 6 2 7 1 3 .7 6 2 7 5 2 7 .2 4 3 7 2 4 5 6 4 1 .2 4 3 7 2 4 5 5 2 6 .7 9 5 2 4 0 .7 9 5 2
IH 4 2 3 .8 3 4 0 .5 3 5 9 .7 3 9 1 6 B 1 7 1 9 .2 3 9 1 6 8 1 3 5 9 .4 4 2 3 1 8 .9 4 2 3 3 8 6 .5 1 8 7 6 8 1 7 4 6 .0 1 8 7 6 8 1 3 8 6 .4 7 4 8 4 5 .9 7 4 8
L I 4 2 3 .8 47 1 4 9 9 .1 8 0 3 2 9 3 2 2 8 .1 8 0 3 2 9 3 4 9 8 .7 5 7 2 7 .7 5 7 5 2 5 .9 5 9 9 2 9 3 2 5 4 .9 5 9 9 2 9 3 5 2 5 .7 8 9 4 5 4 .7 8 9 4
LH 4 2 3 .8 7 23 6 3 4 .9 5 8 0 4 8 6 9 -8 8 .0 4 1 9 5 1 6 3 4 .4 8 4 4 - S 8 .5 1 5 6 6 6 1 .7 3 7 6 4 8 6 9 -6 1 .2 6 2 3 5 1 6 6 1 .5 1 7 - 6 1 .4 8 3
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
HT PREDICTED MT PREDICTED ME PREDICTED HT PREDICTED
BASED DISTANCE BASED OH DISTANCE BASED O S DISTANCE BASED OS DISTANCE
FDECADE3 N H U H ACT h t U A H DATA FRCH HEAH EACH V IS IT FROM HEAH HEAH DATA FR fK KEAN EACH V IS IT FRCH HEAH
SH 47 3 0 . 6 2 0 6 .6 8 0 8 1 3 6 .1 2 3 5 7 0 6 4 - 7 0 .5 5 7 2 2 9 1 3 5 .1 5 2 8 - 7 1 .5 2 8 1 3 4 .9 9 5 9 7 0 6 4 -7 1 .6 8 4 B 2 9 1 3 4 .5 9 2 2 -7 2 .0 8 B 6
S I 47 3 0 . 6 2 6 6 .4 2 5 5 2 7 6 .7 1 9 8 5 8 4 4 1 0 .2 9 4 3 5 S 4 2 7 6 .2 6 2 9 9 .8 3 7 4 2 7 5 .5 9 2 2 5 8 4 4 9 .1 6 6 7 5 B 4 4 2 7 5 .7 0 2 3 9 .2 7 6 8
SH 47 3 0 . 6 3 6 6 .7 6 6 4 0 5 .0 9 7 3 9 8 2 3 3 8 .3 3 1 3 9 8 2 4 0 4 .6 5 8 3 7 .8 9 2 4 0 3 .9 6 9 7 9 8 2 3 3 7 .2 0 3 7 9 8 2 4 0 4 .0 9 7 3 3 7 .3 3 1 3
HH 47 3 0 . 6 2 5 8 .8 9 3 6 2 5 3 .5 1 9 8 5 7 9 4 -5 .3 7 3 7 4 2 0 2 5 3 .4 3 8 7 - 5 ,4 5 4 9 2 5 2 .3 9 2 2 5 7 9 4 -6 .5 0 1 3 4 2 0 2 5 2 .8 7 8 - 6 .0 1 5 6
m 47 3 0 . 6 3 6 9 .4 4 6 B 3 9 7 .6 3 9 2 4 1 8 7 2 8 .1 9 2 4 4 1 8 3 9 7 .5 5 3 2 2 8 ,1 0 6 4 3 9 6 .5 1 1 6 4 1 8 7 2 7 .0 6 4 8 4 1 8 3 9 6 .9 9 2 6 2 7 .5 4 5 8
HH 47 3 0 . 6 4 7 9 .7 4 4 7 5 3 7 .1 7 4 5 8 9 3 1 5 7 .4 2 9 8 8 9 3 5 3 5 .8 4 1 7 5 6 .0 9 7 5 3 6 .0 4 6 9 8 9 3 1 5 6 .3 0 2 2 8 9 3 5 3 5 .2 8 1 1 5 5 .5 3 6 4
LH 47 3 0 . 6 4 0 3 .5 3 1 9 3 8 5 .7 3 6 3 8 3 8 2 - 1 7 .7 9 5 5 1 6 3 8 5 .7 5 9 8 -1 7 ,7 7 2 1 3 8 4 .6 0 8 7 8 3 8 2 -1 8 .9 2 3 1 1 6 3 8 5 .1 9 9 1 - 1 8 .3 3 2 8
L I 47 3 0 .6 5 1 8 .4 2 5 5 5 3 7 .1 8 7 4 6 B 4 9 1 8 .7 6 1 9 6 8 4 5 3 7 .2 3 8 5 1 8 .8 1 3 5 3 6 .0 5 9 8 6 8 4 9 1 7 .6 3 4 3 6 8 4 5 3 6 .6 7 8 1 8 .2 5 2 5
IN 47 3 0 .6 6 7 6 .0 8 5 1 6 8 3 .7 0 5 5 9 1 7 6 7 .6 2 0 4 9 1 7 6 6 B 3 .7 9 6 7 7 .7 1 1 6 6 8 2 .5 7 7 9 9 1 7 6 6 .4 9 2 8 9 1 7 6 6 8 3 .2 3 6 1 7 .1 5 1
£
FORMULA 73A FORMULA 73A FORMULA 73B FORMULA 73B
ME PREDICTED MT PREDICTED ME PREDICTED MT PREDICTED
BASED OB DISTANCE ba se d OH DISTANCE BASED ON DISTANCE BASED OS DISTABCE
f d E c a r r i h m ean l a HT HEAH DATA FRCM MEAN EACH V IS IT FROM MEAN MEAN DATA FROM HEAH EACH V IS IT FROM MEAN
SH 47 3 9 . 5 1 9 4 .0 4 2 6 1 4 6 .2 6 1 6 2 8 2 5 -4 7 .7 8 0 9 7 1 1 4 5 .2 4 5 5 - 4 8 .7 9 7 1 1 2 1 .1 8 4 1 2 8 2 4 7 -7 2 .8 5 8 4 7 1 1 2 0 .9 1 3 4 - 7 3 .1 2 9 2
S I 4 7 3 9 .5 2 6 1 .8 2 9 8 2 9 8 .5 9 2 0 2 7 4 4 3 6 .7 6 2 2 2 7 4 2 9 7 .7 1 6 5 3 5 .8 8 6 7 2 7 3 .5 1 4 5 2 7 4 4 1 1 .6 8 4 7 2 7 4 2 7 3 .3 8 4 4 1 1 .5 5 4 6
SH 47 3 9 .5 3 6 4 .8 5 1 1 4 4 2 .7 3 7 4 8 4 6 7 7 7 .8 8 6 3 8 4 6 4 4 1 .9 5 7 3 7 7 .1 0 6 2 4 1 7 .6 5 9 9 8 4 6 7 5 2 .8 0 8 8 8 4 6 4 1 7 .6 2 5 2 5 2 .7 7 4 1
tm 47 3 9 .5 2 5 4 .1 7 0 2 2 7 8 .9 2 4 5 3 6 3 2 2 4 .7 5 4 3 3 6 3 2 7 8 .5 0 9 3 2 4 .3 3 9 1 2 5 3 .8 4 7 0 3 6 3 2 -0 .3 2 3 1 6 3 6 2 5 4 .1 7 7 2 0 .0 0 7
MI 47 3 9 . 5 3 6 3 .1 9 1 5 4 3 5 .8 2 9 0 9 0 9 9 7 2 .6 3 7 5 9 0 9 4 3 5 .5 2 3 1 7 2 .3 3 1 6 4 1 0 .7 5 1 5 9 0 9 9 4 7 .5 6 0 0 9 0 9 4 1 1 .1 9 1 4 7 .9 9 9 5
HH 47 3 9 .5 4 9 1 .1 0 6 4 5 8 9 .8 5 1 6 3 0 7 9 9 8 .7 4 5 2 3 0 7 5 8 9 .4 8 1 1 9 8 .3 7 4 7 5 6 4 .7 7 4 1 3 0 7 9 7 3 .6 6 7 7 3 0 7 5 6 5 .1 4 9 7 4 .0 4 2 6
IW 47 3 9 .5 3 8 5 .6 5 9 6 4 2 2 .3 2 6 0 5 4 6 7 3 6 .6 6 6 4 5 4 6 4 2 2 .1 4 7 9 3 6 .4 8 8 3 3 9 7 .2 4 8 5 5 4 6 7 1 1 .5 8 8 9 5 4 6 3 9 7 .8 1 5 8 1 2 .1 5 6 2
L I 47 3 9 .5 5 2 0 .9 7 8 7 5 8 8 .0 1 8 5 6 6 9 6 6 7 .0 3 9 8 6 6 9 5B 7 .8 1 4 6 6 .8 3 5 3 5 6 2 .9 4 1 0 6 6 9 6 4 1 .9 6 2 3 6 6 9 5 6 3 .4 8 1 8 4 2 .5 0 3 1
LN 47 3 9 .5 6 7 1 .2 3 4 1 7 4 9 .3 0 0 3 1 4 0 7 7 B .0662 1 4 0 7 4 9 .0 0 9 6 7 7 .7 7 5 5 7 2 4 .2 2 2 8 1 4 0 7 5 2 .9 8 8 7 1 4 0 7 2 4 .6 7 7 4 5 3 .4 4 3 3
FORMULA 73A FORMOLA 73A FORKOLA 73S FORMOLA 73 B
MT PREDICTED MI PREDICTED MI PREDICTED HT PREDICTED
BASED ON DISTANCE BASED ON d is t a n c e BASED OB DISTANCE BASED ON DISTANCE
FDECADE5 H HEAH AGE KT HEAH DATA FROM HEAH EACH V IS IT FRCM HEAH KEAH DATA FRCH MEAN EACH V IS IT FROM HEAH
SH 42 50 2 0 4 .1 4 2 9 1 6 4 .5 2 7 1 8 4 6 7 -3 9 .6 1 5 7 1 5 1 6 3 .8 0 5 8 - 4 0 .3 3 7 1 1 2 9 .5 2 7 1 8 4 6 7 -7 4 .6 1 5 7 1 5 1 2 9 .6 0 9 4 -7 4 .5 3 3 5
S I 42 50 29 7 3 2 8 .2 3 8 8 0 4 2 3 3 1 .2 3 8 8 0 4 2 3 2 7 .9 4 1 8 3 0 .9 4 1 8 2 9 3 .2 3 8 8 0 4 2 3 - 3 .7 6 1 1 9 5 7 2 9 3 .7 4 5 5 - 3 .2 5 4 5
SH 42 50 4 1 4 .7 1 4 3 4 8 5 .6 6 3 5 1 8 8 1 7 0 .9 4 9 2 1 8 8 4 8 5 .2 2 0 9 7 0 .5 0 6 6 4 5 0 .6 6 3 5 1 8 8 1 3 5 .9 4 9 2 1 8 8 4 5 1 .0 2 4 6 3 6 .3 1 0 3
HH 42 50 2 8 2 .7 1 4 3 3 0 5 .6 1 5 1 8 4 4 6 2 2 .9 0 0 8 8 4 4 3 0 5 .5 6 6 3 2 2 .8 5 2 2 7 0 . 6151B 446 -1 2 .0 9 9 1 1 5 2 7 1 .3 6 9 9 - 1 1 .3 4 4 4
H I 42 50 408 4 7 8 .3 9 2 8 8 7 4 5 7 0 .3 9 2 8 8 7 4 4 7 8 .3 8 1 5 7 0 .3 8 1 5 4 4 3 .3 9 2 8 8 7 4 5 3 5 .3 9 2 8 8 7 4 4 4 4 .1 8 5 3 6 .1 8 5
MN 42 50 5 5 9 .4 2 8 6 6 4 9 .4 8 6 5 9 1 0 7 9 0 .0 5 7 9 9 1 0 6 4 9 .4 8 4 4 9 0 .0 5 5 8 6 1 4 .4 8 6 5 9 1 0 7 5 5 .0 5 7 9 9 1 0 6 1 5 .2 8 8 5 5 .8 5 9 4
LH 42 50 4 3 6 .7 1 4 3 4 6 4 .7 8 6 6 3 1 6 9 2 8 .0 7 2 3 3 1 6 4 6 4 .8 7 0 5 2 8 .1 5 6 2 4 2 9 .7 8 6 6 3 1 6 9 -6 .9 2 7 6 6 8 3 4 3 0 .6 7 4 2 - 6 .0 4 0 1
L I 42 50 5 7 7 .4 2 8 6 6 4 8 .4 9 3 4 2 1 3 3 7 1 .0 6 4 8 2 1 3 6 4 8 .6 0 2 5 7 1 .1 7 3 9 6 1 3 .4 9 3 4 2 1 3 3 3 6 .0 6 4 8 2 1 3 6 1 4 .4 0 6 1 3 6 .9 7 7 5
IB 42 50 7 6 0 .5 7 1 4 8 1 9 .7 8 3 3 5 8 1 1 5 9 .2 1 1 9 5 8 1 8 1 5 .7 9 6 3 5 5 .2 2 4 9 7 8 4 .7 8 3 3 5 8 1 1 2 4 .2 1 1 9 5 8 1 7 B 1 .5 9 9 9 2 1 .0 2 8 5
FORMULA 73A FORMULA 73A FORKOLA 73B FORMULA 73B
ME PREDICTED ME PREDICTED MT PREDICTED M I PREDICTED
BASED OH DISTANCE BASED ON DISTANCE BASED ON DISTANCE BASED OH DISTANCE
m t a r z e N MEAN ASX MT MEAN DATA FRCH MEAN EACH V IS IT FRCM HEAH MEAN SATA FRCH HEAH EACH V IS IT FRCH HEAN
SH 68 5 9 .4 2 1 9 .0 8 8 2 1 8 0 .2 7 1 4 4 0 9 3 -3 8 .8 1 6 7 5 9 1 7 9 .3 5 6 - 3 9 .7 3 2 2 1 5 3 .2 2 3 8 4 0 9 3 -6 5 .8 6 4 3 5 9 1 5 2 .9 7 7 4 - 6 6 .1 1 0 8
S I 68 5 9 .4 3 1 5 .2 6 4 7 3 5 5 .2 0 8 9 1 9 7 6 3 9 .9 4 4 2 1 9 7 3 5 4 .6 9 2 4 3 9 .4 2 7 7 3 2 8 .1 6 1 3 1 9 7 6 1 2 .8 9 6 6 1 9 7 3 2 8 .3 1 3 9 1 3 .0 4 9 2
SH 68 5 9 .4 4 5 0 .4 4 1 2 5 2 4 .4 9 8 3 0 8 5 9 7 4 .0 5 7 1 0 8 5 5 2 3 .8 3 4 2 7 3 .3 9 3 4 9 7 .4 5 0 7 0 8 5 9 4 7 .0 0 9 5 0 8 5 4 9 7 .4 5 5 B 4 7 .0 1 4 6
KH 68 5 9 .4 2 9 1 .0 8 8 2 3 3 1 .0 6 5 3 6 7 2 8 3 9 .9 7 7 1 6 7 2 3 3 0 .8 5 5 6 3 9 .7 6 7 4 3 0 4 .0 1 7 7 6 7 2 8 1 2 .9 2 9 5 6 7 2 3 0 4 .4 7 7 1 13.3B B 9
H I 68 5 9 .4 4 2 2 .1 1 7 6 5 1 6 .8 2 2 5 2 5 9 3 9 4 .7 0 4 9 2 5 9 5 1 6 .6 2 2 7 9 4 .5 0 5 1 4 8 9 .7 7 4 9 2 5 9 3 € 7 .6 5 7 3 2 5 9 4 9 0 .2 4 4 2 6 8 .1 2 6 6
HH 68 5 9 .4 5 6 8 .7 6 4 7 6 9 9 .1 0 4 4 0 9 0 4 1 3 0 .3 3 9 7 0 9 6 9 6 .2 3 2 8 1 2 7 .4 6 8 1 6 7 2 .0 5 6 8 0 9 0 4 1 0 3 .2 9 2 1 0 9 6 6 9 .8 5 4 2 1 0 1 .0 8 9 5
LH 68 5 9 .4 4 5 9 5 0 4 .3 8 8 4 5 4 0 4 4 5 .3 8 8 4 5 4 0 5 0 4 .2 8 2 3 4 5 .2 8 2 3 4 7 7 .3 4 0 8 5 4 0 4 1 8 .3 4 0 8 5 4 0 4 7 7 .9 0 3 7 1 8 .9 0 3 7
L I 68 5 9 .4 6 0 9 .7 9 4 1 7 0 2 .7 6 2 0 7 0 6 9 9 2 .9 6 7 9 7 0 6 7 0 2 .6 4 6 3 9 2 .8 5 2 2 6 7 5 .7 1 4 4 7 0 6 9 6 5 .9 2 0 3 7 0 6 6 7 6 .2 6 7 9 6 6 .4 7 3 8
IB 68 5 9 .4 8 1 6 .1 7 6 5 B 9 4 .7 0 4 9 4 0 1 1 7 8 .5 2 8 4 4 0 1 8 9 4 .5 6 0 4 7 8 .3 8 3 9 8 6 7 .6 5 7 3 4 0 1 1 5 1 .4 8 0 8 4 0 1 8 6 8 .1 8 1 9 5 2 .0 0 5 4
FORMULA 73A FORMULA 73A FORKOLA 73B FORMULA 73B
ME PREDICTED M I PREDICTED HT PREDICTED M I PREDICTED
BASED ON DISTANCE BASED ON DISTANCE BASED OB DISTANCE BASED ON DISTANCE
FDECADE7 N HEAH ASX MI KEAH DATA FRCH KEAN EACH V IS IT FRCH KEAH HEAH DATA FRCH HEAH EACH V IS IT FRCH HEAH
SH 53 6 8 .9 2 4 4 .6 4 1 5 1 9 9 .8 5 2 4 9 8 9 4 -4 4 .7 8 9 0 0 1 1 9 9 .0 1 7 - 4 5 .6 2 4 5 1 9 7 .0 0 1 3 9 8 9 4 -4 7 .6 4 0 1 0 1 1 9 7 .0 9 6 2 - 4 7 .5 4 5 3
S I 53 6 8 ,9 3 3 5 .7 7 3 6 3 8 3 .0 2 6 5 9 3 7 9 4 7 .2 5 2 9 9 3 7 3 8 2 .0 8 3 7 4 6 .3 1 0 1 3 8 0 .1 7 5 4 9 3 7 9 4 4 .4 0 1 8 9 3 7 3 B 0 .1 6 2 9 4 4 .3 8 9 3
SH 53 6 8 .9 4 8 0 .9 0 5 7 5 6 4 .9 0 5 3 4 0 0 4 8 3 .9 9 9 6 4 0 0 5 6 4 .1 4 5 4 8 3 .2 3 9 7 5 6 2 .0 5 4 2 4 0 0 4 8 1 .1 4 8 5 4 0 0 5 6 2 .2 2 4 8 8 1 .3 1 9 1
HH 53 6 8 .9 3 2 6 .9 4 3 4 3 5 7 .1 2 6 7 6 3 5 5 3 0 .1 8 3 3 6 3 5 3 5 6 .9 4 3 8 3 0 .0 0 0 4 3 5 4 .2 7 5 6 6 3 5 5 2 7 .3 3 2 2 6 3 5 3 5 5 .0 2 3 1 2 8 .0 7 9 7
MI 53 6 8 .9 4 5 7 .9 2 4 5 5 5 7 .7 6 8 2 5 9 9 3 9 9 .8 4 3 7 5 9 9 5 5 7 .6 7 3 3 9 9 .7 4 8 8 5 5 4 .9 1 7 1 5 9 9 3 9 6 .9 9 2 6 5 9 9 5 5 5 .7 5 2 4 9 7 .8 2 7 9
HH 53 6 8 .9 6 2 7 .9 6 2 3 7 5 7 .9 8 7 1 2 3 8 6 1 3 0 .0 2 4 8 2 3 7 5 7 .9 8 9 3 1 3 0 .0 2 7 7 5 5 .1 3 6 0 2 3 8 6 1 2 7 .1 7 3 7 2 3 7 5 6 .0 6 8 6 1 2 8 .1 0 6 3
IH 53 6 8 .9 5 1 9 .3 9 6 2 5 4 3 .4 7 7 1 5 8 8 4 2 4 .0 8 0 9 5 8 8 5 4 3 .5 5 7 9 2 4 .1 6 1 7 5 4 0 .6 2 6 0 5 8 8 4 2 1 .2 2 9 8 5 8 8 5 4 1 .6 3 7 2 2 .2 4 0 8
L I 53 6 8 .9 6 7 7 .2 0 7 5 7 5 7 .0 7 0 2 0 6 1 3 7 9 .8 6 2 7 0 6 1 7 5 7 .2 8 3 4 8 0 .0 7 5 9 7 5 4 .2 1 9 1 0 6 1 3 7 7 .0 1 1 6 0 6 1 7 5 5 .3 6 2 6 7 8 .1 5 5 1
IB 5 3 6 8 .9 9 0 1 .2 4 5 3 9 6 4 .8 6 2 7 6 1 8 5 6 3 .6 1 7 4 6 1 8 9 6 5 .1 1 3 6 6 3 .8 6 8 3 9 6 2 .0 1 1 6 6 1 8 5 6 0 .7 6 6 3 6 1 8 9 6 3 .1 9 2 9 6 1 .9 4 7 6
FDICADE8 H MEAN ASX MT
FORKOLA 73A
M l PREDICTED
BASED ON
MEAN DATA
DISTANCE
FRCM MEAN
SH 9 7 8 .1 2 8 9 .3 3 3 3 2 1 1 .2 7 4 3 4 3 1 8 - 7 8 .0 5 8 9 5 6
S I 9 7 a . i 3 8 6 .6 6 6 7 4 1 6 .9 4 2 3 5 0 9 7 3 0 .2 7 5 6 5 0 9
SN 9 7 a . i 5 4 5 .3 3 3 3 6 0 7 .1 4 3 6 7 9 2 1 6 1 .8 1 0 3 7 9 2
HH 9 7 8 .1 36 0 3 8 5 .1 1 3 7 3 2 7 8 2 5 .1 1 3 7 3 2 7
M I 9 7 8 .1 4 9 2 .6 6 6 7 6 0 0 .2 1 6 4 2 2 1 7 1 0 7 .5 4 9 7 2 2
HK 9 7 8 .1 7 0 6 .6 6 6 7 8 1 2 .1 6 4 1 8 3 8 3 1 0 5 .4 9 7 4 8 3
LH 9 7 8 .1 5 5 6 .6 6 6 7 5 8 4 .0 2 0 0 2 8 8 2 2 7 .3 5 3 3 2 B 8
L I 9 7 8 .1 7 9 6 .6 6 6 7 8 1 0 .4 3 7 7 2 3 7 5 1 3 .7 7 1 0 2 3 7
IN 9 7 8 .1 9 3 7 .3 3 3 3 1 0 3 3 .0 2 4 7 9 5 1 9 5 .6 9 1 4 9 5 0
FDECADE9 N m ean a s s MT
FORMOLA 73A
K I PREDICTED
BASED ON
MEAN DATA
DISTANCE
FROM MEAN
SH 1 94 408 2 3 7 .9 7 8 9 9 7 3 9 -1 7 0 .0 2 1 0 0
81 1 94 642 4 2 9 .0 7 7 0 4 7 7 6 -2 1 2 .9 2 2 9 5
SN 1 94 780 6 5 1 .3 8 7 9 8 8 5 6 -1 2 8 .6 1 2 0 1
M W 1 94 540 4 1 3 .2 8 8 0 4 3 7 1 -1 2 6 .7 1 1 9 5
MI 1 94 822 6 5 6 .1 8 6 6 0 6 0 6 -1 6 5 .8 1 3 3 9
MH 1 94 1128 8 9 4 .7 8 4 6 5 2 9 3 -2 3 3 .2 1 5 3 4
LH 1 94 10 6 2 6 4 6 .9 0 6 4 1 4 6 1 -4 1 5 .0 9 3 5 8
L I 1 94 12 0 0 9 0 3 .2 8 7 4 7 5 3 1 -2 9 6 .7 1 2 5 2
IN 1 94 16 0 2 1 1 4 4 .7 1 5 7 7 1 3 -4 5 7 .2 8 4 2 2
ALL
SUBJECTS N MEAN ACE MT
FORMULA 69A
MT PREDICTED
BASED ON DISTANCE
MEAN DATA FRCM KEAN
SH 1 3 1 8 5 0 .2 2 1 7 .7 8 9 1 1 7 5 .3 9 9 8 6 4 2 -4 2 .3 8 9 2 3 5
S I 13 1 8 5 0 .2 3 2 2 .8 1 6 4 2 8 7 .4 4 6 1 6 3 2 9 -3 5 .3 7 0 2 3 6
SN 13 1 8 5 0 .2 4 7 9 .2 9 4 4 4 2 5 .7 9 9 9 3 2 1 -5 3 .4 9 4 4 6 7
HH 1 3 1 8 5 0 .2 2 9 7 .9 6 5 1 2 8 4 .4 7 7 5 1 0 4 7 -1 3 .4 8 7 5 8 9
M I 13 1 8 5 0 .2 4 4 0 .5 4 4 8 4 3 0 .5 4 5 2 2 6 3 9 -9 .9 9 9 5 7 3 6
HH 1 3 1 B 5 0 .2 6 1 1 .6 9 0 4 5 8 5 .9 1 9 5 7 4 3 5 -2 5 .7 7 0 8 2 5
LH 13 1 8 5 0 .2 4 6 0 .3 7 9 4 4 2 6 .5 3 3 8 1 2 0 4 -3 3 .8 4 5 5 8 7
L I 13 1 8 5 0 .2 6 2 8 .6 3 4 3 5 9 0 .5 1 0 2 8 0 5 4 - 3 8 .1 2 4 0 1 9
IN 131 8 5 0 .2 8 2 5 .8 9 6 8 7 5 2 .9 9 0 9 7 4 0 5 - 7 2 .9 0 5 8 2 5
MALES H MEAN ASE MI
FORMULA 69A
M I PREDICTED
BASED CM DISTANCE
KEAN DATA FRCH KEAN
SH 104 7 4 9 .9 2 1 7 .8 1 6 6 1 7 4 .9 1 5 4 5 1 2 4 - 4 2 .9 0 1 1 4 8
S I 1 0 4 7 4 9 .9 3 2 8 .4 9 2 8 2 8 6 .6 6 7 4 0 8 0 4 - 4 1 .8 2 5 3 9 1
SN 1 0 4 7 4 9 .9 4 9 3 .4 6 7 4 2 4 .6 5 7 7 2 5 6 2 - 6 8 .8 0 9 2 7 4
M l 104 7 4 9 .9 3 0 0 .8 0 8 2 8 3 .7 0 6 5 5 3 7 9 - 1 7 .1 0 1 4 4 6
MI 104 7 4 9 . 9 4 4 8 .4 4 1 3 4 2 9 .3 9 0 5 5 4 1 7 -1 9 .0 5 0 7 4 5
MN 104 7 4 9 .9 6 2 6 .2 5 7 9 5 8 4 .3 5 6 7 3 8 3 5 - 4 1 .9 0 1 1 6 1
LH 104 7 4 9 .9 4 6 3 .3 9 2 5 4 2 5 .3 B 9 6 7 7 6 8 -3 8 .0 0 2 8 2 2
L I 104 7 4 9 .9 6 3 7 .8 4 5 3 5 8 8 .9 3 5 3 8 4 8 9 -4 8 .9 0 9 9 1 5
IN 1047 4 9 .9 8 3 7 .6 9 6 3 7 5 0 .9 8 9 2 4 6 4 5 -8 6 .7 0 7 0 5 3
FORMOLA 73A
M I PREDICTED
BASED OH DISTANCE
EACH V IS IT FRCH MEAN
2 1 0 .5 3 9 4 - 7 8 .7 9 3 9
4 1 5 .5 7 8 6 2 8 .9 1 1 9
6 0 6 .5 2 7 7 6 1 .1 9 4 4
3 8 4 .9 1 0 4 2 4 .9 1 0 4
6 0 0 ,1 8 0 1 1 0 7 .5 1 3 4
8 1 2 .0 7 7 1 0 5 .4 1 0 3
5 8 3 ,9 5 5 3 2 7 .2 8 8 6
8 1 0 .4 7 0 9 1 3 .8 0 4 2
1 0 3 3 .0 9 4 9 5 .7 6 0 7
FORMULA 73A
M l PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCM MEAN
2 3 7 .9 7 9 - 1 7 0 .0 2 1
4 2 9 .0 7 7 - 2 1 2 .9 2 3
6 5 1 .3 8 7 9 - 1 2 8 .6 1 2 1
4 1 3 .2 8 8 - 1 2 6 .7 1 2
6 5 6 .1 8 6 5 - 1 6 5 .8 1 3 5
8 9 4 .7 8 4 5 - 2 3 3 .2 1 5 5
6 4 6 .9 0 6 4 - 4 1 5 .0 9 3 6
9 0 3 .2 8 7 4 - 2 9 6 .7 1 2 6
1 1 4 4 .7 1 6 - 4 5 7 .2 8 4
FORMULA 69A
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FROM MEAN
1 7 5 .4 6 9 9 - 4 2 .3 1 9 2
2 8 7 .5 5 9 1 - 3 5 .2 5 7 3
4 2 5 .9 6 6 2 - 5 3 .3 2 8 2
2 8 4 .5 8 9 3 - 1 3 .3 7 5 8
4 3 0 .7 1 3 1 - 9 .8 3 1 7
5 8 6 .1 4 5 9 - 2 5 .5 4 4 5
4 2 6 .7 0 0 2 - 3 3 .6 7 9 2
5 9 0 .7 3 3 5 - 3 7 .9 0 0 8
7 5 3 .2 8 2 - 7 2 .6 1 4 8
FORMULA 69A
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH MEAN
1 7 4 .9 1 0 2 - 4 2 .9 0 6 4
2 8 6 .6 5 9 1 - 4 1 .8 3 3 7
4 2 4 .6 4 5 9 - 6 8 .8 2 1 1
2 8 3 .6 9 8 5 - 1 7 .1 0 9 5
4 2 9 .3 7 8 8 - 1 9 .0 6 2 5
5 8 4 .3 4 - 4 1 .9 1 7 9
4 2 5 .3 7 8 4 - 3 8 .0 1 4 1
5B B .9173 - 4 8 .9 2 8
7 5 0 .9 6 8 6 - 8 6 .7 2 7 7
FORMULA 73 B
HT PREDICTED
BASED MI DISTANCE
MEAN DATA FRCM M EAN
2 4 7 .3 3 9 2 4 3 1 8 - 4 1 .9 9 4 0 5 6
4 5 3 .0 0 7 2 5 0 9 7 6 6 .3 4 0 5 5 0 9
6 4 3 .2 0 8 5 7 9 2 1 9 7 .8 7 5 2 7 9 2
4 2 1 .1 7 8 6 3 2 7 8 6 1 .1 7 8 6 3 2 7
6 3 6 .2 8 1 3 2 2 1 7 1 4 3 .6 1 4 6 2 2
8 4 8 .2 2 9 0 8 3 8 3 1 4 1 .5 6 2 3 8 3
6 2 0 .0 8 4 9 2 8 8 2 63.41B 228B
8 4 6 .5 0 2 6 2 3 7 5 4 9 .8 3 5 9 2 3 7
1 0 6 9 .0 8 9 6 9 5 1 1 3 1 .7 5 6 3 9 5
FORMOLA 73B
ME PREDICTED
BASED ON DISTANCE
MEAN DATA FROM MEAN
3 7 7 .2 1 8 9 9 7 3 9 -3 0 .7 8 1 0 0 2
5 6 8 .3 1 7 0 4 7 7 6 -7 3 .6 8 2 9 5 2
7 9 0 .6 2 7 9 8 8 5 6 1 0 .6 2 7 9 8 8 5
5 5 2 .5 2 8 0 4 3 7 1 1 2 .5 2 8 0 4 3 7
7 9 5 .4 2 6 6 0 6 0 6 -2 6 .5 7 3 3 9 3
1 0 3 4 .0 2 4 6 5 2 9 -9 3 .9 7 5 3 4 7
7 8 6 .1 4 6 4 1 4 6 1 -2 7 5 .8 5 3 5 8
1 0 4 2 .5 2 7 4 7 5 3 -1 5 7 .4 7 2 5 2
1 2 8 3 .9 5 5 7 7 1 3 -3 1 8 .0 4 4 2 2
FORMOLA 69B
MT PREDICTED
BASED ON DISTANCE
MEAN DATA HUM HEAH
1 7 4 .7 4 9 8 6 4 2 -4 3 .0 3 9 2 3 5
2 8 6 .7 9 6 1 6 3 2 9 - 3 6 .0 2 0 2 3 6
4 2 5 .1 4 9 9 3 2 1 - 5 4 .1 4 4 4 6 7
2 8 3 .8 2 7 5 1 0 4 7 - 1 4 .1 3 7 5 8 9
4 2 9 .8 9 5 2 2 6 3 9 -1 0 .6 4 9 5 7 3
5 8 5 .2 6 9 5 7 4 3 5 -2 6 .4 2 0 8 2 5
4 2 5 .8 8 3 8 1 2 0 4 -3 4 .4 9 5 5 8 7
5 8 9 .8 6 0 2 8 0 5 4 -3 8 .7 7 4 0 1 9
7 5 2 .3 4 0 9 7 4 0 5 -7 3 .5 5 5 8 2 5
FORMOLA 69B
MT PREDICTED
BASED ON DISTANCE
MEAN DATA FROM MEAN
1 7 4 .4 9 0 4 5 1 2 4 -4 3 .3 2 6 1 4 8
2 8 6 .2 4 2 4 0 8 0 4 -4 2 .2 5 0 3 9 1
4 2 4 .2 3 2 7 2 5 6 2 -6 9 .2 3 4 2 7 4
2 8 3 .2 8 1 5 5 3 7 9 - 1 7 .5 2 6 4 4 6
4 2 8 .9 6 5 5 5 4 1 7 - 1 9 .4 7 5 7 4 5
5 8 3 .9 3 1 7 3 8 3 5 -4 2 .3 2 6 1 6 1
4 2 4 .9 6 4 6 7 7 6 8 - 3 8 .4 2 7 8 2 2
5 B 8 .5 1 0 3 8 4 8 9 - 4 9 .3 3 4 9 1 5
7 5 0 .5 6 4 2 4 6 4 5 - 8 7 .1 3 2 0 5 3
FORMULA 73B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH MEAN
2 4 7 .2 4 9 4 -4 2 .0 B 3 9
4 52.2B B 7 6 5 .6 2 2
6 4 3 .2 3 7 7 9 7 .9 0 4 4
4 2 1 .6 2 0 5 6 1 .6 2 0 5
6 3 6 .8 9 0 1 1 4 4 .2 2 3 4
8 4 8 .7 8 7 1 4 2 .1 2 0 3
6 2 0 .6 6 5 3 6 3 .9 9 8 6
8 4 7 .1 8 0 9 5 0 .5 1 4 2
1 0 6 9 .8 0 4 1 3 2 .4 7 0 7
FORMULA 73 B
MT PREDICTED
BASED OH DISTANCE
EACH V IS IT FRCM MEAN
3 7 7 .2 1 9 - 3 0 .7 8 1
5 6 8 .3 1 7 - 7 3 .6 8 3
7 9 0 .6 2 7 9 1 0 .6 2 7 9
5 5 2 .5 2 8 1 1 2 .5 2 8 1
7 9 5 .4 2 6 5 - 2 6 .5 7 3 5
1 0 3 4 .0 2 5 - 9 3 .9 7 5
7 8 6 .1 4 6 4 - 2 7 5 .8 5 3 6
1 0 4 2 .5 2 7 - 1 5 7 .4 7 3
1 2 8 3 .9 5 6 - 3 1 8 .0 4 4
FORMOLA 69B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCM MEAN
1 7 4 .7 8 7 2 - 4 3 .0 0 1 9
2 8 6 .8 7 6 4 - 3 5 . 9 4
4 2 5 .2 8 3 4 - 5 4 .0 1 1
2 8 3 .9 0 6 6 - 1 4 .0 5 8 5
4 3 0 .0 3 0 3 - 1 0 .5 1 4 5
5 8 5 .4 6 3 3 - 2 6 .2 2 7 1
4 2 6 .0 1 7 5 - 3 4 .3 6 1 9
5 9 0 .0 5 0 9 — 3 8 .5 B 3 4
7 5 2 .5 9 9 2 - 7 3 .2 9 7 6
FORMULA 69B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCM MEAN
1 7 4 .4 8 7 5 - 4 3 .3 2 9 1
2 8 6 .2 3 6 5 - 4 2 .2 5 6 3
4 2 4 .2 2 3 2 - 6 9 .2 4 3 8
2 8 3 .2 7 5 8 - 1 7 .5 3 2 2
4 2 8 .9 5 6 2 -1 9 .4 B 5 1
5 8 3 .9 1 7 4 - 4 2 .3 4 0 5
4 2 4 .9 5 5 7 - 3 8 .4 3 6 8
5 8 B .4 9 4 8 - 4 9 .3 5 0 5
7 5 0 .5 4 5 8 - 8 7 .1 5 0 5
FEMALES N MEAN ACE KT
FORMOLA 69A
XT PREDICTED
BASED ON DISTANCE
MEAN DATA FROM MEAN
SH 2 71 5 1 .6 2 1 7 .6 3 2 7 1 7 7 .6 6 0 4 5 7 9 8 -4 0 .0 2 2 2 4 2
S I 2 71 5 1 . 6 3 0 0 .8 8 5 6 2 9 1 .0 8 0 3 5 4 4 3 -9 .8 0 5 2 4 5 5
SN 2 71 5 1 . 6 4 2 4 .5 3 8 8 4 3 1 .1 3 0 2 2 8 9 9 6 .5 9 1 4 2 8 9 8
HH 2 71 5 1 .6 2 8 6 .9 3 1 5 2 8 8 .0 7 5 3 0 B 3 2 1 .0 9 3 8 0 8 3 2
H I 2 71 5 1 . 6 4 1 0 .0 3 6 9 4 3 5 .9 3 3 6 9 6 7 7 2 5 .8 9 6 7 9 6 7
KN 2 7 1 5 1 .6 5 5 5 .4 0 9 6 5 9 3 .2 1 2 B 0 9 0 7 3 7 .8 0 3 2 0 9 0
IN 2 7 1 5 1 .6 4 4 B .7 3 8 4 3 1 .8 7 3 1 0 5 7 - 1 6 .8 6 4 8 9 4
L I 2 7 1 5 1 .6 5 9 3 .0 4 8 5 9 7 .8 5 9 7 9 3 6 2 4 .8 1 1 7 9 3 6 1
IN 2 7 1 5 1 .6 7 8 0 .3 0 9 9 7 6 2 .3 3 2 3 6 9 5 3 - 1 7 .9 7 7 5 3 0
DEGADE2 N MEAN ACE MI
FORMULA 69A
H I PREDICTED
BASED ON DISTANCE
HEAN DAXA FRCM MEAN
SH 35 2 1 .7 1 9 7 .3 1 4 3 1 2 9 .3 8 0 6 3 3 6 4 -6 7 .9 3 3 6 6 6
S I 35 2 1 .7 2 7 5 .8 2 8 6 2 1 3 .4 6 4 4 1 5 0 1 - 6 2 .3 6 4 1 8 4
SH 3 5 2 1 .7 3 7 1 .8 2 8 6 3 1 7 .2 9 0 3 1 6 8 2 - 5 4 .5 3 8 2 8 3
HH 3 5 2 1 .7 2 5 3 .2 2 1 1 .2 3 6 6 2 5 6 3 - 4 1 .9 6 3 3 7 4
H I 3 5 2 1 .7 3 5 5 .2 3 2 0 .8 5 1 3 6 5 1 7 - 3 4 .3 4 8 6 3 4
MN 35 2 1 .7 4 7 6 .2 2 8 6 4 3 7 .4 5 0 1 5 3 4 3 -3 8 .7 7 8 4 4 6
LH 35 2 1 .7 3 8 4 .6 8 5 7 3 1 7 .8 4 1 0 4 8 0 9 -6 6 .8 4 4 6 5 1
L I 35 2 1 .7 4 9 7 .8 2 8 6 4 4 0 .8 9 5 1 9 3 0 2 -5 6 .9 3 3 4 0 6
IN 35 2 1 .7 6 3 7 .7 1 4 3 5 6 2 .8 2 6 8 5 1 8 1 -7 4 .8 8 7 4 4 8
DECADES N KEAN ACE MT
FORMOLA 69A
HE PREDICTED
BASED ON DISTANCE
HEAN DAXA FRCH MEAN
SH 2 4 4 2 9 .9 1 9 8 .7 6 2 3 1 4 2 .6 2 1 2 5 4 3 6 -5 6 .1 4 1 0 4 5
S I 2 4 4 2 9 .9 2 7 4 .4 0 1 6 2 3 4 .7 5 0 3 9 1 7 -3 9 .6 5 1 2 0 8
SB 2 4 4 2 9 .9 3 9 0 .0 2 4 6 3 4 8 .5 1 0 6 2 7 1 8 - 4 1 .5 1 3 9 7 2
HH 24 4 2 9 .9 2 5 7 .6 8 0 3 2 3 2 .3 0 9 4 4 1 6 2 - 2 5 .3 7 0 8 5 8
H I 24 4 2 9 .9 3 7 2 .5 1 6 4 3 5 2 .4 1 2 4 0 5 9 4 -2 0 .1 0 3 9 9 4
MN 24 4 2 9 .9 5 0 4 .4 6 7 2 4 8 0 .1 6 7 6 7 1 0 3 -2 4 .2 9 9 5 2 8
IN 24 4 2 9 .9 3 9 6 .9 3 4 4 3 4 9 .1 1 4 0 5 3 8 6 -4 7 .8 2 0 3 4 6
L I 2 4 4 2 9 .9 5 3 4 .3 9 3 4 4 8 3 .9 4 2 3 4 1 0 1 -5 0 .4 5 1 0 5 8
IN 244 2 9 . 9 6 8 8 .7 7 0 5 6 1 7 .5 4 0 7 3 9 6 1 - 7 1 .2 2 9 7 6 0
DECADE4 N MEAN ACE MT
FORMULA. 69A
M I PREDICTED
BASED ON DISTANCE
MEAN DAXA FROM MEAN
SH 2 5 0 3 9 . 6 2 0 0 .3 2 8 1 5 8 .2 8 3 9 3 9 8 5 -4 2 .0 4 4 0 6 0
81 2 5 0 3 9 .6 2 9 3 .0 8 8 2 5 9 .9 3 0 1 4 4 6 3 -3 3 .1 5 7 8 5 5
SN 250 3 9 .6 4 4 1 .7 6 8 3 8 5 .4 4 1 9 6 9 9 3 -5 6 .3 2 6 0 3 0
HH 250 3 9 . 6 2 7 1 .6 S 2 5 7 .2 3 7 0 4 1 0 2 -1 4 .4 4 2 9 5 8
MI 250 3 9 . 6 4 0 4 .7 3 6 3 8 9 .7 4 6 8 0 7 8 3 -1 4 .9 8 9 1 9 2
M N 250 3 9 . 6 5 7 2 .6 8 8 5 3 0 .6 9 9 3 6 8 6 8 -4 1 .9 8 8 6 3 1
IN 2 50 3 9 . 6 4 1 8 .4 1 6 3 8 6 .1 0 7 7 3 1 4 1 - 3 2 .3 0 8 2 6 8
L I 2 50 3 9 . 6 5 7 3 .6 4 8 5 3 4 .8 6 3 9 6 7 2 9 -3 8 .7 8 4 0 3 2
IN 25 0 3 9 . 6 7 7 0 .6 4 6 8 2 .2 6 3 2 6 5 4 3 -8 8 .3 7 6 7 3 4
00
FORMULA 69A
M I PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH KEAN
1 7 7 .6 3 3 - 4 0 .0 4 9 7
2 9 1 .0 3 6 2 - 9 .8 4 9 4
4 3 1 .0 6 5 6 6 .5 2 6 8
2 8 8 .0 3 1 7 1 .0 5 0 2
4 3 5 .8 6 8 3 2 5 .8 3 1 4
5 9 3 .1 2 4 4 3 7 .7 1 4 8
4 3 1 .8 0 8 3 - 1 6 .9 2 9 7
5 9 7 .7 7 0 8 4 .7 2 2 8
7 6 2 .2 1 8 9 - 1 8 .0 9 1
FORMULA 69A
ME PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCM MEAN
1 2 9 .4 0 3 7 - 6 7 .9 1 0 6
2 1 3 .5 0 1 5 - 6 2 .3 2 7 1
3 1 7 .3 4 4 7 - 5 4 .4 8 3 9
2 1 1 .2 7 3 4 - 4 1 .9 2 6 6
3 2 0 .9 0 6 4 - 3 4 .2 9 3 6
4 3 7 .5 2 4 6 - 3 8 .7 0 4
3 1 7 .8 9 5 4 - 6 6 .7 9 0 3
4 4 0 .9 7 0 2 - 5 6 .8 5 8 4
5 6 2 .9 2 2 2 - 7 4 .7 9 2 1
FORMOLA 69A
ME PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH HEAN
1 4 2 .5 4 4 5 - 5 6 .2 1 7 8
2 3 4 .6 2 7 - 3 9 .7 7 4 6
3 4 8 .3 2 9 3 - 4 1 .6 9 5 3
2 3 2 .1 8 7 4 - 2 5 .4 9 2 9
3 5 2 .2 2 9 5 - 2 0 .2 8 6 9
4 7 9 .9 2 0 2 - 2 4 .5 4 7
3 4 8 .9 3 2 9 - 4 8 .0 0 1 5
4 8 3 .6 9 3 5 - 5 0 .6 9 9 9
6 1 7 .2 2 3 1 - 7 1 .5 4 7 4
FORKOLA 69A
M I PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCH MEAN
1 5 8 .2 3 8 7 - 4 2 .0 8 9 3
2 5 9 .8 5 7 3 - 3 3 .2 3 0 7
3 8 5 .3 3 5 4 - 5 6 .4 3 2 6
2 5 7 .1 6 4 9 - 1 4 .5 1 5 1
3 8 9 .6 3 9 - 1 5 .0 9 7
5 3 0 .5 5 3 2 - 4 2 .1 3 4 8
3 8 6 .0 0 0 8 - 3 2 .4 1 5 2
5 3 4 .7 1 6 6 - 3 8 .9 3 1 4
6 8 2 .0 7 7 3 - 8 8 .5 6 2 7
FORMOLA 69 b
ME PREDICTED
BASED ON DISTANCE
HEAH DATA HUM MEAN
1 7 5 .9 6 0 4 5 7 9 8 -4 1 .7 2 2 2 4 2
2 8 9 .3 8 0 3 5 4 4 3 -1 1 .5 0 5 2 4 5
4 2 9 .4 3 0 2 2 B 9 9 4 .8 9 1 4 2 S 9 8
2 8 6 .3 7 5 3 0 B 3 2 -0 .6 0 6 1 9 1 6
4 3 4 .2 3 3 6 9 6 7 7 2 4 .1 9 6 7 9 6 ?
5 9 1 .5 1 2 8 0 9 0 7 3 6 .1 0 3 2 0 9 0
4 3 0 .1 7 3 1 0 5 7 - I B . 5 6 4 8 9 4
5 9 6 .1 5 9 7 9 3 6 2 3 .1 1 1 7 9 3 6 1
7 6 0 .6 3 2 3 6 9 5 3 -1 9 .6 7 7 5 3 0
rORMOLA 69B
H I PREDICTED
BASED ON DISTANCE
MEAN DATA H U H MEAN
1 5 0 .1 0 5 6 3 3 6 4 - 4 7 .2 0 8 6 6 6
2 3 4 .1 8 9 4 1 5 0 1 -4 1 .6 3 9 1 8 4
3 3 8 .0 1 5 3 1 6 8 2 -3 3 .8 1 3 2 8 3
2 3 1 .9 6 1 6 2 5 6 3 -2 1 .2 3 8 3 7 4
3 4 1 .5 7 6 3 6 5 1 7 -1 3 .6 2 3 6 3 4
4 5 8 .1 7 5 1 5 3 4 3 - 1 8 .0 5 3 4 4 6
3 3 8 .5 6 6 0 4 8 0 9 -4 6 .1 1 9 6 5 1
4 6 1 .6 2 0 1 9 3 0 2 -3 6 .2 0 8 4 0 6
5 8 3 .5 5 1 8 5 1 8 1 -5 4 .1 6 2 4 4 8
FORMULA 69B
H I PREDICTED
BASED ON DISTANCE
MEAN DAXA FRCH KEAN
1 5 7 .1 9 6 2 5 4 3 6 - 4 1 .5 6 6 0 4 5
2 4 9 .3 2 5 3 9 1 7 -2 5 .0 7 6 2 0 8
3 6 3 .0 8 5 6 2 7 1 8 - 2 6 .9 3 8 9 7 2
2 4 6 .8 8 4 4 4 1 6 2 -1 0 .7 9 5 8 5 8
3 6 6 .9 8 7 4 0 5 9 4 -5 .5 2 8 9 9 4 0
4 9 4 .7 4 2 6 7 1 0 3 - 9 .7 2 4 5 2 8 9
3 6 3 .6 8 9 0 5 3 8 6 - 3 3 .2 4 5 3 4 6
4 9 8 .5 1 7 3 4 1 0 1 - 3 5 .8 7 6 0 5 8
6 3 2 .1 1 5 7 3 9 6 1 -5 6 .6 5 4 7 6 0
FORHOZA 69B
H I PREDICTED
BASED ON DISTANCE
MEAN DAXA FRCH KEAN
1 6 5 .5 0 3 9 3 9 8 5 - 3 4 .7 4 4 0 6 0
2 6 7 .2 3 0 1 4 4 6 3 - 2 5 .8 5 7 8 5 5
3 9 2 .7 4 1 9 6 9 9 3 - 4 9 .0 2 6 0 3 0
2 6 4 .5 3 7 0 4 1 0 2 -7 .1 4 2 9 5 8 9
3 9 7 .0 4 6 B 0 7 8 3 - 7 .6 8 9 1 9 2 1
5 3 7 .9 9 9 3 6 8 6 8 - 3 4 .6 8 8 6 3 1
3 9 3 .4 0 7 7 3 1 4 1 -2 5 .0 0 8 2 6 8
5 4 2 .1 6 3 9 6 7 2 9 - 3 1 .4 8 4 0 3 2
6 8 9 .5 6 3 2 6 5 4 3 - 8 1 .0 7 6 7 3 4
FORMOLA 69B
HT PREDICTED
BASED OR DISTANCE
EACH V IS IT FRCH MEAN
1 7 5 .9 4 5 8 - 4 1 .7 3 6 9
2 8 9 .3 4 8 9 - 1 1 .5 3 6 7
4 2 9 .3 7 8 4 4 .8 3 9 6
2 8 6 .3 4 4 5 - 0 . 6 3 7
4 3 4 .1 8 1 2 4 .1 4 4 1
5 9 1 .4 3 7 1 3 6 .0 2 7 5
4 3 0 .1 2 1 1 - 1 8 .6 1 6 9
5 9 6 .0 8 3 6 3 .0 3 5 6
7 6 0 .5 3 1 7 - 1 9 .7 7 8 2
FORMOLA 69B
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH HEAN
1 5 0 .1 1 8 - 4 7 .1 9 6 3
2 3 4 .2 1 5 8 - 4 1 .6 1 2 8
3 3 8 .0 5 9 - 3 3 .7 6 9 6
2 3 1 .9 8 7 7 - 2 1 .2 1 2 3
3 4 1 .6 2 0 6 - 1 3 .5 7 9 4
4 5 8 .2 3 8 B - 1 7 .9 8 9 8
3 3 8 .6 0 9 8 - 4 6 .0 7 5 9
4 6 1 .6 8 4 4 - 3 6 .1 4 4 2
5 8 3 .6 3 6 5 -5 4 .0 7 7 8
FORMOLA 69B
HE PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCM MEAN
1 5 7 .1 5 5 2 - 4 1 .6 0 7 1
2 4 9 .2 3 7 7 - 2 5 .1 6 3 9
3 6 2 .9 4 - 2 7 .0 8 4 6
2 4 6 .7 9 8 - 1 0 .8 8 2 3
3 6 6 .8 4 0 1 - 5 .6 7 6 3
4 9 4 .5 3 0 9 - 9 .9 3 6 3
3 6 3 .5 4 3 5 - 3 3 .3 9 0 9
4 9 8 .3 0 4 1 - 3 6 .0 8 9 3
6 3 1 .8 3 3 6 -5 6 .9 3 6 9
FORMULA 69B
HT PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCH HEAH
1 6 5 .5 5 9 7 - 3 4 .7 6 8 3
2 6 7 .1 7 8 3 - 2 5 .9 0 9 7
3 9 2 .6 5 6 4 - 4 9 .1 1 1 6
2 6 4 .4 8 5 8 - 7 .1 9 4 2
3 9 6 .9 6 - 7 . 7 7 6
5 3 7 .8 7 4 3 - 3 4 .8 1 3 7
3 9 3 .3 2 1 7 - 2 5 .0 9 4 3
5 4 2 .0 3 7 7 - 3 1 .6 1 0 3
6 8 9 .3 9 8 4 - 8 1 .2 4 1 6
DECADES B MEAN ABE H I
FORMULA 69A
MT PREDICTED
BASED ON DISTANCE
HEAN DAXA FRCH MEAN
FORMULA 69A
H I PREDICTED
BASED ON
EACH V IS IT
SH 271 4 9 .7 2 0 4 .6 8 6 3 1 7 4 .5 9 2 5 0 9 2 8 - 3 0 .0 9 3 7 9 0 1 7 4 .5 9 4 3
S I 271 4 9 .7 3 0 5 .1 1 4 4 2 8 6 .1 4 8 2 3 7 8 8 - 1 8 .9 6 6 1 6 2 2 8 6 .1 5 1 1
SB 271 4 9 .7 4 8 2 .9 2 2 5 4 2 3 .8 9 6 2 5 4 6 4 -5 9 .0 2 6 2 4 5 4 2 3 .9 0 0 5
HH 271 4 9 .7 2 8 6 .5 3 B 8 2 8 3 .1 9 2 5 8 2 6 7 -3 .3 4 6 2 1 7 3 2 8 3 .1 9 5 3
MI 271 4 9 .7 4 3 4 .1 0 3 3 4 2 8 .6 2 0 7 7 2 6 9 -5 .4 8 2 5 2 7 3 4 2 8 .6 2 5 2
MB 271 4 9 .7 6 0 6 .6 8 6 3 5 8 3 .3 1 4 8 4 7 6 7 - 2 3 .3 7 1 4 5 2 5 B 3 .3 2 0 7
LW 271 4 9 .7 4 3 2 .8 1 9 2 4 2 4 .6 2 6 9 2 1 4 4 - 8 .1 9 2 2 7 8 5 4 2 4 .6 3 1
1 2 271 4 9 .7 6 0 6 .1 7 7 1 5 8 7 .8 8 5 4 5 4 4 5 - 1 8 .2 9 1 6 4 5 5 8 7 .B 9 1 2
i n 271 4 9 .7 8 0 7 .2 7 6 7 7 4 9 .6 5 4 7 6 1 3 8 - 5 7 .6 2 1 9 3 8 7 4 9 .6 6 2 1
DECADES B HEAN ABE H I
FORMULA 69A
H I PREDICTED
BASED OB DISTANCE
MEAN DATA FRCM MEAN
FORMULA 69A
I B PREDICTED
BASED ON
EACH V IS IT
SH 21 2 5 9 .5 2 1 6 .1 6 9 8 1 9 0 .4 1 6 6 6 5 7 5 -2 5 .7 5 3 1 3 4 1 9 0 .4 6 2 3
S I 212 5 9 .5 3 2 9 .8 5 8 5 3 1 1 .5 8 7 5 7 5 8 8 - 1 8 .2 7 0 9 2 4 3 1 1 .6 6 1
SB 212 5 9 .5 4 9 2 .3 3 9 6 4 6 1 .2 0 8 3 3 2 8 7 - 3 1 .1 3 1 2 6 7 4 6 1 .3 1 6 2
HH 212 5 9 .5 3 0 0 .6 7 9 3 3 0 8 .3 7 7 1 6 7 6 3 7 .6 9 7 8 6 7 6 2 3 0 8 .4 4 9 8
MI 212 5 9 .5 4 4 9 .8 5 8 5 4 6 6 .3 4 0 0 6 5 3 2 1 6 .4 8 1 5 6 5 3 4 6 6 .4 4 9 2
MN 212 5 9 .5 6 2 8 .1 3 2 1 6 3 4 .3 6 7 4 9 0 6 6 6 .2 3 5 3 9 0 6 5 6 3 4 .5 1 4 9
I X 212 5 9 .5 4 6 8 .3 9 6 2 4 6 2 .0 0 1 9 7 7 1 2 -6 .3 9 4 2 2 2 8 4 6 2 .1 1 0 1
L I 212 5 9 .5 6 4 7 .2 6 4 2 6 3 9 .3 3 2 0 4 5 9 5 -7 .9 3 2 1 5 4 0 6 3 9 .4 8 0 4
l i l 212 5 9 .5 8 6 1 .0 2 8 3 8 1 5 .0 4 4 5 2 9 7 3 - 4 5 .9 8 3 7 7 0 8 1 5 .2 3 2 8
DECADE? H HEAN ABE HT
FORMOLA 69A
H I PREDICTED
BASED OH DISTANCE
HEAR DATA FRCM MEAN
FORMOLA 69A
MT PREDICTED
BASED ON
EACH V IS IT
SH 2 1 7 8 9 .8 2 5 0 .5 3 4 6 2 0 6 .7 2 5 2 3 5 1 7 -4 3 .8 0 9 3 6 4 2 0 6 .7 9 0 7
S I 2 1 7 8 9 .8 3 8 2 .2 3 0 4 3 3 7 .8 0 5 6 6 9 1 3 -4 4 .4 2 4 7 3 0 3 3 7 .9 1 1
SB 217 8 9 .6 5 5 8 .1 6 5 9 4 9 9 .6 6 2 6 1 7 5 9 -5 8 .5 0 3 2 8 2 4 9 9 .8 1 6 9
tm 217 8 9 .6 3 4 4 .4 3 3 2 3 3 4 .3 3 2 7 0 9 2 7 -1 0 .1 0 0 4 9 0 3 3 4 .4 3 6 6
H I 217 6 9 .6 5 1 2 .8 7 5 5 5 0 5 .2 1 4 0 3 0 1 B -7 .6 6 1 4 6 9 8 5 0 5 .3 6 9 6
MB 217 6 9 .6 7 1 3 .2 2 5 8 6 8 6 .9 8 2 9 6 9 6 5 -2 6 .2 4 2 8 3 0 6 8 7 .1 9 4
IH 217 6 9 .6 5 4 7 .1 6 1 3 5 0 0 .5 2 1 1 6 7 1 5 -4 6 .6 4 0 1 3 2 5 0 0 .6 7 5 6
1 2 217 6 9 .6 7 3 5 .8 9 8 6 6 9 2 .3 5 3 5 3 3 1 1 -4 3 .5 4 5 0 6 6 6 9 2 .5 6 6 2
IN 217 6 9 .6 9 5 3 .0 0 4 6 8 8 2 .4 3 6 0 2 5 6 9 -7 0 .5 6 8 5 7 4 8 8 2 .7 0 7 8
DECADES B MEAN ACS MT
FORMULA 69A
M I PREDICTED
BASED OB DISTANCE
MEAN DATA FRCM HEAH
FORKOLA 69A
MT PREDICTED
BASED QB
EACH V IS IT
SH 81 7 8 .3 2 8 3 .5 5 5 5 2 2 0 .7 7 3 2 1 0 8 2 -6 2 .7 8 2 2 8 9 2 2 0 .8 4 7
S I 61 7 8 .3 4 3 3 .7 7 7 8 3 6 0 .3 8 9 5 7 1 2 4 -7 3 .3 8 8 2 2 8 3 6 0 .5 0 8 3
SH S I 7 8 .3 6 1 6 .2 9 6 3 5 3 2 .7 8 6 6 0 5 4 1 -8 3 .5 0 9 6 9 4 5 3 2 .9 6 0 6
MH 81 7 8 .3 3 9 9 .4 0 7 4 3 5 6 .6 9 0 4 5 3 0 7 - 4 2 .7 1 6 9 4 6 3 5 6 .8 0 7 7
MI 81 7 8 .3 5 6 0 .5 1 8 5 5 3 8 .6 9 9 5 2 4 6 6 - 2 1 .8 1 8 9 7 5 5 3 B .8 7 5 4
MB 61 7 8 .3 7 7 2 .2 9 6 3 7 3 2 .3 0 5 2 1 3 9 3 -3 9 .9 9 1 0 8 6 7 3 2 .5 4 3 1
LW 81 7 8 .3 6 0 5 .4 0 7 4 5 3 3 .7 0 1 0 6 3 5 1 -7 1 .7 0 6 3 3 6 5 3 3 .8 7 5 4
1 2 81 7 8 .3 8 2 6 .4 4 4 5 7 3 8 .0 2 5 5 0 7 1 9 - 8 8 .4 1 8 9 9 2 7 3 8 .2 6 5 3
IN 81 7 8 .3 1 0 5 8 .6 6 7 9 4 0 .4 8 6 1 2 6 1 6 -1 1 8 .1 8 0 8 7 9 4 0 .7 9 1 1
FORMOLA 69B FORMOLA 69B
H I PREDICTED H I PREDICTED
DISTANCE BASED OB DISTANCE BASED ON DISTANCE
FRCM MEAN HEAN DAXA FRCH MEAN EACH V IS IT RtCH MEAN
- 3 0 .0 9 2 1 7 4 .3 1 7 5 0 9 2 8 - 3 0 .3 6 8 7 9 0 1 7 4 .3 1 8 5 - 3 0 .3 6 7 8
- 1 8 .9 6 3 3 2 8 5 .8 7 3 2 3 7 8 8 - 1 9 .2 4 1 1 6 2 2 8 5 .8 7 5 2 - 1 9 .2 3 9 2
- 5 9 .0 2 2 4 2 3 .6 2 1 2 5 4 6 4 - 5 9 .3 0 1 2 4 5 4 2 3 .6 2 4 7 - 5 9 .2 9 7 8
- 3 .3 4 3 5 2 8 2 .9 1 7 5 8 2 6 7 - 3 .6 2 1 2 1 7 3 2 8 2 .9 1 9 5 - 3 .6 1 9 3
- 5 .4 7 8 1 4 2 8 .3 4 5 7 7 2 6 9 -5 .7 5 7 5 2 7 3 4 2 8 .3 4 9 3 - 5 .7 5 4
- 2 3 .3 6 5 6 5 B 3 .0 3 9 B 4 7 6 7 -2 3 .6 4 6 4 5 2 5 8 3 .0 4 4 9 - 2 3 .6 4 1 4
- 8 .1 8 8 2 4 2 4 .3 5 1 9 2 1 4 4 - 8 .4 6 7 2 7 8 5 4 2 4 .3 5 5 1 - 8 .4 6 4 1
- I B . 28 5 9 5 8 7 .6 1 0 4 5 4 4 5 - 1 8 .5 6 6 6 4 5 5 8 7 .6 1 5 3 - 1 8 .5 6 1 8
-5 7 .6 1 4 6 7 4 9 .3 7 9 7 6 1 3 8 -5 7 .8 9 6 9 3 8
7 4 9 .3 8 6 3 - 5 7 .8 9 0 4
FORKOLA 69b FORMOLA 69B
M l PREDICTED MT PREDICTED
DISTANCE BASED ON DISTANCE BASED CN DISTANCE
FRCH MEAN MEAN DATA FRCH HEAN EACH V IS IT FRCH HEAH
- 2 5 .7 0 7 5 1 8 2 .7 9 1 6 6 5 7 5 - 3 3 .3 7 8 1 3 4 1 6 2 .8 1 6 1 -3 3 .3 5 3 7
- 1 8 .1 9 7 5 3 0 3 .9 6 2 5 7 5 8 8 - 2 5 .8 9 5 9 2 4 3 0 4 .0 1 4 8 - 2 5 .8 4 3 7
- 3 1 .0 2 3 4 4 5 3 .5 8 3 3 3 2 8 7 - 3 8 .7 5 6 2 6 7 4 5 3 .6 7 - 3 8 .6 6 9 6
7 .7 7 0 5 3 0 0 .7 5 2 1 6 7 6 3 0 .0 7 2 8 6 7 6 2 3 0 0 .8 0 3 6 0 .1 2 4 3
1 6 .5 9 0 7 4 5 8 .7 1 5 0 6 5 3 2 8 .8 5 6 5 6 5 3 2 4 5 B .8 0 3 8 .9 4 4 5
6 .3 8 2 8 6 2 6 .7 4 2 4 9 0 6 6 - 1 .3 8 9 6 0 9 3 6 2 6 .8 6 8 6 - 1 .2 6 3 5
- 6 .2 8 6 1 4 5 4 .3 7 6 9 7 7 1 2 - 1 4 .0 1 9 2 2 2 4 5 4 .4 6 3 9 -1 3 .9 3 2 3
- 7 .7 8 3 8 6 3 1 .7 0 7 0 4 5 9 5 - 1 5 .5 5 7 1 5 4 6 3 1 .8 3 4 2 - 1 5 .4 3
- 4 5 .7 9 5 5 8 0 7 .4 1 9 5 2 9 7 3 -5 3 .6 0 8 7 7 0 8 0 7 .5 8 6 7 - 5 3 .4 4 1 6
FORKOLA 69B FORMULA 69B
H I PREDICTED MT PREDICTED
DISTANCE BASED ON DISTANCE BASED ON DISTANCE
FRCH MEAN HEAN DATA FRCH MEAN EACH V IS IT FRCH HEAN
- 4 3 .7 4 3 9 1 9 1 .5 2 5 2 3 5 1 7 - 5 9 .0 0 9 3 6 4 1 9 1 .5 6 0 3 - 5 8 .9 7 4 3
- 4 4 .3 1 9 4 3 2 2 .6 0 5 6 6 9 1 3 -5 9 .6 2 4 7 3 0 3 2 2 .6 8 0 5 - 5 9 .5 4 9 9
- 5 8 .3 4 9 4 8 4 .4 6 2 6 1 7 5 9 -7 3 .7 0 3 2 B 2 4 8 4 .5 8 6 5 - 7 3 .5 7 9 4
- 9 .9 9 6 6 3 1 9 .1 3 2 7 0 9 2 7 - 2 5 .3 0 0 4 9 0 3 1 9 .2 0 6 3 - 2 5 .2 2 6 9
- 7 .5 0 5 9 4 9 0 .0 1 4 0 3 0 1 8 - 2 2 .8 6 1 4 6 9 4 9 0 .1 3 9 2 - 2 2 .7 3 6 3
- 2 6 .0 3 1 8 6 7 1 .7 B 2 9 6 9 6 5 - 4 1 .4 4 2 8 3 0 6 7 1 .9 6 3 8 - 4 1 .2 6 2
- 4 6 .4 8 5 7 4 8 5 .3 2 1 1 6 7 1 5 -6 1 .8 4 0 1 3 2 4 8 5 .4 4 5 2 - 6 1 .7 1 6 1
- 4 3 .3 3 2 4 6 7 7 .1 5 3 5 3 3 1 1 - 5 8 .7 4 5 0 6 6 6 7 7 .3 3 5 8 -5 8 .5 6 2 8
- 7 0 .2 9 6 8 8 6 7 .2 3 6 0 2 5 6 9 -8 5 .7 6 8 5 7 4 8 6 7 .4 7 7 4 - 8 5 .5 2 7 2
FORMULA 69B FORMULA 69B
H I PREDICTED MT PREDICTED
DISTANCE BASED OH DISTANCE BASED CN DISTANCE
FRCH MEAN HEAN DAXA FRCH KEAH EACH V I8 IS FRCH MEAN
- 6 2 .7 0 8 5 1 9 9 .0 4 8 2 1 0 8 2 - 8 4 .5 0 7 2 8 9 1 9 9 .0 8 7 7 - 8 4 .4 6 7 S
- 7 3 .2 6 9 5 3 3 8 .6 6 4 5 7 1 2 4 - 9 5 .1 1 3 2 2 8 3 3 8 .7 4 9 - 9 5 .0 2 8 8
- 8 3 .3 3 5 7 5 1 1 .0 6 1 6 0 5 4 1 - 1 0 5 .2 3 4 6 9 5 1 1 .2 0 1 4 - 1 0 5 .0 9 4 9
-4 2 .5 9 9 7 3 3 4 .9 6 5 4 5 3 0 7 -6 4 .4 4 1 9 4 6 3 3 5 .0 4 8 5 - 6 4 .3 5 8 9
-2 1 .6 4 3 1 5 1 6 .9 7 4 5 2 4 6 6 - 4 3 .5 4 3 9 7 5 5 1 7 .1 1 6 1 - 4 3 .4 0 2 4
- 3 9 .7 5 3 2 7 1 0 .5 8 0 2 1 3 9 3 -6 1 .7 1 6 0 B 6 7 1 0 .7 8 3 9 - 6 1 .5 1 2 4
- 7 1 .5 3 2 5 1 1 .9 7 6 0 6 3 5 1 -9 3 .4 3 1 3 3 6 5 1 2 .1 1 6 1 - 9 3 .2 9 1 3
- 8 8 .1 7 9 2 7 1 6 .3 0 0 5 0 7 1 9 - 1 1 0 .1 4 3 9 9 7 1 6 .5 0 6 - 1 0 9 .9 3 8 5
-1 1 7 .B 7 5 9 9 1 8 .7 6 1 1 2 6 1 6 -1 3 9 .9 0 5 8 7 9 1 9 .0 3 1 8 - 1 3 9 .6 3 5 2
DECADE9 H MEAN ABE MT
FORKOLA 69A
HT PREDICTED
BASED ON DISTANCE
KEAN DAXA FROM MEAN
SH 6 9 0 .2 393 2 3 9 .9 8 B 2 5 7 9 6 - 1 5 3 .0 1 1 7 4
81 6 9 0 .2 64 6 3 9 1 .2 8 0 1 9 5 9 6 - 2 5 4 .7 1 9 8 0
SN £ 9 0 .2 839 5 7 8 .0 9 4 1 2 8 9B - 2 6 0 .9 0 5 8 7
HH 6 9 0 .2 647 3 B 7 .2 7 1 7 3 4 8 - 2 5 9 .7 2 8 2 6
H I £ 9 0 .2 860 5 8 4 .5 0 1 5 2 2 8 5 -2 7 5 .4 9 8 4 7
HH £ 9 0 .2 1 06 5 7 9 4 .2 9 7 7 0 8 9 8 -2 7 0 .7 0 2 2 9
LH 6 9 0 .2 101 4 5 7 9 .0 8 5 0 5 9 6 9 - 4 3 4 .9 1 4 9 4
L I 6 9 0 .2 118 9 8 0 0 .4 9 6 3 6 8 3 - 3 8 8 .5 0 3 6 3
IH 6 9 0 .2 150 4 1 0 1 9 .8 8 7 9 8 7 7 3 -4 8 4 .1 1 2 0 1
DECADE10 N HEAN AGE m
FORMULA 69A
HT PREDICTED
BASED CH I DISTANCE
MEAN DAXA FRCM HEAH
SH 2 98 285 2 5 2 .5 8 2 9 9 4 7 5 - 3 2 .4 1 7 0 0 5
S I 2 98 510 4 1 1 .5 2 7 8 3 2 3 3 - 9 8 .4 7 2 1 6 7
SN 2 98 882 6 0 7 .7 9 1 4 9 7 3 7 - 2 7 4 .2 0 8 5 0
M W 2 98 3 45 4 0 7 .3 1 6 6 0 8 5 5 6 2 .3 1 6 6 0 8 5
M I 2 98 630 6 1 4 .5 2 3 0 0 0 6 6 -1 5 .4 7 6 9 9 9
M N 2 98 993 8 3 4 .9 3 1 4 4 5 2 3 -1 5 8 .0 6 8 5 5
IH 2 98 70 5 6 0 8 .8 3 2 5 5 2 9 8 -9 6 .1 6 7 4 4 7
L I 2 98 1 0 2 6 8 4 1 .4 4 3 6 5 5 4 1 -1 8 4 .5 5 6 3 4
IH 2 98 130 2 1 0 7 1 .9 3 2 9 0 5 4 -2 3 0 .0 6 7 0 9
MDECADE2 N KEAN AGE HT
FORMOLA 69A
MT PREDICTED
BASED ON DISTANCE
MEAN DATA FRCH HEAN
SH 3 1 2 1 .5 1 9 9 .9 3 5 5 1 2 9 .0 5 7 6 9 1 6 7 - 7 0 .8 7 7 8 0 8
S I 3 1 2 1 .5 2 8 2 .9 6 7 7 2 1 2 .9 4 5 2 4 4 8 4 - 7 0 .0 2 2 4 5 5
SN 31 2 1 .5 3 7 3 .3 5 4 8 3 1 6 .5 2 8 8 4 5 8 4 -5 6 .8 2 5 9 5 4
MN 3 1 2 1 .5 2 5 7 .4 1 9 3 2 1 0 .7 2 2 6 5 4 5 1 -4 6 .6 9 6 6 4 5
MI 3 1 2 1 .5 3 5 8 .4 5 1 6 3 2 0 .0 8 1 5 B 3 6 8 -3 8 .3 7 0 0 1 6
HH 31 2 1 .5 4 7 4 .9 6 7 7 4 3 6 .4 0 8 2 6 2 7 6 -3 8 .5 5 9 4 3 7
LH 3 1 2 1 .5 3 9 0 .3 8 7 1 3 1 7 .0 7 8 2 9 1 8 5 -7 3 .3 0 8 8 0 8
L I 3 1 2 1 .5 5 0 1 .2 9 0 3 4 3 9 .8 4 5 2 6 2 5 8 -6 1 .4 4 5 0 3 7
IH 31 2 1 .5 6 2 6 .7 0 9 7 5 6 1 .4 9 2 3 6 6 7 4 -6 5 .2 1 7 3 3 3
HDECADE3 N MEAN ASE MT
FORKOLA 69A
HT PREDICTED
BASED OH DISTANCE
KEAN DAXA FRCH HEAN
SH 1 97 2 9 .7 1 9 6 .8 7 3 1 1 4 2 • 29B 31239 -5 4 .5 7 4 7 8 7
S I 19 7 2 9 .7 2 7 6 .3 0 4 6 2 3 4 .2 3 1 2 2 1 5 4 -4 2 .0 7 3 3 7 8
SN 197 2 9 .7 3 9 5 .5 7 3 6 3 4 7 .7 4 9 1 5 6 2 - 4 7 .8 2 4 4 4 3
HH 197 2 9 .7 2 5 7 .3 9 0 9 2 3 1 .7 9 5 4 7 0 5 - 2 5 .5 9 5 4 2 9
MI 197 2 9 .7 3 7 3 .2 4 8 7 3 5 1 .6 4 2 6 2 4 4 6 -2 1 .6 0 6 0 7 5
HH 197 2 9 .7 5 1 0 .3 6 5 5 4 7 9 .1 2 5 7 8 0 3 6 -3 1 .2 3 9 7 1 9
LH 197 2 9 .7 3 9 5 .3 6 0 4 3 4 8 .3 5 1 2 9 7 6 2 -4 7 .0 0 9 1 0 2
L I 197 2 9 .7 5 3 8 .2 0 3 1 4 8 2 .8 9 2 4 1 0 5 7 -5 5 .3 1 0 6 8 9
IH 1 9 7 2 9 .7 6 9 1 .7 9 6 9 6 1 6 .2 0 6 2 5 4 5 4 -7 5 .5 9 0 6 4 5
FORMULA 69A
MT PREDICTED
BASED OH DISTANCE
EACH V IS IT FRCH HEAN
2 3 9 .9 3 4 4 - 1 5 3 .0 6 5 6
3 9 1 .1 9 3 6 - 2 5 4 .8 0 6 4
5 7 7 .9 6 7 2 - 2 6 1 .0 3 2 8
3 8 7 .1 8 6 1 - 2 5 9 .8 1 3 9
5 8 4 .3 7 3 2 - 2 7 5 .6 2 6 a
7 9 4 .1 2 4 1 - 2 7 0 .8 7 5 9
5 7 8 .9 5 7 9 - 4 3 5 .0 4 2 1
8 0 0 .3 2 1 4 - 3 8 8 .6 7 8 6
1 0 1 9 .6 6 6 - 4 8 4 .3 3 4
FORKOLA 69A
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH MEAN
2 5 2 .5 8 3 - 3 2 .4 1 7
4 1 1 .5 2 7 8 - 9 8 .4 7 2 2
6 0 7 .7 9 1 5 - 2 7 4 .2 0 8 5
4 0 7 .3 1 6 6 6 2 .3 1 6 6
6 1 4 .5 2 2 9 - 1 5 .4 7 7 1
8 3 4 .9 3 1 5 - 1 5 8 .0 6 8 5
6 0 8 .8 3 2 5 - 9 6 .1 6 7 5
8 4 1 .4 4 3 7 - 1 8 4 .5 5 6 3
1 0 7 1 .9 3 3 - 2 3 0 .0 6 7
FORMOLA 69A
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT n u n m ean
1 2 8 .9 7 9 6 - 7 0 .9 5 5 9
2 1 2 .8 1 9 6 - 7 0 .1 4 8 1
3 1 6 .3 4 4 6 - 5 7 .0 1 0 2
2 1 0 .5 9 8 3 - 4 6 .8 2 1
3 1 9 .8 9 5 4 - 3 8 .5 5 6 2
4 3 6 .1 5 6 2 - 3 8 .8 1 1 5
3 1 6 .8 9 3 7 - 7 3 .4 9 3 4
4 3 9 .5 9 1 2 - 6 1 .6 9 9 1
5 6 1 .1 6 9 6 - 6 5 .5 4 0 1
FORMULA 69A
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH MEAN
1 4 2 .2 5 - 5 4 .6 2 3 1
2 3 4 .1 5 3 4 - 4 2 .1 5 1 2
3 4 7 .6 3 5 2 - 4 7 .9 3 8 4
2 3 1 .7 1 8 5 - 2 5 .6 7 2 4
3 5 1 .5 2 7 3 - 2 1 .7 2 1 4
4 7 8 .9 7 - 3 1 .3 9 5 5
3 4 8 .2 3 7 1 - 4 7 .1 2 3 3
4 8 2 .7 3 5 7 - 5 5 .4 6 7 4
6 1 6 .0 0 6 7 - 7 5 .7 9 0 2
FORMULA £9B
UT PREDICTED
BASED OH DISTANCE
MEAN DAXA FROM HEAH
2 0 9 .3 3 9 2 5 7 9 6 - 1 8 3 .6 6 1 7 4
3 6 0 .6 3 0 1 9 5 9 6 - 2 8 5 .3 6 9 8 0
5 4 7 .4 4 4 1 2 8 9 3 - 2 9 1 .5 5 5 8 7
3 5 6 .6 2 1 7 3 4 8 - 2 9 0 .3 7 8 2 6
5 5 3 .8 5 1 5 2 2 8 5 -3 0 6 .1 4 8 4 7
7 6 3 .6 4 7 7 0 8 9 8 -3 0 1 .3 5 2 2 9
5 4 8 .4 3 5 0 5 9 6 9 - 4 6 5 .5 6 4 9 4
7 6 9 .8 4 6 3 6 8 3 - 4 1 9 .1 5 3 6 3
9 8 9 .2 3 7 9 8 7 7 3 -5 1 4 .7 6 2 0 1
FORHQLA69B
H I PREDICTED
BASED OH DISTANCE
HEAN DAXA FROM HEAN
2 1 6 .0 8 2 9 9 4 7 5 -6 8 .9 1 7 0 0 5
3 7 5 .0 2 7 8 3 2 3 3 -1 3 4 .9 7 2 1 6
5 7 1 .2 9 1 4 9 7 3 7 - 3 1 0 .7 0 8 5 0
3 7 0 .8 1 6 6 0 8 5 5 2 5 .8 1 6 6 0 8 5
5 7 8 .0 2 3 0 0 0 6 6 - 5 1 .9 7 6 9 9 9
7 9 8 .4 3 1 4 4 5 2 3 -1 9 4 .5 6 8 5 5
5 7 2 .3 3 2 5 5 2 9 8 -1 3 2 .6 6 7 4 4
8 0 4 .9 4 3 6 5 5 4 1 - 2 2 1 .0 5 6 3 4
1 0 3 5 .4 3 2 9 0 5 4 -2 6 6 .5 6 7 0 9
FORMULA 69B
MT PREDICTED
BASED OS DISTANCE
KEAN DATA FRCH MEAN
1 4 9 .9 3 2 6 9 1 6 7 -5 0 .0 0 2 8 0 8
2 3 3 .8 2 0 2 4 4 8 4 -4 9 .1 4 7 4 5 5
3 3 7 .4 0 3 8 4 5 B 4 -3 5 .9 5 0 9 5 4
2 3 1 .5 9 7 6 5 4 5 1 -2 5 .8 2 1 6 4 5
3 4 0 .9 5 6 5 8 3 6 8 -1 7 .4 9 5 0 1 6
4 5 7 .2 8 3 2 6 2 7 6 -1 7 .6 8 4 4 3 7
3 3 7 .9 5 3 2 9 1 8 5 -5 2 .4 3 3 8 0 8
4 6 0 .7 2 0 2 6 2 5 8 -4 0 .5 7 0 0 3 7
5 8 2 .3 6 7 3 6 6 7 4 - 4 4 .3 4 2 3 3 3
FORKOLA 69B
MT PREDICTED
BASED OH DISTANCE
HEAN DATA FRCH KEAN
1 5 7 .0 2 3 3 1 2 3 9 -3 9 ,8 4 9 7 8 7
2 4 8 .9 5 6 2 2 1 5 4 -2 7 .3 4 8 3 7 8
3 6 2 .4 7 4 1 5 6 2 -3 3 .0 9 9 4 4 3
2 4 6 .5 2 0 4 7 0 5 -1 0 .8 7 0 4 2 9
3 6 6 .3 6 7 6 2 4 4 6 - 6 .8 8 1 0 7 5 5
4 9 3 .8 5 0 7 8 0 3 6 - 1 6 .5 1 4 7 1 9
3 6 3 .0 7 6 2 9 7 6 2 - 3 2 .2 8 4 1 0 2
4 9 7 .6 1 7 4 1 0 5 7 - 4 0 .5 8 5 6 8 9
6 3 0 .9 3 1 2 5 4 5 4 - 6 0 .8 6 5 6 4 5
FORKOLA 69B
MT PREDICTED
BASED OH DISTANCE
EACH V IS IT FRCH KEAN
2 0 9 .3 0 9 4 -1 8 3 .6 9 0 6
3 6 0 .5 6 8 6 - 2 8 5 .4 3 1 4
5 4 7 .3 4 2 2 - 2 9 1 .6 5 7 8
3 5 6 .5 6 1 1 - 2 9 0 .4 3 8 9
5 5 3 .7 4 8 2 -3 0 6 .2 5 1 B
7 6 3 .4 9 9 1 - 3 0 1 .5 0 0 9
5 4 8 .3 3 2 9 - 4 6 5 .6 6 7 1
7 6 9 .6 9 6 4 - 4 1 9 .3 0 3 6
9 8 9 .0 4 0 6 - 5 1 4 .9 5 9 4
FORMOLA 69B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH MEAN
2 1 6 .0 8 3 - 6 8 .9 1 7
3 7 5 .0 2 7 8 - 1 3 4 .9 7 2 2
5 7 1 .2 9 1 5 - 3 1 0 .7 0 8 5
3 7 0 .8 1 6 6 2 5 .8 1 6 6
5 7 8 .0 2 2 9 - 5 1 .9 7 7 1
7 9 8 .4 3 1 5 - 1 9 4 .5 6 8 5
5 7 2 .3 3 2 5 - 1 3 2 .6 6 7 5
8 0 4 .9 4 3 7 - 2 2 1 .0 5 6 3
1 0 3 5 .4 3 3 - 2 6 6 .5 6 7
FORKOLA 69B
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCM HEAN
1 4 9 .8 9 0 9 - 5 0 .0 4 4 6
2 3 3 .7 3 0 9 - 4 9 .2 3 6 8
3 3 7 .2 5 5 9 - 3 6 .0 9 8 9
2 3 1 .5 0 9 6 - 2 5 .9 0 9 7
3 4 0 .6 0 6 6 - 1 7 .6 4 5
4 5 7 .0 6 7 4 - 1 7 .9 0 0 3
3 3 7 .8 0 5 -5 2 .5 B 2 1
4 6 0 .5 0 2 5 - 4 0 .7 8 7 8
5 8 2 .0 8 0 8 - 4 4 .6 2 8 9
FORMOLA 69B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FROM KEAN
1 5 6 .9 9 7 4 - 3 9 .8 7 5 7
2 4 8 .9 0 0 9 - 2 7 .4 0 3 7
3 6 2 .3 8 2 7 - 3 3 .1 9 0 9
2 4 6 .4 6 5 9 - 1 0 .9 2 5
3 6 6 .2 7 4 7 - 6 . 9 7 4
4 9 3 .7 1 7 5 - 1 6 .6 4 8
3 6 2 .9 8 4 5 - 3 2 .3 7 5 9
4 9 7 .4 8 3 2 - 4 0 .7 1 9 9
6 3 0 .7 5 4 2 - 6 1 .0 4 2 7
MDECADK4 N MEAN ASE MX
FORMULA 69A
HT PREDICTED
BASED ON DISTANCE
HEAH DAXA FRCH MEAN
SH 203 3 9 . 6 2 0 1 .7 8 3 2 1 5 8 .2 8 3 9 3 9 8 5 -4 3 .4 9 9 2 6 0
S I 203 3 9 . 6 3 0 0 .3 2 5 1 2 5 9 .9 3 0 1 4 4 6 3 - 4 0 .3 9 4 9 5 5
SN 20 3 3 9 . 6 4 5 9 .5 7 6 4 3 8 5 .4 4 1 9 6 9 9 3 - 7 4 .1 3 4 4 3 0
HH 20 3 3 9 . 6 2 7 5 .7 3 4 2 5 7 .2 3 7 0 4 1 0 2 - 1 8 .4 9 6 9 5 8
H I 20 3 3 9 . 6 4 1 4 .3 5 4 7 3 8 9 .7 4 6 8 0 7 8 3 - 2 4 .6 0 7 8 9 2
UN 20 3 3 9 .6 5 9 1 .5 7 6 4 5 3 0 .6 9 9 3 6 8 6 8 - 6 0 .8 7 7 0 3 1
LW 20 3 3 9 .6 4 2 6 3 8 6 .1 0 7 7 3 1 4 1 -3 9 .8 9 2 2 6 8
L I 20 3 3 9 .6 5 8 5 .8 4 2 3 5 3 4 .8 6 3 9 6 7 2 9 -5 0 .9 7 8 3 3 2
IN 20 3 3 9 .6 7 9 3 .6 5 5 2 6 8 2 .2 6 3 2 6 5 4 3 - 1 1 1 .3 9 1 9 3
HDECADE5 N HEAN ASE MX
FORMULA 69A
M X PREDICTED
BASED ON DISTANCE
MEAN DAXA FRCH MEAN
SH 2 2 9 4 9 .6 2 0 4 .7 8 6 1 7 4 .4 3 1 0 3 8 2 9 -3 0 .3 5 4 9 6 1
S I 2 29 4 9 .6 3 0 6 .6 0 2 6 2 8 5 .8 8 8 6 5 2 8 -2 0 .7 1 3 9 4 7
SN 2 2 9 4 9 .6 4 9 5 .4 3 2 3 4 2 3 .5 1 5 5 1 9 1 5 -7 1 .9 1 6 7 8 0
M W 2 2 9 .4 9 .6 2 8 7 .2 4 0 2 2 8 2 .9 3 5 5 9 7 1 1 - 4 .3 0 4 6 0 2 8
H I 2 2 9 4 9 .6 4 3 8 .8 9 0 8 4 2 8 .2 3 5 8 8 1 9 5 -1 0 .6 5 4 9 1 8
MN 229 4 9 . 6 6 1 5 .3 5 3 7 5 8 2 .7 9 3 9 0 2 3 4 -3 2 .5 5 9 7 9 7
LH 2 2 9 4 9 .6 4 3 2 .1 0 4 8 4 2 4 .2 4 5 5 4 3 3 2 -7 .8 5 9 2 5 6 6
L I 2 2 9 4 9 .6 6 1 1 .4 4 9 8 5 8 7 .3 6 0 4 8 9 2 3 -2 4 .0 8 9 3 1 0
IN 2 2 9 4 9 .6 8 1 5 .8 4 2 8 7 4 8 .9 8 7 5 1 8 8 5 -6 6 .8 5 5 2 B 1
HDECADE6 N MEAN ASE MI
FORMOLA 69A
M X PREDICTED
EASED ON DISTANCE
MEAN DAXA FRCM MEAN
SH 1 4 4 5 9 .5 2 1 4 .7 9 1 7 1 8 8 .2 4 9 1 2 1 1 5 -2 6 .5 4 2 5 7 8
S I 1 4 4 5 9 .5 3 3 6 .7 5 3 0 8 .1 5 4 3 9 0 4 9 - 2 8 .5 9 5 6 0 9
SN 14 4 5 9 .5 5 1 2 .1 2 5 4 5 6 .2 1 2 3 4 5 5 3 -5 5 .9 1 2 6 5 4
HH 14 4 5 9 .5 3 0 5 .2 0 8 3 3 0 4 .9 7 7 5 1 5 2 3 - 0 .2 3 0 7 8 4 7
H I 14 4 5 9 .5 4 6 2 .9 5 8 3 4 6 1 .2 9 0 4 7 6 5 8 - 1 .6 6 7 8 2 3 4
MN 1 4 4 5 9 .5 6 5 6 .1 6 6 7 6 2 7 .5 6 2 8 4 0 6 9 - 2 8 .6 0 3 8 5 9
JM 1 4 4 5 9 .5 4 7 2 .8 3 3 3 4 5 6 .9 9 7 7 0 0 0 8 - 1 5 .8 3 5 5 9 9
L I 1 4 4 5 9 .5 6 6 4 .9 5 8 3 6 3 2 .4 7 5 5 4 0 7 7 - 3 2 .4 8 2 7 5 9
IN 1 4 4 5 9 .5 8 8 2 .2 0 8 3 8 0 6 .3 5 2 6 9 2 2 2 -7 5 .8 5 5 6 0 7
MDECADE7 N MEAN ASE MT
FORMOLA 69A
MX PREDICTED
BASED CN DISTANCE
HEAN DAXA FRCH MEAN
SH 1 6 4 6 9 .6 2 5 2 .4 3 9 2 0 4 .1 9 5 9 7 7 9 3 - 4 8 .2 4 3 0 2 2
S I 16 4 6 9 .6 3 9 7 .2 4 3 9 3 3 3 .7 9 0 9 8 4 7 8 - 6 3 .4 5 2 9 1 5
SN 16 4 6 9 .6 5 8 3 .1 3 4 2 4 9 3 .8 1 3 7 4 1 1 2 -8 9 .3 2 0 4 5 8
HH 1 6 4 6 9 .6 3 5 0 .0 8 5 4 3 3 0 .3 5 7 3 8 1 1 3 - 1 9 .7 2 8 0 1 8
MI 16 4 6 9 .6 5 3 0 .6 3 4 2 4 9 9 .3 0 2 2 4 4 1 1 - 3 1 .3 3 1 9 5 5
UN 164 6 9 .6 7 4 0 .7 8 0 5 6 7 9 .0 1 1 3 4 5 1 9 - 6 1 .7 6 9 1 5 4
IH 164 6 9 .6 5 5 6 .1 3 4 2 4 9 4 .6 6 2 5 6 1 4 4 - 6 1 .4 7 1 6 3 8
L I 164 6 9 .6 7 5 4 .8 6 5 8 6 8 4 .3 2 1 0 4 8 4 6 - 7 0 .5 4 4 7 5 1
IN 164 6 9 .6 9 6 9 .7 3 1 7 8 7 2 .2 4 9 4 9 1 9 7 - 9 7 .4 8 2 2 0 8
vO
o
FORKOLA 69A
MT PREDICTED
BASED CM DISTANCE
EACH V IS IT FRCH HEAN
1 5 8 .2 7 7 6 - 4 3 .5 0 5 6
2 5 9 .9 1 9 8 - 4 0 .4 0 5 3
3 8 5 .4 2 7 - 7 4 .1 4 9 4
2 5 7 .2 2 6 7 -1 8 - 5 0 7 3
3 8 9 .7 3 1 6 - 2 4 .6 2 3 1
5 3 0 .6 7 8 6 - 6 0 .8 9 7 8
3 8 6 .0 9 2 4 - 3 9 .9 0 7 6
5 3 4 .8 4 3 1 - 5 0 .9 9 9 2
6 8 2 .2 3 7 1 - 1 1 1 .4 1 8 1
FORMULA 69A
H I PREDICTED
BASED OB DISTANCE
EACH V IS IT FRCH HEAN
1 7 4 .4 9 8 7 - 3 0 .2 8 7 3
2 8 5 .9 9 7 5 - 2 0 .6 0 5 1
4 2 3 .6 7 5 2 - 7 1 .7 5 7 1
2 8 3 .0 4 3 3 - 4 .1 9 6 9
4 2 8 .3 9 7 3 - 1 0 .4 9 3 5
5 8 3 .0 1 2 5 - 3 2 .3 4 1 2
4 2 4 .4 0 5 3 - 7 .6 9 9 5
5 8 7 .5 8 0 8 - 2 3 .8 6 9
7 4 9 .2 6 7 3 - 6 6 .5 7 5 5
FORMOLA 69A
HE PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH HEAN
1 9 0 .5 7 3 6 - 2 4 .2 1 8 1
3 1 1 .8 3 9 9 - 2 4 .9 1 0 1
4 6 1 .5 7 8 5 - 5 0 .5 4 6 5
3 0 8 .6 2 6 9 3 .4 1 8 6
4 6 6 .7 1 4 3 .7 5 5 7
6 3 4 .8 7 3 8 - 2 1 .2 9 2 9
4 6 2 .3 7 2 7 - 1 0 .4 6 0 6
6 3 9 .8 4 2 2 - 2 5 .1 1 6 1
8 1 5 .6 9 3 7 - 6 6 .5 1 4 6
FORKOLA 69A
M X PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH KEAN
2 0 7 .1 5 4 4 - 4 5 .2 8 4 6
3 3 8 .4 9 5 9 - 5 8 .7 4 8
5 0 0 .6 7 4 8 - 8 2 .4 5 9 4
3 3 5 .0 1 5 7 - 1 5 .0 6 9 7
5 0 6 .2 3 6 9 - 2 4 .3 9 7 3
6 8 8 .3 6 8 2 - 5 2 .4 1 2 3
5 0 1 .5 3 5 1 - 5 4 .5 9 9 1
6 9 3 .7 4 9 1 - 6 1 .1 1 6 7
B B 4.2099 - 8 5 .5 2 1 8
FORMULA. 69B
ME PREDICTED
BASED O S DISTANCE
MEAN DATA TSLCtt MEAN
1 6 5 ,5 9 3 9 3 9 8 5 -3 6 .1 9 9 2 6 0
2 6 7 .2 3 0 1 4 4 6 3 -3 3 .0 9 4 9 5 5
3 9 2 .7 4 1 9 6 9 9 3 -6 6 .8 3 4 4 3 0
2 6 4 .5 3 7 0 4 1 0 2 -1 1 .1 9 6 9 5 8
3 9 7 .0 4 6 8 0 7 6 3 -1 7 .3 0 7 8 9 2
5 3 7 .9 9 9 3 6 8 6 B -5 3 .5 7 7 0 3 1
3 9 3 .4 0 7 7 3 1 4 1 -3 2 .5 9 2 2 6 8
5 4 2 .1 6 3 9 6 7 2 9 -4 3 .6 7 8 3 3 2
6 8 9 .5 6 3 2 6 5 4 3 -1 0 4 .0 9 1 9 3
FORMULA 69B
H I PREDICTED
BASED OB DISTANCE
KEAN DAXA FRCM MEAN
1 7 4 .2 3 1 0 3 8 2 9 -3 0 .5 5 4 9 6 1
2 8 5 .6 8 8 6 5 2 8 -2 0 .9 1 3 9 4 7
4 2 3 .3 1 5 5 1 9 1 5 -7 2 .1 1 6 7 8 0
2 8 2 .7 3 5 5 9 7 1 1 -4 .5 0 4 6 0 2 8
4 2 8 .0 3 5 8 8 1 9 5 -1 0 .8 5 4 9 1 8
5 8 2 .5 9 3 9 0 2 3 4 - 3 2 .7 5 9 7 9 7
4 2 4 .0 4 5 5 4 3 3 2 - 8 .0 5 9 2 5 6 6
5 8 7 .1 6 0 4 8 9 2 3 - 2 4 .2 8 9 3 1 0
7 4 8 .7 8 7 5 1 8 8 5 -6 7 .0 5 5 2 B 1
FORMULA 69B
ME PREDICTED
BASED ON DISTANCE
MEAN DATA FRCM MEAN
2 1 3 .8 0 9 7 1 4 1 5 -0 .9 8 1 9 8 5 8
3 3 3 .7 1 4 9 8 3 4 9 - 3 .0 3 5 0 1 6 5
4 8 1 .7 7 2 9 3 8 5 3 - 3 0 .3 5 2 0 6 1
3 3 0 .5 3 8 1 0 8 2 3 2 5 .3 2 9 8 0 8 2
4 8 6 .8 5 1 0 6 9 5 8 2 3 .8 9 2 7 6 9 5
6 5 3 .1 2 3 4 3 3 6 9 -3 .0 4 3 2 6 6 3
4 8 2 .5 5 8 2 9 3 0 8 9 .7 2 4 9 9 3 0 8
6 5 8 .0 3 6 1 3 3 7 7 -6 .9 2 2 1 6 6 2
8 3 1 .9 1 3 2 8 5 2 2 -5 0 .2 9 5 0 1 4
FORMULA 69B
M I PREDICTED
BASED OR DISTANCE
KEAN DATA FROM MEAN
2 3 7 .3 5 8 6 9 9 5 3 -1 5 .0 8 0 3 0 0
3 6 6 .9 5 3 7 0 6 3 8 -3 0 .2 9 0 1 9 3
5 2 6 .9 7 6 4 6 2 7 2 -5 6 .1 5 7 7 3 7
3 6 3 .5 2 0 1 0 2 7 3 1 3 .4 3 4 7 0 2 7
5 3 2 .4 6 4 9 6 5 7 1 1 .8 3 0 7 6 5 7 0
7 1 2 .1 7 4 0 6 6 7 9 -2 8 .6 0 6 4 3 3
5 2 7 .8 2 5 2 8 3 0 4 - 2 8 .3 0 8 9 1 6
7 1 7 ,4 8 3 7 7 0 0 6 -3 7 ,3 8 2 0 2 9
9 0 5 .4 1 2 2 1 3 5 7 -6 4 .3 1 9 4 8 6
FORMULA 69B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH MEAN
1 6 5 .5 8 0 5 - 3 6 .2 0 2 7
2 6 7 .2 2 2 8 - 3 3 .1 0 2 3
3 9 2 .7 2 9 9 - 6 6 .8 4 6 5
2 6 4 .5 2 9 6 - 1 1 .2 0 4 4
3 9 7 .0 3 4 6 - 1 7 .3 2 0 1
5 3 7 .9 8 1 6 - 5 3 .5 9 4 8
3 9 3 .3 9 5 4 - 3 2 .6 0 4 6
5 4 2 .1 4 6 - 4 3 .6 9 6 3
6 8 9 .5 4 0 1 - 1 0 4 .1 1 5 1
FORMULA 69B
MI PREDICTED
BASED (N T DISTANCE
EACH V IS IT FRCH HEAN
1 7 4 .2 6 7 3 - 3 0 .5 1 8 7
2 8 5 .7 6 6 1 - 2 0 .8 3 6 5
4 2 3 .4 4 3 8 - 7 1 .9 8 8 5
2 8 2 .8 1 1 8 - 4 .4 2 8 4
4 2 8 .1 6 5 9 - 1 0 .7 2 4 9
5 8 2 .7 8 1 1 - 3 2 .5 7 2 6
4 2 4 .1 7 3 8 - 7 . 9 3 1
5 8 7 .3 4 9 4 - 2 4 .1 0 0 4
7 4 9 .0 3 5 8 - 6 6 .8 0 7
FORMULA 69B
KE PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCH KEAH
1 B 2 .8 7 5 7 - 3 1 .9 1 6
3 0 4 .1 4 1 9 - 3 2 .6 0 8 1
4 5 3 .8 8 0 5 - 5 8 .2 4 4 5
3 0 0 .9 2 9 - 4 .2 7 9 3
4 5 9 .0 1 6 2 - 3 .9 4 2 1
6 2 7 .1 7 6 - 2 8 .9 9 0 7
4 5 4 .6 7 4 8 - 1 8 .1 5 8 5
6 3 2 .1 4 4 3 - 3 2 .8 1 4
8 0 7 .9 9 5 8 - 7 4 .2 1 2 5
FORMULA 69B
M X PREDICTED
BASED OH DISTANCE
EACH V IS IT FRCH HEAN
1 9 1 .7 5 5 1 - 6 0 .6 8 3 9
3 2 3 .0 9 6 5 - 7 4 .1 4 7 4
4 B 5 .2 7 5 5 - 9 7 .8 5 8 7
3 1 9 .6 1 6 3 - 3 0 .4 6 9 1
4 9 0 .8 3 7 6 - 3 9 .7 9 6 6
6 7 2 .9 6 8 9 - 6 7 .8 1 1 6
4 8 6 .1 3 5 7 -6 9 .9 9 B 5
6 7 8 .3 4 9 7 - 7 6 .5 1 6 1
8 6 8 .8 1 0 5 - 1 0 0 .9 2 1 2
FORMOLA 69A FORMULA 69A FORMULA 69B
FORMULA 69B
M X PREDICT 1 0 M X PREDICTED MI PREDICTED MX PREDICTED
BASED ON DISTANCE BASED OK DISTANCE BASED ON DISTANCE BASED OH DISTANCE
MDECADE8 N MIAS AS2 lex MEAN DAXA FROM HEAH EACH V IS IT FRCH HEAN HEAN DATA FRCH KEAN EACH V IS IT FRCH MEAN
SH 7 2 7 8 .3 2 8 2 .0 3 3 3 2 2 0 .7 7 3 2 1 0 8 2 -6 2 .0 6 0 0 8 9 2 2 0 .8 9 4 3 - 6 1 .9 3 9 1 9 9 .0 4 8 2 1 0 0 2 - 8 3 .7 8 5 0 8 9 1 9 9 .1 1 3 1 - 8 3 .7 2 0 2
s x 7 2 7 0 .3 4 3 9 .£ 0 6 7 3 6 0 .3 8 9 5 7 1 2 4 -7 9 .2 7 7 1 2 B 3 6 0 .5 8 4 4 - 7 9 .0 8 2 3 3 3 8 .6 6 4 5 7 1 2 4 - 1 0 1 .0 0 2 1 2 3 3 8 .8 0 3 1 - 1 0 0 .8 6 3 6
SH 72 7 0 .3 6 2 5 .1 6 6 7 5 3 2 .7 8 6 6 0 5 4 1 - 9 2 .3 8 0 0 9 4 5 3 3 .0 7 2 2 - 9 2 .0 9 4 5 5 1 1 .0 6 1 6 0 5 4 1 - 1 1 4 .1 0 5 0 9 5 1 1 .2 9 1 -1 1 3 .B 7 5 7
M W 72 7 0 .3 4 0 4 .3 3 3 3 3 5 6 .6 9 0 4 5 3 0 7 -4 7 .6 4 2 8 4 6 3 5 6 .8 0 3 1 - 4 7 .4 5 0 2 3 3 4 .9 6 5 4 5 3 0 7 - 6 9 .3 6 7 8 4 6 3 3 5 .1 0 1 0 - 6 9 .2 3 1 5
M X 72 7 8 .3 5 6 9 5 3 0 .6 9 9 5 2 4 6 6 - 3 0 .3 0 0 4 7 5 5 3 8 .9 8 8 2 - 3 0 .0 1 1 8 5 1 6 .9 7 4 5 2 4 6 6 - 5 2 .0 2 5 4 7 5 5 1 7 .2 0 6 9 - 5 1 .7 9 3 1
HH 72 7 S .3 7 8 0 .5 7 3 2 .3 0 5 2 1 3 9 3 - 4 8 .1 9 4 7 8 6 7 3 2 .6 9 5 9 - 4 7 .8 0 4 1 7 1 0 .5 8 0 2 1 3 9 3 - 6 9 .9 1 9 7 8 6 7 1 0 .9 1 4 6 - 6 9 .5 8 5 4
IH 72 7 8 .3 6 1 1 .5 5 3 3 .7 0 1 0 6 3 5 1 -7 7 .7 9 8 9 3 6 5 3 3 .9 8 7 1 - 7 7 .5 1 2 9 5 1 1 .9 7 6 0 6 3 5 1 - 9 9 .5 2 3 9 3 6 5 1 2 .2 0 5 8 - 9 9 .2 9 4 2
X I 72 7 0 .3 0 3 0 .1 6 6 7 7 3 8 .0 2 5 5 0 7 1 9 -9 2 .1 4 1 1 9 2 7 3 8 .4 1 9 3 - 9 1 .7 4 7 4 7 1 6 .3 0 0 5 0 7 1 9 - 1 1 3 .8 6 6 1 9 7 1 6 .6 3 8 -1 1 3 .5 2 8 7
IN 72 7 0 .3 1 0 7 3 .8 3 3 9 4 0 .4 0 6 1 2 6 1 6 -1 3 3 .3 4 6 B 7 9 4 0 .9 0 6 0 - 1 3 2 .8 4 6 2 9 1 8 .7 6 1 1 2 6 1 6 - 1 5 5 .0 7 1 8 7 9 1 9 .2 0 5 5 -1 5 4 .6 2 7 5
FORMULA 69A FORMULA 69A FORMOLA 69B FORMULA 69B
MI PREDICTED NX PREDICTED MT PREDICTED HT PREDICTED
BASED ON DISTANCE BASED ON DISTANCE BASED OK DISTANCE BASED ON DISTANCE
HDECADE9 H MEAN ASS M X MEAN DAXA FRCH MEAN EACH V IS IT FRCH MEAN HEAN BATA FRCH MEAN EACH V IS IT FRCH MEAN
SH 5 9 0 .2 390 2 3 9 .9 8 8 2 5 7 9 6 -1 5 0 .0 1 1 7 4 2 3 0 .6 9 6 5 - 1 5 1 .3 0 3 5 2 0 9 .3 3 8 2 5 7 9 6 -1 8 0 .6 6 1 7 4 2 0 8 .6 4 6 5 - 1 8 1 .3 5 3 5
SX 5 9 0 .2 6 4 6 .0 3 9 1 .2 8 0 1 9 5 9 6 -2 5 5 .5 1 9 8 0 3 8 9 .2 0 3 5 - 2 5 7 .5 9 6 5 3 6 0 .6 3 0 1 9 5 9 6 -2 8 6 .1 6 9 8 0 3 5 9 .1 5 3 5 -2 8 7 .6 4 6 5
SH 5 9 0 .2 8 5 0 .8 5 7 8 .0 9 4 1 2 8 9 0 - 2 7 2 .7 0 5 8 7 5 7 5 .0 4 8 2 - 2 7 5 .7 5 1 8 5 4 7 .4 4 4 1 2 8 9 8 -3 0 3 .3 5 5 B 7 5 4 4 .9 9 8 2 - 3 0 5 .8 0 1 8
M W 5 9 0 .2 £ 6 8 .4 3 8 7 ,2 7 1 7 3 4 8 -2 8 1 .1 2 B 2 6 3 8 5 .2 1 5 9 - 2 8 3 .1 8 4 1 3 5 6 .6 2 1 7 3 4 8 -3 1 1 .7 7 8 2 6 3 5 5 .1 6 5 8 - 3 1 3 .2 3 4 2
MT 5 9 0 .2 8 6 7 .6 5 8 4 .5 0 1 5 2 2 8 5 -2 B 3 .0 9 8 4 7 5 6 1 .4 2 2 4 - 2 8 6 .1 7 7 6 5 5 3 .8 5 1 5 2 2 8 5 - 3 1 3 .7 4 8 4 7 5 5 1 .3 7 2 4 - 3 1 6 .2 2 7 6
HH 5 9 0 .2 1 0 5 2 .4 7 9 4 .2 9 7 7 0 0 9 8 - 2 5 8 .1 0 2 2 9 7 9 0 .1 3 0 2 - 2 6 2 .2 6 9 8 7 6 3 .6 4 7 7 0 8 9 8 - 2 8 8 .7 5 2 2 9 7 6 0 .0 8 0 2 - 2 9 2 .3 1 9 8
IH 5 9 0 .2 1 0 0 4 .4 5 7 9 .0 8 5 0 5 9 6 9 -4 2 5 .3 1 4 9 4 5 7 6 .0 3 4 - 4 2 8 .3 6 6 5 4 8 .4 3 5 0 5 9 6 9 -4 5 5 .9 6 4 9 4 5 4 5 .9 8 4 - 4 5 8 .4 1 6
L I 5 9 0 .2 1 1 8 6 .8 8 0 0 .4 9 6 3 6 8 3 -3 8 6 .3 0 3 6 3 7 9 6 .2 9 6 6 - 3 9 0 .5 0 3 4 7 6 9 .8 4 6 3 6 8 3 - 4 1 6 .9 5 3 6 3 7 6 6 .2 4 6 6 - 4 2 0 .5 5 3 4
LH 5 9 0 .2 1 4 8 4 .4 1 0 1 9 .8 8 7 9 8 7 7 3 - 4 6 4 .5 1 2 0 1 1 0 1 4 .5 5 - 4 6 9 .8 5 9 8 9 .2 3 7 9 8 7 7 3 - 4 9 5 .1 6 2 0 1 9 8 4 .5 0 0 1 - 4 9 9 .8 9 9 9
FORMULA 69A FORMULA 69A FORMULA 69B FORMULA 69B
MX PREDICTED M X PREDICTED MX PREDICTED MX PREDICTED
BASED OH DISTANCE BASED ON DISTANCE BASED CN DISTANCE BASED ON DISTANCE
MDECADE10 H MEAM ASS M X HEAN DATA FROM MEAN EACH V IS IT FRCH MEAH MEAN DATA FRCH HEAN EACH V IS IT FRCH MEAN
SH 2 90 285 2 5 2 .5 8 2 9 9 4 7 5 -3 2 .4 1 7 0 0 5 2 5 2 .5 8 3 - 3 2 .4 1 7 2 1 6 .0 8 2 9 9 4 7 5 - 6 8 .9 1 7 0 0 5 2 1 6 .0 8 3 -6 B .9 1 7
SX 2 90 510 4 1 1 .5 2 7 8 3 2 3 3 -9 8 .4 7 2 1 6 7 4 1 1 .5 2 7 8 - 9 8 .4 7 2 2 3 7 5 .0 2 7 0 3 2 3 3 - 1 3 4 .9 7 2 1 6 3 7 5 .0 2 7 8 - 1 3 4 .9 7 2 2
SH 2 98 882 6 0 7 .7 9 1 4 9 7 3 7 -2 7 4 .2 0 8 5 0 6 0 7 .7 9 1 5 - 2 7 4 .2 0 8 5 5 7 1 .2 9 1 4 9 7 3 7 -3 1 0 .7 0 8 5 0 5 7 1 .2 9 1 5 - 3 1 0 .7 0 8 5
HH 2 90 3 4 5 4 0 7 .3 1 6 6 0 8 5 5 6 2 .3 1 6 6 0 0 5 4 0 7 .3 1 6 6 6 2 .3 1 6 6 3 7 0 .8 1 6 6 0 8 5 5 2 5 .8 1 6 6 0 8 5 3 7 0 .8 1 6 6 2 5 .8 1 6 6
M X 2 98 630 6 1 4 .5 2 3 0 0 0 6 6 -1 5 .4 7 6 9 9 9 6 1 4 .5 2 2 9 - 1 5 .4 7 7 1 5 7 S .0 2 3 0 0 0 6 6 - 5 1 .9 7 6 9 9 9 5 7 8 .0 2 2 9 - 5 1 .9 7 7 1
MN 2 90 993 8 3 4 .9 3 1 4 4 5 2 3 -1 5 8 .0 6 8 5 5 0 3 4 .9 3 1 5 - 1 5 8 .0 6 8 5 7 9 8 .4 3 1 4 4 5 2 3 - 1 9 4 .5 6 8 5 5 7 9 8 .4 3 1 5 -1 9 4 .5 6 8 5
LH 2 98 70 5 6 0 B .03255298 -9 6 .1 6 7 4 4 7 6 0 8 .8 3 2 5 - 9 6 .1 6 7 5 5 7 2 .3 3 2 5 5 2 9 8 - 1 3 2 .6 6 7 4 4 5 7 2 .3 3 2 5 -1 3 2 .6 6 7 5
L I 2 90 1 0 2 6 8 4 1 .4 4 3 6 5 5 4 1 - 1 8 4 .5 5 6 3 4 8 4 1 .4 4 3 7 - 1 8 4 .5 5 6 3 8 0 4 .9 4 3 6 5 5 4 1 - 2 2 1 .0 5 6 3 4 8 0 4 .9 4 3 7 -2 2 1 .0 5 6 3
IH 2 98 1 30 2 1 0 7 1 .9 3 2 9 0 5 4 - 2 3 0 .0 6 7 0 9 1 0 7 1 .9 3 3 - 2 3 0 .0 6 7 1 0 3 5 .4 3 2 9 0 5 4 - 2 6 6 .5 6 7 0 9 1 0 3 5 .4 3 3 - 2 6 6 .5 6 7
FORMULA 69A FORMULA 69A FORMULA 69B FORMULA 69B
M X PREDICTED MT PREDICTED MT PREDICTED M X PREDICTED
BASED OS DISTANCE BASED O M DISTANCE BASED Ctt DISTANCE BASED CN DISTANCE
FEECADE2 N MEAH ACT MX MEAN DAXA ISOM HEAN EACH V IS IT FRCH MEAH HEAN DATA FRCM HEAN EACH V IS IT F R « MEAN
SH 4 2 3 .0 177 1 3 2 .7 7 1 5 2 4 3 1 -4 4 .2 2 8 4 7 5 1 3 2 .6 9 0 B - 4 4 .3 0 9 2 1 5 1 .9 2 1 5 2 4 3 1 -2 5 .0 7 8 4 7 5 1 5 1 .8 7 8 3 - 2 5 .1 2 1 7
SX 4 2 3 .0 2 2 0 .5 2 1 8 .9 1 5 7 0 1 7 2 - 1 . 58429B 2 2 1 8 .7 8 5 9 - 1 .7 1 4 1 2 3 8 .0 6 5 7 0 1 7 2 1 7 .5 6 5 7 0 1 7 2 3 7 .9 7 3 4 1 7 .4 7 3 4
SH 4 2 3 .0 3 60 3 2 5 .2 8 5 7 6 2 1 6 - 3 4 .7 1 4 2 3 7 3 2 5 .0 9 5 4 - 3 4 .9 0 4 6 3 4 4 .4 3 5 7 6 2 1 6 - 1 5 .5 6 4 2 3 7 3 4 4 .2 8 2 9 - 1 5 .7 1 7 1
HH 4 2 3 .0 2 2 0 .5 2 1 6 .6 3 3 3 2 2 4 1 - 3 .8 6 6 6 7 7 5 2 1 6 .5 0 4 8 - 3 .9 9 5 2 2 3 5 .7 8 3 3 2 2 4 1 1 5 .2 8 3 3 2 2 4 2 3 5 .6 9 2 3 1 5 .1 9 2 3
MI 4 2 3 .0 330 3 2 8 .9 3 4 0 7 0 7 3 - 1 .0 6 5 9 2 9 2 3 2 8 .7 4 1 6 - 1 .2 5 8 4 3 4 8 .0 8 4 0 7 0 7 3 1 8 .0 8 4 0 7 0 7 3 4 7 .9 2 9 1 1 7 .9 2 9 1
HH 4 2 3 .0 48 6 4 4 8 .3 9 0 0 0 5 5 -3 7 .6 0 9 9 9 4 4 4 8 .1 2 9 5 - 3 7 .8 7 0 5 4 6 7 .5 4 0 0 0 5 5 -1 8 .4 5 9 9 9 4 4 6 7 .3 1 7 - 1 8 .6 8 3
LH 4 2 3 .0 3 4 0 .5 3 2 5 .8 4 9 9 8 8 5 9 - 1 4 .6 5 0 0 1 1 3 2 5 .6 5 9 3 - 1 4 .8 4 0 7 3 4 4 .9 9 9 9 8 8 5 9 4 .4 9 9 9 8 8 5 8 3 4 4 .8 4 6 8 4 .3 4 6 8
L I 4 2 3 .B 471 4 5 1 .9 1 9 4 6 2 6 3 - 1 9 .0 8 0 5 3 7 4 5 1 .6 5 7 - 1 9 .3 4 3 4 7 1 .0 6 9 4 6 2 6 3 0 .0 6 9 4 6 2 6 2 4 7 0 .8 4 4 5 - 0 .1 5 5 5
IH 4 2 3 .8 723 5 7 6 .8 3 8 9 4 5 0 3 -1 4 6 .1 6 1 0 5 5 7 6 .5 0 5 2 -1 4 6 .4 9 4 8 5 9 5 .9B894503 -1 2 7 .0 1 1 0 5 5 9 5 .6 9 2 7 - 1 2 7 .3 0 7 3
FDEGADE3 H MEAN ASE HT
FORMOLA 69A
MT PREDICTED
BASED CN
MEAN DATA
DISTANCE
FRCH MEAH
SH 47 3 0 . 6 2 0 6 .6 8 0 8 1 4 3 .7 5 1 5 5 1 2 5 -6 2 .9 2 9 2 4 8
S I 47 3 0 . 6 2 6 6 .4 2 5 5 2 3 6 .5 6 7 4 8 7 2 8 - 2 9 .8 5 8 0 1 2
SN 47 3 0 . 6 3 6 6 .7 6 6 3 5 1 .1 7 5 7 7 5 6 3 - 1 5 .5 9 0 2 2 4
HH 47 3 0 . 6 2 5 8 .8 9 3 6 2 3 4 .1 0 8 3 4 0 5 5 - 2 4 .7 8 5 2 5 9
m 47 3 0 .6 3 6 9 .4 4 6 8 3 5 5 .1 0 6 6 4 1 1 3 -1 4 .3 4 0 1 5 8
MS 47 3 0 .6 4 7 9 .7 4 4 7 4 8 3 .8 1 4 2 8 8 3 9 4 .0 6 9 5 8 8 3 8
IH 47 3 0 .6 4 0 3 .5 3 1 9 3 5 1 .7 8 3 7 0 0 6 9 -5 1 .7 4 8 1 9 9
L I 47 3 0 .6 5 1 8 .4 2 5 5 4 8 7 .6 1 7 0 9 7 5 4 - 3 0 .8 0 8 4 0 2
IN 47 3 0 .6 6 7 6 .0 8 5 1 6 2 2 .2 1 1 4 3 7 3 5 - 5 3 .8 7 3 6 6 2
FDECADE4 N KEAN ASE ME
FORMOLA 69A
MT PREDICTED
BASED ON
MEAN DATA
DISTANCE
FRCH MEAH
SH 47 3 9 .5 1 9 4 .0 4 2 6 1 5 8 .1 2 2 4 6 8 8 7 -3 5 .9 2 0 1 3 1
S I 47 3 9 .5 2 6 1 .8 2 9 8 2 5 9 .6 7 0 5 5 9 5 5 -2 .1 5 9 2 4 0 4
SH 47 3 9 .5 3 6 4 .8 5 1 1 3 8 5 .0 6 1 2 3 4 4 3 2 0 .2 1 0 1 3 4 4
HH 47 3 9 .5 2 5 4 .1 7 0 2 2 5 6 .9 8 0 0 5 5 4 6 2 .8 0 9 8 5 5 4 6
MI 47 3 9 .5 3 6 3 .1 9 1 5 3 8 9 .3 6 1 9 1 7 0 9 2 6 .1 7 0 4 1 7 0
MN 47 3 9 .5 4 9 1 .1 0 6 4 5 3 0 .1 7 8 4 2 3 3 4 3 9 .0 7 2 0 2 3 3
IH 47 3 9 .5 3 8 5 .6 5 9 6 3 8 5 .7 2 6 3 5 3 2 9 0 .0 6 6 7 5 3 2 9
L I 47 3 9 .5 5 2 0 .9 7 8 7 5 3 4 .3 3 9 0 0 2 0 7 1 3 .3 6 0 3 0 2 0
IN 47 3 9 .5 6 7 1 .2 3 4 1 6 8 1 .5 9 6 0 2 2 8 9 1 0 .3 6 1 9 2 2 8
FDECADE5 H HEAN ASE HT
FORMOLA 69A
HT PREDICTED
BASED ON
KEAN DATA
DISTANCE
FRCH MEAH
SH 42 50 2 0 4 .1 4 2 9 1 7 5 .0 7 6 9 2 2 2 3 - 2 9 .0 6 5 9 7 7
S I 42 50 29 7 2 8 6 .9 2 6 9 9 3 1 2 -1 0 .0 7 3 0 0 6
SN 42 50 4 1 4 .7 1 4 3 4 2 5 .0 3 8 4 6 1 1 1 1 0 .3 2 4 1 6 1 1
HH 42 50 2 8 2 .7 1 4 3 2 8 3 .9 6 3 5 3 9 3 5 1 .2 4 9 2 3 9 3 4
H I 42 50 408 4 2 9 .7 7 5 4 4 4 9 1 2 1 .7 7 5 4 4 4 9
MN 42 50 5 5 9 .4 2 8 6 5 8 4 .6 7 7 6 8 3 6 8 2 5 .4 4 9 0 8 3 6
LH 42 50 4 3 6 .7 1 4 3 4 2 5 .7 7 1 0 5 5 8 -1 0 .9 4 3 2 4 4
L I 42 50 5 7 7 .4 2 8 6 5 8 9 .4 6 0 3 5 0 1 1 1 2 .0 3 1 7 5 0 1
IN 42 50 7 6 0 .5 7 1 4 7 5 1 .6 5 6 4 8 8 9 8 - 8 .9 1 4 9 1 1 0
FDECADE6 N KEAN ASE HT
FORMOLA 69A
MI PREDICTED
BASED ON
HEAH DAXA
DISTANCE
FRCH MEAH
SH 68 5 9 .4 2 1 9 .0 8 8 2 1 9 0 .2 5 5 1 9 4 7 6 -2 8 .8 3 3 0 0 5
S I 68 5 9 .4 3 1 5 .2 6 4 7 3 1 1 .3 2 7 9 9 0 8 - 3 .9 3 6 7 0 9 1
SN 68 5 9 .4 4 5 0 .4 4 1 2 4 6 0 .8 2 7 5 9 7 3 8 1 0 .3 8 6 3 9 7 3
HH 68 5 9 .4 2 9 1 .0 8 8 2 3 0 8 .1 2 0 1 8 2 0 7 1 7 .0 3 1 9 B 2 0
H I 68 5 9 .4 4 2 2 .1 1 7 6 4 6 5 .9 5 5 1 7 4 5 8 4 3 .8 3 7 5 7 4 5
HH 68 5 9 .4 5 6 8 .7 6 4 7 6 3 3 .8 4 6 5 4 5 3 2 6 5 .0 B 1 8 4 5 3
IN 68 5 9 .4 4 5 9 4 6 1 .6 2 0 5 9 9 2 .6 2 0 5 9 8 9 9
L I 68 5 9 .4 6 0 9 .7 9 4 1 6 3 8 .8 0 7 0 8 0 7 3 2 9 .0 1 2 9 8 0 7
IN e a 5 9 .4 8 1 6 .1 7 6 5 8 1 4 .3 7 7 2 8 7 2 - 1 .7 9 9 2 1 2 8
FORKOLA 69A
H I PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCH HEAN
1 4 3 .7 7 9 - 6 2 .9 0 1 8
2 3 6 .6 1 1 7 - 2 9 .8 1 3 8
3 5 1 .2 4 0 6 - 1 5 .5 2 5 4
2 3 4 .1 5 2 1 - 2 4 .7 4 1 5
3 5 5 .1 7 2 2 - 1 4 .2 7 4 6
4 8 3 .9 0 3 4 .1 5 8 3
3 5 1 .8 4 8 6 - 5 1 .6 8 3 3
4 8 7 .7 0 6 5 - 3 0 .7 1 9
6 2 2 .3 2 5 - 5 3 .7 6 0 1
FORHDLA 69A
HT PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCH HEAN
1 5 8 .0 7 0 9 - 3 5 .9 7 1 7
2 5 9 .5 6 7 7 - 2 .2 4 2 1
3 8 4 .9 3 9 7 2 0 .0 8 8 6
2 5 6 .8 9 8 2 .7 2 7 8
3 8 9 .2 3 9 1 2 6 .0 4 7 6
5 3 0 .0 1 2 3 8 .9 0 5 6
3 8 5 .6 0 4 6 - 0 . 0 5 5
5 3 4 .1 7 1 5 1 3 .1 9 2 8
6 8 1 .3 8 2 9 1 0 .1 4 8 8
FORMOLA 69A
MT PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCH HEAN
1 7 5 .1 1 5 3 - 2 9 .0 2 7 6
2 8 6 .9 8 8 8 - 1 0 .0 1 1 2
4 2 5 .1 2 9 2 1 0 .4 1 4 9
2 8 4 .0 2 4 7 1 .3 1 0 4
4 2 9 .8 6 7 1 2 1 .8 6 7 1
5 8 5 .0 0 1 7 2 5 .5 7 3 1
4 2 5 .8 6 1 8 - 1 0 .8 5 2 5
5 8 9 .5 8 5 3 1 2 .1 5 6 7
7 5 1 .8 1 5 3 - 8 .7 5 6 1
FORMULA 69A
H I PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCM HEAH
1 9 0 .2 2 6 7 - 2 8 .8 6 1 5
3 1 1 .2 8 2 1 - 3 .9 8 2 6
4 6 0 .7 6 0 4 1 0 .3 1 9 2
3 0 8 .0 7 4 9 1 6 .9 8 6 7
4 6 5 .8 8 7 2 4 3 .7 6 9 6
6 3 3 .7 5 4 4 6 4 .9 8 9 7
4 6 1 .5 5 3 3 2 .5 5 3 3
6 3 B .7 1 4 4 2 8 .9 2 0 3
8 1 4 .2 5 9 5 - 1 . 9 1 7
FOKMUIA 69B
HT PREDICTED
BAD ED ON DISTANCE
M EAN DATA FRCM HEAH
1 5 7 .8 0 1 5 5 1 2 5 - 4 8 .8 7 9 2 4 8
2 5 0 .6 1 7 4 8 7 2 8 - 1 5 .8 0 8 0 1 2
3 6 5 .2 2 5 7 7 5 6 3 -1 .5 4 0 2 2 4 3
2 4 8 .1 5 8 3 4 0 5 5 - 1 0 .7 3 5 2 5 9
3 6 9 .1 5 6 6 4 1 1 3 -0 .2 9 0 1 5 8 8
4 9 7 .8 6 4 2 8 8 3 9 1 8 .1 1 9 5 8 8 3
3 6 5 .8 3 3 7 0 0 6 9 -3 7 .6 9 8 1 9 9
5 0 1 .6 6 7 0 9 7 5 4 -1 6 .7 5 8 4 0 2
6 3 6 .2 6 1 4 3 7 3 5 -3 9 .8 2 3 6 6 2
FORMULA 69B
HT PREDICTED
BASED OH DISTANCE
MEAN DATA FRCM HEAN
1 6 5 .4 9 7 4 6 8 8 7 -2 8 .5 4 5 1 3 1
2 6 7 .0 4 5 5 5 9 5 5 5 .2 1 5 7 5 9 5 4
3 9 2 .4 3 6 2 3 4 4 3 2 7 .5 B 5 1 3 4 4
2 6 4 .3 5 5 0 5 5 4 6 1 0 .1 8 4 8 5 5 4
3 9 6 .7 3 6 9 1 7 0 9 3 3 .5 4 5 4 1 7 0
5 3 7 .5 5 3 4 2 3 3 4 4 6 .4 4 7 0 2 3 3
3 9 3 .1 0 1 3 5 3 2 9 7 .4 4 1 7 5 3 2 9
5 4 1 .7 1 4 0 0 2 0 7 2 0 .7 3 5 3 0 2 0
6 8 8 .9 7 1 0 2 2 8 9 1 7 .7 3 6 9 2 2 8
roHMOIA 69B
HT PREDICTED
BASED ON DISTANCE
HEAN DATA FRCM HEAN
1 7 4 .5 7 6 9 2 2 2 3 -2 9 .5 6 5 9 7 7
2 8 6 .4 2 6 9 9 3 1 2 - 1 0 .5 7 3 0 0 6
4 2 4 .5 3 8 4 6 1 1 1 9 .8 2 4 1 6 1 1 1
2 8 3 .4 6 3 5 3 9 3 5 0 .7 4 9 2 3 9 3 4
4 2 9 .2 7 5 4 4 4 9 1 2 1 .2 7 5 4 4 4 9
5 B 4 .3 7 7 6 8 3 6 8 2 4 .9 4 9 0 8 3 6
4 2 5 .2 7 1 0 5 5 8 - 1 1 .4 4 3 2 4 4
5 8 8 .9 6 0 3 5 0 1 1 1 1 .5 3 1 7 5 0 1
7 5 1 .1 5 6 4 8 8 9 8 - 9 .4 1 4 9 1 1 0
FORMULA 69B
HT PREDICTED
BASED ON DISTANCE
HEAN DATA FRCH HEAN
1 8 2 .7 0 5 1 9 4 7 6 -3 6 .3 8 3 0 0 5
3 0 3 .7 7 7 9 9 0 8 -1 1 .4 B 6 7 0 9
4 5 3 .2 7 7 5 9 7 3 8 2 .8 3 6 3 9 7 3 8
3 0 0 .5 7 0 1 8 2 0 7 9 .4 8 1 9 8 2 0 6
4 5 8 .4 0 5 1 7 4 5 8 3 6 .2 8 7 5 7 4 5
6 2 6 .2 9 6 5 4 5 3 2 5 7 .5 3 1 8 4 5 3
4 5 4 .0 7 0 5 9 9 - 4 .9 2 9 4 0 1 0
6 3 1 .2 5 7 0 8 0 7 3 2 1 .4 6 2 9 8 0 7
8 0 6 .8 2 7 2 8 7 2 -9 .3 4 9 2 1 2 8
FORMULA 69B
H I PREDICTED
BASED CN DISTANCE
EACH V IS IT FROH MEAN
1 5 7 .8 1 6 3 - 4 8 .8 6 4 5
2 5 0 .6 4 8 9 - 1 5 .7 7 6 6
3 6 5 .2 7 7 8 - 1 .4 8 8 2
2 4 8 .1 8 9 3 - 1 0 .7 0 4 3
3 6 9 .2 0 9 4 - 0 .2 3 7 4
4 9 7 .9 4 0 2 1 8 .1 9 5 5
3 6 5 .8 8 5 9 - 3 7 .6 4 6
5 0 1 .7 4 3 7 - 1 6 .6 8 1 8
6 3 6 .3 6 2 2 - 3 9 .7 2 2 9
FORMULA 69B
HT PREDICTED
BASED ON DISTANCE
BACH V IB IT FRCH HEAH
1 6 5 .4 6 9 8 - 2 8 .5 7 2 8
2 6 6 .9 8 6 6 5 .1 5 6 8
3 9 2 .3 3 8 7 2 7 .4 8 7 6
2 6 4 .2 9 7 1 0 .1 2 6 8
3 9 6 .6 3 8 3 3 .4 4 6 5
5 3 7 .4 1 1 4 6 .3 0 4 6
3 9 3 .0 0 3 5 7 .3 4 3 9
5 4 1 .5 7 0 4 2 0 .5 9 1 7
6 8 8 .7 8 1 9 1 7 .5 4 7 8
FORMULA 69B
MT PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCH HEAH
1 7 4 .5 9 7 5 - 2 9 .5 4 5 4
2 8 6 .4 7 0 9 - 1 0 .5 2 9 1
4 2 4 .6 1 1 3 9 .8 9 7
2 8 3 .5 0 6 8 0 .7 9 2 5
4 2 9 .3 4 9 2 2 1 .3 4 9 2
5 8 4 .4 8 3 9 2 5 .0 5 5 3
4 2 5 .3 4 4 - 1 1 .3 7 0 3
5 8 9 .0 6 7 5 1 1 .6 3 8 9
7 5 1 .2 9 7 5 - 9 .2 7 3 9
FORMULA 69B
MT PREDICTED
BASED CN DISTANCE
EACH V IS IT FRCH MEAN
1 8 2 .6 8 9 9 - 3 6 .3 9 8 3
3 0 3 .7 4 5 4 - 1 1 .5 1 9 3
4 5 3 .2 2 3 6 2 .7 8 2 4
3 0 0 .5 3 8 1 9 .4 4 9 9
4 5 8 .3 5 0 4 3 6 .2 3 2 8
6 2 6 .2 1 7 7 5 7 .4 5 3
4 5 4 .0 1 6 5 - 4 .9 8 3 5
6 3 1 .1 7 7 6 2 1 .3 8 3 5
8 0 6 .7 2 2 8 - 9 .4 5 3 7
TDECADS7 N MEAN ASE ME
FORKOLA 69A
H I PREDICTED
BASED ON
HEAN DAXA
DISTANCE
rfi£ U MEAN
s tr 53 6 8 .9 2 4 4 .6 4 1 5 2 0 5 .5 9 4 9 3 8 2 8 -3 9 .0 4 6 5 6 1
S I 53 6 8 .9 3 3 5 .7 7 3 6 3 3 5 .9 8 8 5 7 3 5 6 0 .2 1 4 9 7 3 5 6
SH 53 6 8 .9 4 8 0 .9 0 5 7 4 9 6 .9 9 7 4 6 9 1 4 1 6 .0 9 1 7 6 9 1
M W 53 6 8 .9 3 2 6 .9 4 3 4 3 3 2 .5 3 3 8 1 0 3 5 5 .5 9 0 4 1 0 3 4
M I 53 6 8 .9 4 5 7 .9 2 4 5 5 0 2 .5 1 9 7 9 4 9 9 4 4 .5 9 5 2 9 4 9
MS 53 6 8 .9 6 2 7 .9 6 2 3 6 8 3 .3 3 6 3 5 2 2 9 5 5 .3 7 4 0 5 2 2
IH 53 6 8 .9 5 1 9 .3 9 6 2 4 9 7 .8 5 1 5 2 0 3 1 -2 1 .5 4 4 6 7 9
XX 53 6 8 .9 6 7 7 .2 0 7 5 6 8 8 .6 7 6 7 7 6 5 7 1 1 .4 7 1 2 7 6 5
IN 53 6 8 .9 9 0 1 .2 4 5 3 8 7 7 .7 6 5 3 2 7 9 5 -2 3 .4 7 9 9 7 2
FDBCADE8 N MEAN ACE HE
FORMULA 69A
HT PREDICTED
BASED ON
mean d a t a
DISTANCE
FROM MEAN
SW 9 7 8 .1 2 8 9 .3 3 3 3 2 2 0 .4 5 0 2 6 8 8 5 - 6 8 .8 8 3 0 3 1
S I 9 7 8 .1 3 8 6 .6 6 6 7 3 5 9 .8 7 0 4 0 1 0 8 - 2 6 .7 9 6 2 9 8
SN 9 7 8 .1 5 4 5 .3 3 3 3 5 3 2 .0 2 5 1 3 4 4 2 - 1 3 .3 0 8 1 6 5
m 9 7 8 .1 36 0 3 5 6 .1 7 6 4 8 1 9 4 - 3 .8 2 3 5 1 6 0
M I 9 7 8 .1 4 9 2 .6 6 6 7 5 3 7 .9 2 9 7 4 3 1 7 4 5 .2 6 3 0 4 3 1
MN 9 7 8 .1 7 0 6 .6 6 6 7 7 3 1 .2 6 3 3 2 3 2 6 2 4 .5 9 6 6 2 3 2
LH 9 7 8 . 1 5 5 6 .6 6 6 7 5 3 2 .9 3 8 3 0 7 2 7 - 2 3 .7 2 8 3 9 2
L I 9 7 8 .1 7 9 6 .6 6 6 7 7 3 6 .9 7 5 5 7 6 7 6 -5 9 .6 9 1 1 2 3
IN 9 7 8 .1 9 3 7 .3 3 3 3 9 3 9 .1 5 1 6 4 1 0 9 1 .8 1 8 3 4 1 0 9
FDECADE9 H MEAN ASE MT
FORMULA 69A
MT PREDICTED
BASED CN
KEAN DAXA
DISTANCE
FRCM MEAN
SH 1 94 408 2 4 6 .1 2 4 1 5 5 3 7 - 1 6 1 .8 7 5 8 4
S I 1 94 642 4 0 1 .1 4 4 4 2 9 0 6 - 2 4 0 .8 5 5 5 7
SN 1 94 780 5 9 2 .5 6 2 0 7 7 6 9 - 1 8 7 .4 3 7 9 2
JM 1 94 54 0 3 9 7 .0 3 7 1 8 6 1 2 -1 4 2 .9 6 2 8 1
MI 1 94 8 2 2 5 9 9 .1 2 7 3 7 1 0 2 - 2 2 2 .8 7 2 6 2
HH 1 94 1128 8 1 4 .0 9 3 6 3 1 7 7 - 3 1 3 .9 0 6 3 6
IH 1 94 106 2 5 9 3 .5 7 7 4 2 8 2 1 -4 6 8 .4 2 2 5 7
L I 1 94 120 0 8 2 0 .4 4 5 0 4 6 6 4 -3 7 9 .5 5 4 9 5
IN 1 94 160 2 1 0 4 5 .2 4 3 2 0 4 -5 5 6 .7 5 6 7 9
vo
U J
FORKOLA 69A
M X PREDICTED
BASED OB DISTAHCE
EACH V IS IT FROM KEAN
2 0 5 .6 6 5 - 3 8 .9 7 6 5
3 3 6 .1 0 1 2 0 .3 2 7 6
4 9 7 .1 6 2 7 1 6 .2 5 7
3 3 2 .6 4 5 4 5 .7 0 2
5 0 2 .6 8 6 9 4 4 .7 6 2 4
6 8 3 .5 6 2 4 5 5 .6 0 0 1
4 9 8 .0 1 7 2 - 2 1 .3 7 9
6 8 8 .9 0 6 6 1 1 .6 9 9 1
8 7 8 .0 5 4 7 - 2 3 .1 9 0 6
FORMOLA 69A
HZ PREDICTED
BASED C H I DISTANCE
EACH V IS IT FROM MEAN
2 2 0 .4 6 B 2 - 6 8 .8 6 5 1
3 5 9 .8 9 9 2 - 2 6 .7 6 7 5
5 3 2 .0 6 7 4 - 1 3 .2 6 5 9
3 5 6 .2 0 5 - 3 .7 9 5
5 3 7 .9 7 2 4 - 4 5 .3 0 5 7
7 3 1 .3 2 1 2 2 4 .6 5 4 5
5 3 2 .9 8 0 7 - 2 3 .6 8 6
7 3 7 .0 3 3 9 - 5 9 .6 3 2 8
9 3 9 .2 2 5 8 1 .8 9 2 5
FORKOLA 69A
HT PREDICTED
BASED ON DISTANCE
EACH V IS IT FROM MEAN
2 4 6 .1 2 4 1 - 1 6 1 .8 7 5 9
4 0 1 .1 4 4 4 - 2 4 0 .8 5 5 6
5 9 2 .5 6 2 - 1 8 7 .4 3 8
3 9 7 .0 3 7 2 - 1 4 2 .9 6 2 8
5 9 9 .1 2 7 3 - 2 2 2 .8 7 2 7
8 1 4 .0 9 3 6 - 3 1 3 .9 0 6 4
5 9 3 .5 7 7 5 - 4 6 8 .4 2 2 5
8 2 0 .4 4 5 1 - 3 7 9 .5 5 4 9
1 0 4 5 .2 4 3 - 5 5 6 .7 5 7
rOEHUIA 69B
MX PREDICTED
BASED OH DISTANCE
HEAH DATA FRCH HEAR
1 9 0 .9 1 9 9 3 8 2 8 - 5 3 .7 2 1 5 8 1
3 2 1 .3 1 3 5 7 3 5 8 - 1 4 .4 8 0 0 2 6
4 8 2 .3 2 2 4 6 9 1 4 1 .4 1 6 7 6 9 1 4
3 1 7 .8 5 B 6 1 0 3 5 - 9 .0 8 4 5 8 9 8
4 8 7 .8 4 4 7 9 4 9 9 2 9 .9 2 0 2 9 4 9
6 6 8 .6 8 1 3 5 2 2 9 4 0 .6 9 9 0 5 2 2
4 8 3 .1 7 6 5 2 0 3 1 -3 6 .2 1 9 6 7 9
6 7 4 .0 0 3 7 7 6 5 7 - 3 .2 0 3 7 2 3 4
8 6 3 .0 9 0 3 2 7 9 5 - 3 8 ,1 5 4 9 7 2
FORMOIA 69B
M2 PREDICTED
BASED OH DISTANCE
KEAN DATA TRIM MEAN
1 9 B .8 7 5 2 6 8 8 5 - 9 0 ,4 5 8 0 3 1
3 3 8 .2 9 5 4 0 1 0 8 - 4 8 .3 7 1 2 9 8
5 1 0 .4 5 0 1 3 4 4 2 - 3 4 .8 8 3 1 6 5
3 3 4 .6 0 1 4 8 1 9 4 - 2 5 .3 9 8 5 1 8
5 1 6 .3 5 4 7 4 3 1 7 2 3 .6 8 8 0 4 3 1
7 0 9 .6 8 8 3 2 3 2 6 3 .0 2 1 6 2 3 2 5
5 1 1 .3 6 3 3 0 7 2 7 - 4 5 .3 0 3 3 9 2
7 1 5 .4 0 0 5 7 6 7 6 -8 1 .2 6 6 1 2 3
9 1 7 .5 7 6 6 4 1 0 9 -1 9 .7 5 6 6 5 8
FORMOLA 69B
H I PREDICTED
EASED CN DISTANCE
HEAN DATA FRCH M EAN
2 1 2 .6 2 4 1 5 5 3 7 - 1 9 5 .3 7 5 8 4
3 6 7 .6 4 4 4 2 9 0 6 - 2 7 4 .3 5 5 5 7
5 5 9 .0 6 2 0 7 7 6 9 - 2 2 0 .9 3 7 9 2
3 6 3 .5 3 7 1 8 6 1 2 -1 7 6 .4 6 2 B 1
5 6 5 .6 2 7 3 7 1 0 2 - 2 5 6 .3 7 2 6 2
7 8 0 .5 9 3 6 3 1 7 7 - 3 4 7 .4 0 6 3 6
5 6 0 .0 7 7 4 2 8 2 1 - 5 0 1 .9 2 2 5 7
7 8 6 .9 4 5 0 4 6 6 4 -4 1 3 .0 5 4 9 5
1 0 1 1 .7 4 3 2 0 4 0 3 - 5 9 0 .2 5 6 7 9
FORKOLA 69B
MT PREDICTED
BASED ON DISTAHCE
EACH V IS IT FROM KEAN
1 9 0 .9 5 7 4 - 5 3 .6 8 4 1
3 2 1 .3 9 3 6 - 1 4 . 3 8
4 8 2 .4 5 5 1 1 .5 4 9 4
3 1 7 .9 3 7 8 - 9 .0 0 5 6
4 8 7 .9 7 9 4 3 0 .0 5 4 9
6 6 8 .8 5 4 8 4 0 .8 9 2 5
4 8 3 .3 0 9 6 -3 6 .0 B 6 6
6 7 4 .1 9 9 2 - 3 .0 0 8 3
8 6 3 .3 4 7 2 - 3 7 .8 9 8 1
FORKOLA 69B
MT PREDICTED
BASED ON DISTANCE
EACH V IS IT FRCM MEAN
1 9 8 .8 8 4 9 - 9 0 .4 4 8 4
3 3 8 .3 1 5 9 - 4 8 .3 5 0 8
5 1 0 .4 8 4 - 3 4 .8 4 9 3
3 3 4 .6 2 1 7 - 2 5 .3 7 8 3
5 1 6 .3 8 9 1 2 3 .7 2 2 4
7 0 9 .7 3 7 9 3 .0 7 1 2
5 1 1 .3 9 7 3 - 4 5 .2 6 9 4
7 1 5 .4 5 0 6 - 8 1 .2 1 6 1
9 1 7 .6 4 2 5 - 1 9 .6 9 0 8
FORMOLA 69B
1ffi PREDICTED
BASED CN DXBTANCE
EACH V IS IT FRCH MEAN
2 1 2 .6 2 4 1 - 1 9 5 .3 7 5 9
3 6 7 .6 4 4 4 - 2 7 4 .3 5 5 6
5 5 9 .0 6 2 - 2 2 0 .9 3 8
3 6 3 .5 3 7 2 - 1 7 6 .4 6 2 8
5 6 5 .6 2 7 3 - 2 5 6 .3 7 2 7
7 8 0 .5 9 3 6 - 3 4 7 .4 0 6 4
5 6 0 .0 7 7 5 - 5 0 1 .9 2 2 5
7 8 6 .9 4 5 1 - 4 1 3 .0 5 4 9
1 0 1 1 .7 4 3 - 5 9 0 .2 5 7
A P P E N D I X Q
S u m m a r y o f E q u a t i o n s F r o m C h a p t e r I I
Error = k S n
MT = a + b log2 (2A/W)
ID = log2 ((A+.5W)/W) = Iog2 (AAV + .5)
MT = a + b log2 (AAV)
MT = K log2 ((A + .5W)AV) = K Iog2 (AAV + .5)
MT = K log2 (A'/W' + 0.5)
MT = K log2 (A’ /(W - c) + 0.5)
movement time = a log2 A1 + b log2 1 AV1
MT = b log2 (A’ AVj) + (b - a) log2 C
d = 814.9 (t/T)1* 4
E2 = E02 + (as du)2
E2 = E02 + (814.9)2 (o62 (tj/T)2'8
MT - a + b (A/W') (13)
MT = b log2 (effective amplitude/effective target area) (14)
MT = b log2 (Ae/(7t(We/2) (De/2») (15)
MT = b log2 (AAVft) + b log2 (A/D& ) (16)
M T = a + b (17)
MT = a + b log2 ((A + W)/W) = a + b log2 (AAV + 1) (18)
T = a + b log2 N (19 - equivalent to Equation 5)
MT = a log2 A’ - b log2 W'j + (b - a) log2 W'0 (20)
1 9 5
A P P E N D IX R
F o r m u la s U s e d to C o m p u te a , b , r ^ , S e , a n d W o '
a = Xy -X x(b)
^ ( l x ) ( S y )
E x y - jj-------
D =
y x2
" N
[ N S x y - ( l x ) ( l y ) ] 2
[n X x2 - (Z x)2] [n X y 2 - (Z y)2]
s . =
*X(y - y)'
e - V N - K - 1
Where y = the predicted value of y for a given set of independent variables
and K = the number of independent variables.
1 9 6
APPENDIX S
M o v e m e n t T im e A N O V A T a b le w ith B o n f e r o n i C r itic a l V a lu e s f o r
L o n g itu d in a l D a ta
MT ANOVA Table
MEAN
AGE
ERROR 1
SUM OF
SQUARES
1 6 8 1 5 6 6 4 8 2
1 2 6 7 8 7 8 3
4 1 0 0 5 4 6 6
D . F .
1
4
1 49
MEAN
SQUARE
*********
3 1 6 9 6 9 6
2 7 5 2 0 4
F
6 1 1 0 . 2 4
1 1 . 5 2
P
0.0000
0.0000
V IS IT 3 0 6 8 8 7 1 8 3 8 3 6 0 9 2 5 . 0 9 0 . 0 0 0 0
V I S I T X AGE 8 9 0 6 6 0 32 2 7 8 3 3 1 . 8 2 0 . 0 0 3 6
ERROR 2 1 8 2 2 3 4 1 9 1 1 9 2 1 5 2 8 8
TARGET 2 6 1 5 1 3 9 4 5 8 3 2 6 8 9 2 4 3 1 9 2 6 . 9 5 0 . 0 0 0 0
TARGET X AGE 2 0 3 4 1 1 2 32 6 3 5 6 6 3 . 7 5 0 . 0 0 0 0
ERROR 3 2 0 2 2 1 3 9 3 1 1 9 2 1 6 9 6 4
V IS IT X TARGET 1 6 6 5 9 3 8 64 2 6 0 3 0 5 . 3 6 0 . 0 0 0 0
V IS IT X TARGET X AGE 1 8 2 6 7 8 4 2 5 6 7 1 3 6 1 . 4 7 0 . 0 0 0 0
ERROR 4 4 6 2 7 5 6 8 7 9 5 3 6 4 8 5 3
Calculation of Bonferoni Critical Difference Values
TARGET V IS IT AGE TV TA VA TVA
a l p h a 0 . 0 5 0 . 0 5 0 . 0 5 0 . 0 5 0 . 0 5 0 . 0 5 0 . 0 5
k 9 9 5 81 45 45 4 0 5
a l p h a / k 0 . 0 0 5 6 0 . 0 0 5 6 0 . 0 1 0 0 0 . 0 0 0 6 0 . 0 0 1 1 0 . 0 0 1 1 0 . 0 0 0 1
d f e r r o r 1 19 2 1 1 9 2 1 4 9 9 5 3 6 1 1 9 2 1 1 9 2 9 5 3 6
ms e r r o r 1 6 9 6 4 1 5 2 8 8 2 7 5 2 0 4 4 8 5 3 1 6 9 6 4 1 5 2 8 8 4 8 5 3
a v e . # o f
o b s / m e a n {n) 1 3 8 6 1 3 8 6 2 7 7 . 2 154 2 7 7 . 2 2 7 7 . 2 3 0 . 8
t 2 . 8 9 2 . 8 9 2 . 5 8 2 . 8 0 3 . 2 8 3 . 2 8 4 . 0 0
t * s q r t ( 2 * m s / n ) =
c r i t i c a l
d i s t a n c e = 1 4 . 3 2 1 3 . 5 9 1 1 4 . 7 9 2 2 . 2 3 3 6 . 2 9 3 4 . 4 5 7 1 . 0 1
1 9 7
APPENDIX T
Y - I n t e r c e p t a n d S lo p e A N O V A T a b le s f o r L o n g itu d in a l D a ta w ith B o n fe ro n i
C r itic a l V a lu e s f o r S lo p e D a ta
Y-Intercept ANOVA
SUM OF MEAN
SQUARES D . F . SQUARE F
P
MEAN 1 7 0 5 6 0 5 1 1 7 0 5 6 0 5 3 0 . 5 1 0 . 0 0 0 0
AGE 3 9 5 7 6 3 4 9 8 9 4 1 1 . 7 7 0 . 1 3 7 9
ERROR 1 8 3 2 9 1 5 5 1 4 9 5 5 9 0 0
V IS IT 3 4 7 1 2 8 4 3 3 9 0 . 8 0 . 6 0 2 5
V IS IT X AGE 3 0 0 3 0 0 32 9 3 8 4 1 . 7 3 0 . 0 0 7 3
ERROR 2 6 4 6 3 5 8 8 1 1 9 2 5 4 2 2
Slope ANOVA
MEAN
AGE
ERROR 1
SUM OF
SQUARES
1 4 0 8 0 7 8 0
8 5 6 7 2
5 9 8 5 1 0
MEAN
D . F . SQUARE
1 1 4 0 8 0 7 8 0
4 2 1 4 1 8
1 4 9 4 0 1 7
F
3 5 0 5 . 4 3
5 . 3 3
P
0.0000
0 . 0 0 0 5
V IS IT
V I S I T X AGE
ERROR 2
2 5 6 9 9
3 0 2 1 5
6 2 6 2 2 6
8
32
1 1 9 2
3 2 1 2
944
5 2 5
6.11
1.8
0.0000
0 . 0 0 4 4
Calculation of Bonferoni Critical Difference Values for Slope Data
V IS IT AGE • VA
a l p h a 0 . 0 5 0 . 0 5 0 . 0 5
k 9 5 45
a l p h a / k 0 . 0 0 5 6 0 . 0 1 0 0 0 . 0 0 1 1
d f e r r o r 1 1 9 2 1 4 9 1 1 9 2
ms e r r o r 5 2 5 4 0 1 7 5 2 5
a v e . # o b s / m e a n (n) 154 2 7 7 . 2 3 0 . 8
t 2 . 8 9 2 . 5 8 3 . 2 8
t * s q r t ( 2 * m s / n ) =
c r i t i c a l d i s t a n c e 7 . 5 6 1 3 . 8 7 1 9 . 1 6
198
APPENDIX U
D e s c r ip tiv e S ta tis tic s f o r M o v e m e n t T im e f o r L o n g itu d in a l D a ta
AGE
RANGE VISIT
MEAN
AGE TARGET n MT SD
UNDER35 . 1 32.2 sw 12 189.0 43.2
UNDER35 2 34.2 sw 12 184.2 47.8
UNDER35 3 36.2 sw 12 189.4 34.5
UNDER35 4 38.2 sw 12 181.9 42.6
UNDER35 5 40.2 sw 12 173.5 47.6
UNDER35 6 42.2 sw 12 189.9 56.5
UNDER35 7 44.2 sw 12 188.1 48.7
UNDER35 8 46.2 sw 12 179.8 38.0
ONDER35 9 48.2 sw 12 188.7 41.2
35T044 1 40.1 sw 50 207 .8 39.1
35T044 2 42.1 sw 50 201.4 36.8
35T044 3 44.1 sw 50 196.4 33.3
35T044 4 46.1 sw 50 197.0 33.7
35T044 5 48.1 sw 50 199.4 37.1
35T044 6 50.1 sw 50 200.6 37.9
35T044 7 52.1 sw 50 198.0 34.2
35T044 8 54.1 sw 50 201.7 34.8
35T044 9 56.1 sw 50 204.4 35.7
45T054 1 49.9 sw 63 208.1 47.1
45T054 2 51.9 sw 63 204.3 40.3
45T054 3 53.9 sw 63 201.9 39.4
45T054 4 55.9 sw 63 216.2 92.5
45T054 5 57.9 sw 63 209.9 46.5
451054 6 59.9 sw 63 207.6 35.9
45T054 7 61.9 sw 63 206.0 40.7
45T054 8 63.9 sw 63 210.2 44.0
45T054 9 65.9 sw 63 215.3 43.3
55T064 1 59.7 sw 19 192.9 31.3
55T064 2 61.7 sw 19 200.2 36.1
55T064 3 63.7 sw 19 196.7 32.4
55T064 4 65.7 sw 19 196.4 28.4
55T064 5 67.7 sw 19 445.9 1066.4
55T064 6 69.7 sw 19 215.9 53.2
55T064 7 71.7 sw 19 201.1 36.0
55T064 8 73.7 sw 19 203.7 36.6
55T064 9 75.7 sw 19 212.8 36.8
OVERS4 1 68.9 sw 10 246.6 53.9
OVER64 2 70.9 sw 10 246.0 59.6
OVER64 3 72.9 sw 10 239.5 53.1
OVER64 4 74.9 sw 10 242.9 43.9
OVER64 5 76.9 sw 10 239.5 41.2
OVERS4 6 78.9 'SW 10 256.4 60.0
OVER64 7 80.9 sw 10 261.3 76.2
OVER64 8 82.9 sw 10 261.0 62.5
OVER64 9 84.9 sw 10 286.9 64.8
AGE MEAN
RANGE VISIT AGE
UNDER35 1 32.2
UNDER35 2 34.2
UNDER35 3 36.2
UNDER35 4 38.2
ONDER35 5 40.2
UNDER35 6 42.2
UNDER35 7 44.2
UNDER35 8 46.2
UNDER35 9 48.2
35T044 1 40.1
35T044 2 42 .1
35T044 3 44.1
35T044 4 46.1
35T044 5 48.1
35T044 6 50.1
35T044 7 52.1
35T044 8 54.1
35T044 9 56.1
45T054 1 49.9
45T054 2 51.9
45T054 3 53.9
45T054 4 55.9
4 5T054 5 57.9
45T054 6 59.9
45T054 7 61.9
45T054 8 63.9
45T054 9 65.9
55T064 1 59.7
55T064 2 61.7
55T064 3 63.7
55T064 4 65.7
55T064 5 67.7
55T064 6 69.7
55T064 7 71.7
55T064 8 73.7
55T064 9 75.7
OVER64 1 68.9
OVER64 2 70.9
OVER64 3 72.9
OVER64 4 74.9
OVER64 5 76.9
OVER64 6 78.9
OVER64 7 80.9
OVER64 8 82.9
OVER64 9 84.9
TARGET n M T
S I 12 314.0
S I 12 292.6
SI 12 269.3
S I 12 262.9
S I 12 281.3
S I 12 269.7
S I 12 250.1
S I 12 248.3
SI 12 257.0
S I 50 322.8
S I 50 324.5
S I 50 296.5
S I 50 284.5
S I 50 282.9
S I 50 283.7
S I 50 276.3
S I 50 274.8
S I 50 286.2
S I 63 330.6
S I 63 336.2
S I 63 307.7
S I 63 296.5
SI 63 298.1
S I 63 292.9
S I 63 290.8
S I 63 298.3
S I 63 325.4
S I 19 331.6
S I 19 312.9
S I 19 305.3
S I 19 298 .1
S I 19 290.6
SI 19 285.8
S I 19 289.9
S I 19 283.6
S I 19 292.3
S I 10 404.4
S I 10 397.1
SI 10 374.8
S I 10 362.3
S I 10 366.5
S I 10 363.7
S I 10 389.1
S I 10 375.5
S I 10 403.1
SD
64.0
59.6
50.7
61.4
77.5
61.5
57.9
65.2
68.2
63.6
65.9
59.6
53.2
62.9
60 .4
57.0
55.2
58.8
69.3
64.1
65.3
66.9
66.9
55.9
63.1
66.1
102.9
56.0
49.5
59.5
41.3
49.6
47 .9
49.3
56.3
58.8
78.1
77.1
79.0
65.4
77.2
83.5
98.9
90.9
91.7
200
AGE
RANGE VISIT
MEAN
AGE TARGET n M T SD
UNDER35 1 32.2 SN 12 514.0 80.8
UNDER35 2 34.2 SN 12 500.9 64.8
UNDER3S 3 36.2 SN 12 435.2 54.7
ONDER35 4 38.2 SN 12 383.3 78.0
UNDER35 5 40.2 SN 12 406.7 91.5
UNDER35 6 42.2 SN 12 428.8 66.0
UNDER35 7 44.2 . SN 12 384.6 71.1
UNDER35 8 46.2 SN 12 393,3 87.8
0NDER35 9 48.2 SN 12 420.2 88.7
35T044 1 40.1 SN 50 525.7 91.1
35T044 2 42.1 SN 50 507 .1 87 .5
35T044 3 44.1 SN 50 447.7 87.8
35T044 4 46.1 SN 50 418.8 80.9
35T 044 5 48.1 SN 50 421.0 84.3
35T044 6 50.1 SN 50 406.3 86.8
35T044 7 52.1 SN 50 403.1 91.6
35T044 8 54.1 SN 50 402.3 106.1
35T044 9 56.1 SN 50 423.6 129.0
45T054 1 49.9 SN 63 543.0 87.8
45T 054 2 51.9 SN 63 536.2 88.0
45T054 3 53.9 SN 63 490.7 95.4
45T054 4 55.9 SN 63 454.5 91.8
45T054 5 57.9 SN 63 449.1 85.7
45T054 6 59.9 SN 63 422.2 84.3
45T054 7 61.9 SN 63 415.1 98.6
45T054 8 63.9 SN 63 434.8 95.4
45T054 9 65.9 SN 63 443.3 110.2
55T064 1 59.7 SN 19 524.2 52.6
55T064 2 61.7 SN 19 492.5 75.0
55T064 3 63.7 SN 19 479.1 65.8
55T064 4 65.7 SN 19 470.1 79.5
55T064 5 67.7 SN 19 457.2 76.5
55T064 6 69.7 SN 19 454 .7 68.5
55T064 7 71.7 SN 19 451.6 54 .0
55T064 8 73.7 SN 19 456.2 91.6
55T064 9 75.7 SN 19 434.6 92.0
OVER64 1 68.9 SN 10 652.8 115.8
OVER64 2 70.9 SN 10 591.9 104.9
OVER64 3 72 .9 SN 10 548.3 75.6
OVER64 4 74.9 SN 10 539.5 93.7
OVER64 5 76.9 SN 10 524.1 80.8
OVER64 6 78.9 SN 10 536.3 131.0
OVER64 7 80.9 SN 10 537.1 106.5
OVER64 8 82.9 SN 10 568.5 221.4
OVER64 9 84.9 SN 10> 554.7 150.3
201
AGE
RANGE V ISIT
MEAN
AGE TARGET n M T SD
UNDER35 1 32.2 M W 12 261.5 60.5
UNDER35 2 34.2 M W 12 261.3 59.3
UNDER35 3 36.2 M W 12 241.2 54.4
UNDER35 4 38 .2 M W 12 250.3 82.0
UNDER35 5 40.2 M W 12 305.3 256.0
UNDER35 6 42.2 M W 12 240 .2 69.8
UNDER35 7 44.2 M W 12 234.4 83.0
UNDER35 8 46.2 M W 12 224 .3 55.2
UNDER35 9 48.2 M W 12 236. 6 56.7
35T 044 1 40.1 M W 50 297.1 57.5
35T044 2 42.1 M W 50 286.0 61.8
35T 044 3 44.1 M W 50 270 .9 56.5
35T044 4 46.1 M W 50 264.3 50.5
35T044 5 48.1 M W 50 264.6 55.4
35T 044 6 50.1 M W 50 263.8 55.0
35T044 7 52.1 M W 50 258.2 49.0
35T044 8 54 .1 M W 50 254.0 48.7
35T044 9 56.1 M W 50' 263.3 54.9
45T054 1 49.9 M W 63 292.2 56.9
45T054 2 51.9 M W 63 287.0 55.3
45T054 3 53.9 M W 63 272.5 50 .5
45T054 4 55.9 M W 63 264.8 51.1
45T054 5 57 .9 M W 63 270.8 53.3
45T054 6 59.9 M W 63 266.9 45.2
45T054 7 61.9 M W 63 266.2 49.2
45T054 8 63.9 M W 63 270.7 54.4
45T054 9 65.9 M W 63 274.5 57.1
55T064 1 59.7 M W 19 287.7 50.5
55T064 2 61.7 M W 19
284 .2 52.5
55T064 3 63.7 M W 19 265.7 47.6
55T064 4 65.7 M W 19 259.3 40.0
55T064 5 67 .7 M W 19 258.7 39.5
55T064 6 69.7 M W 19 263.8 41.7
55T064 7 71.7 M W 19 266.4 43.0
55T064 8 73.7 M W 19 266.0 51.3
55T064 9 75.7 M W 19 275.1 55.5
OVERS4 1 68.9 M W 10 360.0 55.9
OVERS4 2 70 . 9 M W 10 367.6 59.4
OVER64 3 72.9 M W 10 342.8 66.5
OVER64 4 74.9 M W 10 326.0 60.0
OVER64 5 7 6 .9 M W 10 340.7 74.7
OVER64 6 78.9 M W 10 353.1 88.2
OVERS4 7 80.9 M W 10 348.6 66.1
OVER64 8 82.9 M W 10 368.0 71.1
OVER64 9 84.9 M W 10 365.6 67.9
202
AGE
RANGE VISIT
MEAN
AGE TARGET n M T SD
UNDER35 1 32.2 MI 12 436.5 70.3
UNDER35 2 34 .2 MI 12 426.0 55.2
UNDER35 3 36.2 MI 12 397.4 57.4
UNDER35 4 38.2 MI 12 401.6 77.8
UNDER35 5 40.2 MI 12 433.7 196.1
UNDER35 6 42.2 MI 12 400.5 65.3
UNDER35 7 44.2 MI 12 375.9 65.5
UNDER35 8 46.2 MI 12 364.2 60.8
UNDER35 9 48.2 MI 12 391.1 67.6
35T044 1 40.1 MI 50 453.5 65.7
35T044 2 42.1 MI 50 439.7 70.6
35T044 3 44.1 MI 50 402.8 69.4
35T044 4 46.1 MI 50 387 .5 59.1
35T044 5 48.1 MI 50 3 91.1 66.0
35T044 6 50.1 MI 50 382.0 71.1
35T044 7 52.1 MI 50 376.8 73.4
35T044 8 54.1 MI 50 381.2 80.2
35T044 9 56.1 MI 50 395.3 89.8
45T054 1 49.9 MI 63 460.5 75.4
45T054 2 51.9 MI 63 461.6 67.8
45T054 3 53.9 MI 63 433.4 69.9
45T054 4 55.9 MI 63 410 .9 64.0
45T054 5 57.9 MI 63 414.8 68.8
45T054 6 59.9 MI 63 395.1 68.2
45T054 7 61.9 MI 63 396.3 74.8
45T054 8 63.9 MI 63 410.7 73.9
45T054 9 65.9 MI 63 417.4 82.3
55T064 1 59.7 MI 19 470.8 47.5
55T064 2 61.7 MI 19 452.2 65.5
55T064 3 63.7 MI 19 422.9 63.4
55T064 4 65.7 MI 19 429.8 65.6
55T064 5 67.7 MI 19 417.4 64.6
55T064 6 69.7 MI 19 418.7 74 . 6
55T064 7 71.7 MI 19 415.1 60.1
55T064 8 73.7 MI 19 429.0 93.2
55T064 9 75.7 MI 19 447.3 88.6
OVER64 1 68.9 MI 10 555.0 86.5
OVER64 2 70.9 MI 10 537.7 79.0
OVER64 3 72.9 MI 10 529.2 81.6
OVER64 4 74.9 MI 10 521.0 92.7
OVER64 5 76.9 MI 10 510.9 83.0
OVER64 6 78.9 MI 10 519.7 89.9
OVER64 7 80.9 MI 10 524.5 98.3
OVER64 8 82.9 MI 10 529.2 102.3
OVER64 9 8 4.9 MI 10 536.9 100.4
203
AGE
RANGE V ISIT
MEAN
AGE TARGET n M T SD
UNDER35 1 32.2 MN 12 646.5 102.4
UNDER35 2 34 .2 M N 12 640.7 77.9
UNDER35 3 36.2 MN 12 605.3 61.7
UNDER3 5 4 38.2 MN 12 536.8 59.9
UNDER3S 5 40.2 MN 12 528.6 112.6
UNDER35 6 42.2 MN 12 560.1 77.2
UNDER35 7 44.2 MN 12 534.9 110.8
UNDER35 8 46.2 MN 12 531.4 98.1
UNDER35 9 48.2 MN 12 575.8 83.0
35T 044 1 40.1 MN 50 657.6 86.3
35T044 2 42.1 MN 50 654.7 111.9
35T044 3 44.1 MN 50 601.6 92.4
35T044 4 46.1 MN 50 561.9 101.1
35T044 5 48.1 MN 50 542 .1 102.3
35T 044 6 50.1 MN 50 528.6 112.0
35T044 7 52.1 MN 50 520.0 119.4
35T 044 8 54.1 MN 50 518 .2 138.6
35T044 9 56.1 MN 50 546.1 130.9
45T 054 1 49.9 MN 63 685 .0 102.7
45T054 2 51.9 • MN 63 713.4 350.4
45T054 3 53.9 MN 63 638.8 107 .8
45T054 4 55.9 MN 63 608 .8 95.7
45T054 5 57.9 MN 63 592.8 96.7
45T054 6 59.9 MN 63 564.5 103.3
45T054 7 61.9 MN 63 553.2 126.4
45T054 8 63.9 MN 63 571.3 108.7
45T054 9 65.9 MN 63 571.8 114.6
55T064 1 59.7 MN 19 672.9 62.7
55T064 2 61.7 MN 19 651.7 76.3
55T064 3 63.7 MN 19 648.2 82.4
55T064 4 65.7 MN 19 ' 615.2 75.0
55T064 5 67.7 MN 19 615.6 69.2
55T064 6 69.7 MN 19 595.8 93.9
55T 064 7 71.7 MN 19 599.1 69.3
55T064 8 73.7 MN 19 620.1 94.1
55T064 9 75.7 MN 19 610 .4 114.8
OVER64 1 68.9 MN 10 798.6 134.2
OVER64 2 70.9 MN 10 778.3 111.1
OVER64 3 72.9 MN 10 709.3 137.3
OVER64 4 74.9 MN 10 701.9 136.5
OVER64 5 76.9 MN 10 687.8 94.8
OVER64 6 78.9 MN 10 718.0 142.6
OVER64 7 80.9 MN 10 716.5 128.0
OVER64 8 82.9 MN 10 725.0 146.0
OVER64 9 84.9 MN 10 744.4 126.7
204
AGE
RANGE VISIT
MEAN
AGE TARGET n M T SD
UNDER35 1 32.2 LW 12 430.5 70.0
UNDER35 2 34.2 LW 12 435.2 92.5
UNDER35 3 36.2 LW 12 386.2 58.3
UNDER35 4 38.2 LW 12 373.8 50.8
UNDER35 5 40.2 LW 12 374.0 63.6
UNDER35 6 42.2 LW 12 386.9 59.8
UNDER35 7 44 .2 LW 12 381.5 59.3
UNDER35 8 46.2 LW 12 367.3 57.5
UNDER35 9 48.2 LW 12 383.3 63.6
35T044 1 40.1 LW 50 453.6 75.6
35T044 2 42.1 LW 50 449.3 81.5
35T04 4 3 44.1 LW 50 426.2 84.5
35T044 4 46.1 LW 50 409.6 68.4
35T044 5 48.1 LW 50 410.5 75.6
35T044 6 50.1 LW 50 408.4 79.6
35T044 7 52.1 LW 50 395.4 75.3
35T044 8 54.1 LW 50 393.2 75.1
35T044 9 56.1 LW 50 417.3 82.9
45T054 1 49.9 LW 63 456.7 61.1
45T054 2 51.9 LW 63 454.5 65.9
45T054 3 53.9 LW 63 444.5 78.9
45T054 4 55.9 LW 63 436.9 63.6
45T054 5 57.9 LW 63 445.0 109.1
45T054 6 59.9 LW 63 421.5 60.0
45T054 7 61.9 LW 63 420.7 66.8
45T054 8 6 3. 9 LW 63 440.4 74 . 6
45T054 9 6 5 . 9 LW 63 445.7 64.8
55T064 1 59.7 LW 19 477.5 57.7
55T064 2 61.7 LW 19 487.0 78.1
55T064 3 63.7 LW 19 465.1 119.3
55T064 4 65.7 LW 19 462.7 67 .2
55T064 5 67.7 LW 19 444.9 61.8
551064 6 69.7 LW 19 437.5 68.8
55T064 7 71.7 LW 19 433.9 61.4
55T064 8 73.7 LW 19 455.1 76.4
55T064 9 75.7 LW 19 473.9 83.8
OVER64 1 68.9 LW 10 564.0 92.2
OVER64 2 70.9 LW 10 570.1 102.4
OVER64 3 72.9 LW 10 550.1 83.4
OVER64 4 74.9 LW 10 535.7 86.7
OVER64 5 76.9 LW 10 534.1 76.2
OVER64 6 78.9 LW 10 542.4 94.6
OVER64 7 80.9 LW 10 533.9 101.7
OVER64 8 82.9 LW 10 570.3 91.5
OVER64 9 84.9 LW 10 609.1 118.4
205
AGE
RANGE VISIT
MEAN
AGE TARGET n M T SD
UNDER35 1 32.2 LI 12 621.5 75.6
UNDER35 2 34.2 LI 12 619.5 71.6
UNDER35 3 36.2 LI 12 563.8 66.0
UNDER35 4 38.2 LI 12 550.6 75.9
UNDER35 5 40.2 LI 12 586.6 148.0
UNDER35 6 42.2 LI 12 579.5 83.8
UNDER35 7 44.2 LI 12 542.1 91.4
UNDER35 8 46.2 LI 12 550.4 79.1
UNDER35 9 48.2 LI 12 585.3 85.8
35T044 1 40.1 LI 50 633.4 109.7
35T 044 2 42 .1 LI 50 636.7 87.3
35T044 3 44 .1 LI 50 591.1 84.3
35T044 4 46.1 LI 50 561.5 85.2
35T044 5 48.1 LI 50 562.4 101.0
35T044 6 50.1 LI 50 569.0 89.6
35T 044 7 52.1 LI 50 551.2 99.6
35T044 8 54.1 LI 50 550.2 101.1
35T044 9 56.1 LI 50 571.3 119.9
45T054 1 49.9 LI 63 664.8 86.7
45T054 2 51.9 LI 63 ' 659.1 79.7
4 5 1 0 5 4 3 53.9 LI 63 624.3 81.4
45T054 4 55.9 LI 63 596.8 101.7
45T054 5 57.9 LI 63 601.7 82 .7
45T054 6 59.9 LI 63 580.3 88.8
45T054 7 61.9 LI 63 576.0 103.2
45T054 8 63.9 LI 63 602.6 94.3
45T054 9 65.9 LI 63 615.3 87.7
5 5 1 0 6 4 1 59.7 LI 19 672.0 72.4
55T064 2 61.7 LI 19 669.1 65.6
5 5 1 0 6 4 3 63.7 LI 19 651.4 89.7
55T064 4 65.7 LI 19 636.8 77.3
55T064 5 67.7 LI 19 643.4 105.3
5 5 1 0 6 4 6 69.7 LI 19 648.7 61.4
55T064 7 71.7 LI 19 642.2 73.9
55T064 8 73.7 LI 19 648.1 98.8
5 5 1 0 6 4 9 75.7 LI 19 651.0 114.9
OVER64 1 68.9 LI 10 802.2 102.9
OVER64 2 70.9 LI 10 762.8 113.7
OVER64 3 72.9 LI 10 746.9 121.9
OVERS4 4 74 . 9 LI 10 717.6 140.6
OVER64 5 76.9 LI 10 732.9 106.2
OVERS4 6 78.9 LI 10 760.7 127.8
OVER64 7 80.9 LI 10 754.0 100.1
OVER64 8 82.9 LI 10 793.4 90.2
OVER64 9 84.9 LI 10 862.2 138.4
206
AGE
RANGE V IS I1
MEAN
AGE TARGE1 n Ml SD
UNDER35 1 32.2 LN 12 886.0 129.5
UNDER35 2 34.2 LN 12 830.9 144.0
UNDER35 3 36.2 LN 12 785.3 84.8
UNDER35 . 4 38.2 LN 12 746.1 83.8
UNDER35 5 40.2 LN 12 720.8 164.2
UNDER35 6 42.2 LN 12 789.4 115.5
UNDER35 7 44 .2 LN 12 747 .2 125.8
UNDER35 8 46.2 LN 12 752 .5 136.5
UNDER35 9 48.2 LN 12 785.5 115.5
351044 1 40.1 LN 50 891.8 98.9
35T044 2 42 .1 LN 50 861.4 135.2
35T044 3 44.1 LN 50 785.0 112.6
35T044 4 46.1 LN 50 734.4 120.7
35T044 5 48.1 LN 50 738.5 140.3
35T044 6 50.1 LN 50 728.7 147.6
351044 7 52.1 LN 50 734.1 160.8
35T044 8 54.1 LN 50 736.8 182.7
35T044 9 56.1 LN 50 746.2 199.3
45T054 1 49.9 LN 63 885.0 171.4
45T054 2 51.9 LN 63 909.4 120.8
45T054 3 53.9 LN 63 846.8 135.0
45T054 4 55.9 LN 63 821.9 113.9
45T054 5 57.9 LN 63 810.0 142.1
45T054 6 59.9 LN 63 768.0 161.2
45T054 7 61.9 LN 63 769.6 175.0
45T054 8 63.9 LN 63 792.9 164.0
45T054 9 65.9 LN 63 830.7 166.7
55T064 1 59.7 LN 19 862.7 102.8
55T064 2 61.7 LN 19 879.5 121.8
55T064 3 63.7 LN 19 834.6 103.8
551064 4 65.7 LN 19 849.7 102.6
55T064 5 67.7 LN 19 842 .8 121. 6
551064 6 69.7 LN 19 907.2 397.8
551064 7 71.7 LN 19 808.2 100.0
551064 8 73.7 LN 19 827.6 179.2
551064 9 75.7 LN 19 879.5 155.1
OVER64 1 68.9 LN 10 993.0 153.6
OVER64 2 70.9 LN 10 1004.0 152.7
OVER64 3 72.9 LN 10 981.2 183.5
OVER64 4 74.9 LN 10 981.3 173.9
OVER64 5 76.9 LN 10 951.3 194 .0
OVER64 6 78.9 LN 10 953.7 180.3
OVER64 7 80.9 LN 10 939.6 126.1
OVER64 8 82.9 LN 10 961.8 163.7
OVER64 9 84.9 LN 10 983.6 178.4
207
APPENDIX V
D e s c r ip tiv e S ta tis tic s f o r Y - I n t e r c e p t a n d S lo p e f o r L o n g i tu d in a l D a ta
AGE MEAN INTERCEPT SLOPE
RANGE V I S I T AGE n MEAN SD MEAN SD
UNDER35 1 3 2 . 2 12 - 8 2 . 9 7 6 . 1 1 4 1 . 1 2 1 . 9
UNDER35 2 3 4 . 2 12 - 6 6 , 1 1 2 5 . 4 1 3 4 . 0 3 0 . 6
UNDER35 3 3 6 . 2 12 - 8 2 . 3 8 5 . 9 1 2 8 . 1 1 8 . 8
UNDER35 4 3 8 . 2 12 - 6 2 . 2 1 1 7 . 6 1 1 7 . 5 2 3 . 4
UNDER35 5 4 0 . 2 12 - 4 . 9 2 3 5 . 7 1 0 8 . 2 4 8 . 9
UNDER35 6 4 2 . 2 12 - 7 9 . 0 8 7 . 1 1 2 6 . 3 2 0 . 9
UNDER35 7 4 4 . 2 12 - 7 5 . 3 1 1 0 . 1 1 1 9 . 7 2 7 . 1
UNDER35 8 4 6 . 2 12 - 9 8 . 8 9 3 . 9 1 2 4 . 6 2 6 . 5
UNDER35 9 4 8 . 2 12 - 1 0 0 . 1 9 4 . 9 1 3 0 . 5 2 3 . 4
3 5 T 0 4 4 1 4 0 . 1 50 - 4 7 . 5 7 9 . 9 1 3 6 . 5 1 7 . 8
3 5 T 0 4 4 2 4 2 . 1 50 - 3 8 . 4 9 6 . 6 1 3 2 . 3 2 4 . 2
3 5 T 0 4 4 3 4 4 . 1 5 0 - 3 6 . 9 8 0 . 5 1 2 1 . 3 2 0 . 6
3 5 T 0 4 4 4 4 6 . 1 5 0 - 2 2 . 6 8 1 . 6 1 1 1 . 7 2 4 . 3
3 5 T 0 4 4 5 4 8 . 1 5 0 - 2 1 . 9 9 7 . 3 1 1 1 . 2 2 7 . 2
3 5 T 0 4 4 6 5 0 . 1 5 0 - 2 1 . 1 9 4 . 4 1 0 9 . 7 2 8 . 5
3 5 T 0 4 4 7 5 2 . 1 5 0 - 3 3 . 0 9 2 . 2 1 1 0 . 8 3 1 . 9
3 5 T 0 4 4 8 5 4 . 1 50 - 3 6 . 2 9 9 . 6 1 1 1 . 3 3 7 . 2
3 5 T 0 4 4 9 5 6 . 1 50 - 2 4 . 3 1 0 3 . 2 1 1 2 . 6 3 9 . 1
4 5 T 0 5 4 1 4 9 . 9 63 - 4 4 . 9 1 0 4 . 1 1 3 8 . 4 3 0 . 7
4 5 T 0 5 4 2 5 1 . 9 63 - 6 3 . 8 1 0 1 . 2 1 4 4 . 2 3 2 . 2
4 5 T 0 5 4 3 5 3 . 9 63 - 5 5 . 0 8 0 . 2 1 3 2 . 8 2 4 . 9
4 5 T 0 5 4 4 5 5 . 9 63 - 5 8 . 4 8 9 . 5 1 2 8 . 2 2 3 . 7
4 5 T 0 5 4 5 57 .9 63 - 4 8 . 0 1 0 8 . 1 1 2 5 . 5 2 9 . 3
4 5 T 0 5 4 6 5 9 . 9 63 - 3 3 . 6 1 1 2 . 9 1 1 6 . 9 3 3 . 7
4 5 T 0 5 4 7 6 1 . 9 63 - 3 5 . 6 1 2 0 . 7 1 1 6 . 6 3 7 . 3
4 5 T 0 5 4 8 6 3 . 9 63 - 3 6 . 1 1 1 4 . 3 1 2 0 . 6 3 2 . 1
4 5 T 0 5 4 9 6 5 . 9 63 - 3 5 . 8 1 2 2 . 2 1 2 3 . 6 3 4 . 1
5 5 T 0 6 4 1 5 9 . 7 19 - 2 5 . 0 7 1 . 6 1 3 3 . 4 1 9 . 3
5 5 T 0 6 4 2 6 1 . 7 19 - 5 3 . 9 5 7 . 6 1 3 8 . 1 1 7 . 1
5 5 T 0 6 4 3 6 3 . 7 19 - 5 0 . 0 8 9 . 0 1 3 2 . 5 2 0 . 7
5 5 T 0 6 4 4 6 5 . 7 19 - 7 0 . 7 5 2 . 2 1 3 5 . 4 1 6 . 2
5 5 T 0 6 4 5 6 7 . 7 1 9 - 8 3 . 5 8 8 . 5 1 3 6 . 8 2 4 . 0
5 5 T 0 6 4 6 6 9 . 7 1 9 - 1 2 9 . 0 2 9 5 . 7 1 4 8 . 3 7 5 . 4
5 5 T 0 6 4 7 7 1 . 7 19 - 6 1 . 0 7 9 . 9 1 2 9 . 5 1 9 . 0
5 5 T 0 6 4 8 7 3 . 7 19 - 7 0 . 5 1 2 1 . 3 1 3 4 . 0 3 4 . 6
5 5 T 0 6 4 9 7 5 . 7 19 - 8 6 . 2 8 6 . 6 1 3 9 . 7 2 9 . 6
OVER64 1 6 8 . 9 10 1 1 . 4 6 4 . 7 1 4 9 . 4 2 4 . 6
OVER64 2 7 0 . 9 10 2 . 3 6 0 . 4 1 4 8 . 1 2 3 . 2
OVERS4 3 7 2 . 9 10 - 1 7 . 4 6 8 . 1 1 4 5 . 6 3 1 . 0
OVER64 4 7 4 . 9 10 - 3 8 . 7 6 4 . 4 1 4 7 . 6 2 8 . 3
OVER64 5 7 6 . 9 10 - 1 4 . 7 1 1 9 . 9 1 4 0 . 9 3 0 . 7
OVER64 6 7 8 . 9 10 - 1 6 . 4 1 1 2 . 8 1 4 4 . 3 3 2 . 8
OVER64 7 8 0 . 9 10 6 . 0 9 0 . 4 1 3 8 . 5 1 9 . 2
OVERS4 8 8 2 . 9 10 1 . 1 8 1 . 6 1 4 3 . 7 2 2 . 4
OVER64 9 8 4 . 9 10 - 1 . 9 1 0 7 . 7 1 4 9 . 2 2 9 . 9
208
ACKNOWLEDGMENTS
Primary thanks goes to my thesis committee and especially to my thesis chairman,
Dr. Max Vercruyssen, who through patience, persistence, and insight encouraged
and enabled me to complete what I, alone, would never have done. He nurtured
this project through every step, at great personal expense of time and effort. He
was available around the clock to answer questions and help solve crises. At no
time did I doubt his commitment to my academic success. Finally, Dr.
Vercruyssen, through his captivating illustrations and his never-failing positive
attitude, actually made the experience of producing a master's thesis not only
bearable, but enjoyable. The thesis committee members were professors D. B. D.
Smith, A. T. Welford, J. E. Birren, J. E. Fozard, and Michelle Robertson.
Professor Dr. Alan T. Welford, the inspiration and designer of this research over
thirty years ago, provided the foundation of this research, not only by designing
the research, but by his enormous contribution to the field of psychomotor
performance. This contribution is evident by the dominance of Welford's writings
in the review of literature in this thesis. Professor Welford also provided valuable
insight into the theoretical implications of the results of the present study and very
helpful suggestions on including comparisons of key indices by formula and
subject group. Without doubt Professor Welford is the most knowledgeable person
when it comes to Fitts' Law and aging. My most sincere thanks are extended to
Professor Welford for the help he provided to me.
I owe special thanks to Dr. David B. D. Smith, who provided much encouragement
and assistance by helping me through the administrative requirements. Dr. Smith,
well-known for his work in aging, was an encouragement to me in developing the
209
age-related implications of this research. His assistance and encouragement to
consider the practical applications of this research to human factors was especially
appreciated.
Dr. James E. Birren, provided much through his publications and his lifelong
contribution to the field of age-related slowing, but also through specific direction
on how to analyze the data. Thanks are also due to Dr. Birren for his commitment
to meaningful interpretation of research findings and to his hunger for providing
scientific explanations of higher cognitive descriptives such as wisdom. His
discussions on this subject were thought-provoking and helped focus me on higher
purposes. Finally, I must acknowledge the encouragement provided by Dr, Birren
through his expectation that this would be a meaningful contribution to the
understanding of psychomotor behavior and aging.
Without the many provisions of Dr. James L. Fozard, this research would not have
been possible. As Associate Director of the Baltimore Longitudinal Study of
Aging, Dr. Fozard provided the raw data and verified data collection procedures.
In addition, I am particularly grateful for the insight he provided on interpreting the
gender differences found.
Many thanks are due to Michelle Robertson who provided me with much initial
guidance in the whole thesis process and helped me in selecting a thesis topic and
getting a thesis committee established.
210
Olukayode Olofinboba deserves special thanks for his faithful delivery of the early
data conversions and computer programing assistance. With little more than a few
handwritten notes and ambiguous instructions, Mr. Olofinboba returned to me
useful files for data analysis.
Thanks are also due to Carolyn Eames and Cathy Dent of the Baltimore
Longitudinal Study of Aging. Ms. Eames endured my many requests for
increasing amounts of data. She always came through and provided the raw data in
clear and logical formats. Ms. Dent, who helped administer the reciprocal tapping
task, provided valuable information on the procedures and apparatus used and was
able to secure a photograph of a BLSA participant performing the task.
Acknowledgment would not be complete without thanking my fellow students who
not only provided moral support, but reviewed drafts of my thesis and provided me
with helpful comments. Lt. Sara Reynolds provided early copies of her thesis,
which helped me to give form to my thesis, and assisted with data re-formatting.
Dr. Jen Yi Chang displayed selfless generosity of his own time by being available
to help with whatever he could even though there were great pressures upon him.
Capt. Gretchen Greatorex contributed very helpful comments on my review of
literature as well software assistance. Ms. Barbara Jex Courter provided many
encouraging words and helpful comments, especially on preparing the final thesis
document. Finally, thanks to the graduate student who preceded me, especially
Tina Mihaly and Michael T. Cann, who set examples for us to follow.
2 1 1
Acknowledgment is due to my friend, Bill Leone, for helping me think through the
theoretical implications of my findings by pointing out to me that the findings of
this research may have yeilded a much more intuitive explanation of what is
actually happening in terms of information processing. Dr. Virginia Diggles-
Buckles is also due thanks for her provision of important articles on the kinematics
of arm movements in the elderly. I would also like to acknowledge the help of
Larry Reed for the photocopy support as well as the audiovisual equipment
provided graciously and when needed for thesis proposal and defense meetings.
My thanks are extended to Liberty Mutual Insurance Group, Inc. for the financial
support provided. I would especially like to thank my boss, Duke Krum, who
patiently gave me the freedom to complete my thesis without placing on me an
unbearable workload. Virginia Manuel is due my sincere thanks for her patience
and skill in transcribing the review of literature. Very special thanks go to Wayne
Skwarlo and Tom Davidson for the computer equipment loaned to me to help
finish the thesis. I would also like to thank Dr. Stover H. Snook of the Liberty
Mutual Research Center in Hopkinton, Massachusetts, for his encouragement to
pursue my master's degree and his advice to pursue it at the University of Southern
California.
Some personal thanks are also in order. My parents, Eugene and Libby Brogmus,
provided not only faith in me that I would complete my work, but also much
needed financial support! My wife, Laura, who paid the highest price, deserves the
greatest thanks for enduring with my late nights, my undependable moods and my
unreasonable demands for her support. Through it all she was my helper and
212
friend without complaint, never discouraging me from continuing the work. My
sons, Eric and Kyle, who, while not fully aware of why, nonetheless endured the
absence of their father, not only physically, but often mentally and emotionally as
well. Finally, true thanks must go to God, to whom any true credit of
accomplishment is due.
213
RESUME
GEORGE ERICH BROGMUS
Residence: 21019 Lull Street Work: Liberty Mutual Insurance Co.
Canoga Park, CA 91304 2829 Townsgate Rd., Ste. 300
Westlake Village, CA 91359
EXPERIENCE
Technical Consultant. Liberty Mutual Insurance Company. Responsibilities
include analysis of client company operations, accidents, and products to
provide clients with recommendations for improving materials handling,
production flow,workstation design, handtool use and design, lighting,
repetitive tasks re-design, robotic safety, product safety, safety programs
and the design of warning labels. Duties also include extensive training of
new consultants and development and presentation of client training
seminars in Ergonomics, Anthropometry, Workstation Design, Manual
Materials Handling, Machine Guarding, Repetitive Motion Disorders of the
Upper Limbs, Video Display Terminals, Accident Investigations, and
Supervisory Safety Responsibilities, 8/82 to present.
Test Engineer. West Coast Research Corporation, Santa Monica, CA. Responsible
for testing and analysis of transducers, 12/81 to 8/82.
Field Management Assistant. C F Braun Constructors, Inc., Van Nuys construction
site. Responsible for gathering and reporting electrical system installation
data as the project progressed, 6/81 to 9/81.
Plan Checker. Vogel Properties, Walnut, CA. Performed energy calculations for
proposed buildings, 7/80 to 8/80.
Assistant to Systems Analysts and Engineers. McDonnell Douglas Corp., Long
Beach, CA. Developed a computer program for personnel reports, assisted
in technical writing of a user's guide for engineering computer programs,
organized switching information for a circuit trace program for DC-10
wiring, and verified operation of various wiring information computer
programs, summer intern programs 6/79 to 8/79 and 6/78 to 8/78.
EDUCATION
University of Southern California. Candidate for Masters of Science in Human
Factors - Human Performance and Aging option. Fall 1989 to Present.
2 14
Institute of Biblical Counseling. Sexual Abuse Seminar, 1/89.
Institute of Biblical Counseling. Basic Biblical Counseling Seminar, 1/89.
Human Factors Society 1988 Annual Meeting. Dr. Don B. Chaffin's Workshop,
"Biomechanical Assessment of Manual Tasks", 10/88.
Liberty Mutual Ins. Co. Training Courses/Seminars. Low Back Pain Institute
(10/88), Consulting Skills Seminar (1987), Advanced Ergonomics Course
taught by Stover H. Snook, Ph.D. (1986), Advanced Industrial Safety
Training Course (1985), Ergonomics Institutes (various, 1983 to present),
Safety Training Institutes (various, 1983 to present), and Basic Loss
Control (1982).
Robotics Industry Association. Robotic Safety Workshop, 1987.
Rockford Systems. Inc.. Machine Safeguarding Seminar, 1985.
National Safety Council. Power Press Guarding Seminar, 1984.
University of California. Los Angeles. Bachelor of Science degree, Electrical
Engineering, 4/78 to 6/82.
University of California. Davis. 9/77 to 3/78.
California Institute of Technology. Animal Technician Course, 2/77.
PROFESSIONAL SOCIETIES
Creation Research Society. Sustaining Member since 1989.
Ergonomics Society. Ordinary Member since 1988.
Human Factors Society. Member since 1987.
AWARDS AND PUBLICATIONS
Cumulative trauma disorders of the upper extremities: The magnitude of the
problem in U.S. Industry. Proceedings of the International Ergonomics
Association, Human Factors in Design for Manufacturability and Process
Planning, August, 9-11,1990, Honolulu Hawaii.
215
Employee Recognition Award. January, 1990.
Employee Suggestion Award, wrote a computer program for downloading and
automatically analyzing accident information for client companies, 1989.
Employee Suggestion Award, wrote a computer program that assists management
in organizing work assignments geographically and also helps consultants
in planning efficient work schedules, 1988.
SPECIAL PROJECTS
Tutorial Program Development. Finished creation of a computer-based tutorial
program for teaching the use of a workload (lifting) assessment program.
(6/89) Demonstrated the program and research results at the Human
Factors Society Annual Meeting in Denver, Colorado in October, 1989.
Early Return-to-Work Pilot Project. Participated in a pilot project to return injured
workers back to work by modifying their jobs to fit their restrictions.
Developed criteria for selecting cases, evaluated the success of the project
and submitted recommendations for future project improvements and
implementation. (5/88 to 3/89.)
Various Computer Programs for Safety Related Applications.
INTERESTS AND ACTIVITIES
Bible Study Leader/Teacher.
Attendant to Disabled.
Interests include Origins, Photography, Skiing, Prospecting and Fishing.
216
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may
be from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UM I a complete
manuscript and there are missing pages, these will be noted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize m aterials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand corner and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in
reduced form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6" x 9" black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly
to order.
University Microfilms International
A Bell & Howell Information C om pany
3 0 0 North Z eeb Road. Ann Arbor. Ml 48106-1346 USA
3 1 3 /7 61-4700 8 0 0 /5 2 1 -0 6 0 0
Order N um ber 1347074
Effects o f age and gender on speed and accuracy o f hand
m ovem ents and th e refinem ents they suggest for F itts’ Law
Brogmus, George Erich, M.S.
University of Southern California, 1991
UMI
300N. ZeebRd.
Ann Arbor, MI 48106

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

An analysis of nonresponse in a sample of Americans 70 years of age and older in the longitudinal study on aging 1984-1990

PDF

Age and expectancy: cross-sectional and longitudinal analyses of foreperiod effects on reaction time

PDF

The Duration Of Visual Short-Term Memory

PDF

Violent environments and their effects on children

PDF

Lateral variability in predation and taphonomic characteristics of turritelline gastropod assemblages from Middle Eocene - Lower Oligocene strata of the Gulf Coastal Plain, United States

PDF

Meta-analysis on the misattribution of arousal

PDF

Comparison of evacuation and compression for cough assist

PDF

The characterization of Huntington Beach and Newport Beach through Fourier grain-shape, grain-size, and longshore current analyses

PDF

The study of temporal variation of coda Q⁻¹ and scaling law of seismic spectrum associated with the 1992 Landers Earthquake sequence

PDF

Pulse oximetry failure rates

PDF

The Müller-Lyer illusion: a new variant, some old and new results

PDF

The relationship between fatty acid composition of subcutaneous adipose tissue and the risk of proliferateive benign breast disease and breast cancer

PDF

Diminishing worlds?: the impact of HIV/AIDS on the geography of daily life

PDF

Air terrorism and the international aviation regime: the International Civil Aviation Organization

PDF

Rationalizing risk: sexual behavior of gay male couples

PDF

The Hall Canyon pluton: implications for pluton emplacement and for the Mesozoic history of the west-central Panamint Mountains

PDF

A study of the solution crystallization of poly(ether ether ketone) using dynamic light scattering

PDF

Trifluoromethanesulfonates (triflates) for organic syntheses

PDF

Cross-cultural comparisons of long-term care practices: modifications to financing and delivery approaches in seven countries

PDF

The effects of dependence among sites in phylogeny reconstruction

Asset Metadata

Creator Brogmus, George Erich (author)

Core Title Effects of age and gender on speed and accuracy of hand movements: and the refinements they suggest for Fitt's Law

School Graduate School

Degree Master of Science

Degree Program Human Factors

Degree Conferral Date 1991-05

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag gerontology,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Vercruyssen, Max (committee chair), [Welfra, A.J.] (committee member), Birren, James E. (committee member), Fozard, James L. (committee member), Robertson, Michelle (committee member), Smith, David B.D. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-551

Unique identifier UC11357645

Identifier 1347074.pdf (filename),usctheses-c18-551 (legacy record id)

Legacy Identifier 1347074-0.pdf

Dmrecord 551

Document Type Thesis

Rights Brogmus, George Erich

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA