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Pupil Yield--The Relationships Between Selected Housing Unit And Housing Occupant Factors And The Number Of School Age Children

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Pupil Yield--The Relationships Between Selected Housing Unit And Housing Occupant Factors And The Number Of School Age Children

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Content PUPIL YIELD — THE RELATIONSHIPS BETWEEN
SELECTED HOUSING UNIT AND HOUSING
OCCUPANT FACTORS AND THE NUMBER
OF SCHOOL AGE CHILDREN
A Dissertation
Presented to
the Faculty of the School of Education
University of Southern California
In Partial Fulfillment of
the Requirements for the Degree
Doctor of Education
by
David Leo Westwater
June 1973
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Xerox University Microfilms
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WESTWATER, David Leo, 1932-
PUPIL YIELD— THE RELATIONSHIPS BETWEEN SELECTED
HOUSING UNIT AND HOUSING OCCUPANT FACTORS AND
THE NUMBER OF SCHOOL AGE CHILDREN.
University of Southern California, Ed.D., 1973
Education, administration
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
This dissertation, written under the direction
of the Chairman of the candidate’s Guidance
Committee and approved by a ll members of the
Committee, has been presented to and accepted
by the Faculty of the School of Education in
partial fulfillm ent of the requirements fo r the
degree of Doctor of Education.
Date September.,. . . 1 9 7 . 3 . . .
Dean
Chairman
TABLE OP CONTENTS
Chapter
I. THE PROBLEM .................................
Introduction
Purpose of the Study
Significance of the Study
Basic Assumptions
Definition of Terms
The Procedure
Delimitations of the Study
Organization of the Study
II. REVIEW OF THE LITERATURE ..................
Population and Enrollment Projecting
Factors Relating to Pupil Yield
Pupil Yield
Chapter Summary
III. METHODOLOGY ................................
Factor Development
Procedure
Rationale
Chapter Summary
IV. REPORT AND INTERPRETATION OF FINDINGS . . . .
Basic Considerations
A Pupil Yield Model
Suggested Implications
Chapter Summary
V. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS . .
Summary
Conclusions
Recommendations
APPENDIXES
BIBLIOGRAPHY
LIST OF TABLES
Table Page
1. Independent Variables/Factors ................. 28
2. Housing Unit/Pupil Yield Expectancy Table . . . 30
3* Ranked Housing Unit Factors ................. 31
4. Housing Occupant/Pupil Yield Expectancy Table . 32
5. Ranked Housing Occupant Factors ........ 33
6. Pupil Yield 5-17 Prediction Equations ......... 35
7. Stepwise Regression Analysis for Pupil Yield
Factors..................................... 36
8. Two Factor Analysis of Variance Tables .... 38
9. Two Factor Pupil Yield Prediction Equations . . 39
10. Annual Changes in Pupil Yield ................. 40
11. School Age by Pupil Yield for Year of Birth . . 42
iii
CHAPTER I
THE PROBLEM
Introduction
One method of estimating school enrollment develops
pupil projections from available housing unit information.
Used as a component in more sophisticated population models
or as the primary means of forecasting, the housing unit or
pupil yield method retains its popularity because of the
relative accessibility of needed information and simplicity
of operation.
Any forecasting formula requires continued evalua
tion if accuracy is to be maintained. This study provided
an opportunity to identify contemporary pupil yield rela
tionships and to build a common base from which to apply
subsequent adjustments.
Purpose of Study
This study utilized 1970 census data for San Diego
County to determine the relationship between selected
housing unit and occupant variables and the number of
children of school age. An attempt was made 1) to identify
the most significant of selected census factor's and 2) to
construct a pupil yield model from the factors.
1
2
Questions inherent to this investigation were:
1) Which housing unit factors are most related to
school age children?
2) Which housing occupant factors are most
related to school age children?
3) Can school enrollment estimates he made effec
tively by using certain housing unit and occu
pant factors?
4) If so, what grouping of factors is most pre
dictive of pupil enrollment?
5) Is the same combination of factors equally
predictive of pupil yield at elementary,
seventh and eighth grades, and high school
levels?
Significance of the Study
Recent trends involving the educational community
in California have brought even greater demands on educa
tors to minimize error in enrollment predictions. Numbered
among some of the contributing factors are the accounta
bility movement, declining state school enrollment reports,
facility utilization concerns, year round school efforts, a
mandate for long range comprehensive planning, and revenue
projecting under recent school finance legislation (SB-90).
At the same time changing relationships between birth and
death rates and the pattern of in and out migrations have
compounded the hazards in population forecasting. Yet,
accurate pupil projecting remains an essential prerequisite
for implementation of educational program, fiscal and
facility plans. This study is one attempt to evaluate the
usefulness of housing unit methods, specifically one which
Includes housing occupant data, as a means of pupil enroll
ment estimating.
Basic Assumptions
Among the assumptions made in this study are:
1) That a linear relationship exists between the
selected variables and the criterion; unit
modification in the predictors will result in
corresponding changes in pupil enrollment.
2) That the same relationship exists between
Information reported on a census tract basis
and that which would be reported on a housing
unit basis.
Definition of Terms
Key terms used in this study include:
Census Tract.— Geographical reporting areas orig
inally designed to be relatively homogeneous with respect
to population characteristics, economic status and living
conditions. The average census tract has about 4,000
residents.
Factor.— The smallest unit into which a variable is
divided.
Family Income.— The combined Income of all family
members fourteen years and over for the preceding calendar
year reported by mean Income per census tract.
Housing Occupant Factors.— Data reported about
housing occupant or population variables including family
income, race-ethnic, tenure, year moved into unit.
Housing Unit Factors.— Data reported about housing
unit or living quarter variables Including index of housing
values and rent, type of structure, year structure built.
Housing Units.— Living quarters subdivided into
type of structure.
Index of Housing Values and Rents.— A derived
amount obtained by adding the product of the proportion of
occupied housing units per census tract multiplied by the
percent of owner occupied housing units valued at $25,000
or more to the product of the proportion of renter occupied
housing units per census tract multiplied by the percent of
renter occupied housing units with a gross rent of $120.00
or more.
Mobile Homes.— A separate single unit reporting
category which included occupied mobile homes and trailers
used as living quarters.
Multiple Units.— Structures containing two or more
living quarter units.
Number of Bedrooms.— Whole rooms designated as bed
rooms.
Pupil Yield.— A derived amount obtained from
dividing the number of school age children (5-17, 5-11,
12-13, 14-17) by the number of occupied housing units in a
given area or census tract.
Race/Ethnic. The percent of persons reporting
white, black or other racial categories and Spanish
language.
5
Rent.— Reported by monthly contract (net) or gross
rent (contract rent plus monthly cost of utilities).
Single Unit.— Attached or detached structures con
taining one unit living quarters.
Structure.— A separate building having either open
space on all sides (detached) or being divided by walls
extending from roof to ground (attached).
Tenure.— Occupied housing units reported by owner
or renter classification.
Value.— The reported estimate of the current market
price of the property. Obtained only on one unit struc
tures.
Variable.— Class designation containing one or more
factors.
Year Moved Into Unit.— Reported by date of most
recent move.
Year Structure Built.— Reported by the date of
original construction.
The Procedure
Specific housing unit and occupant factors were
studied for relationship to the number of school age chil
dren. These factors were selected on the basis of being
cited in the review of relevant literature or being sus
pected of influencing pupil yield. Selected housing unit
factors relate to the age of the structure, the number of
bedrooms, the rent or value of the structure and the type
of structure. Selected housing occupant factors relate to
family Income, race or ethnic status, date of occupancy,
and tenure status.
Base data utilized came from 1970 decennial census
sources presented in a form suitable for this study. All
San Diego County census tracts were used except those which
encompassed military installations or in which no housing
units or school age children were reported.
Expectancy tables were developed to Indicate rela
tionships between the. factors studied. These tables were
used to identify the factors bearing the strongest rela
tionships to pupil yield and were reported in a manner
suitable for practical utilization irrespective of the
influences of other factors.
Additional statistical treatment sought to deter
mine 1) to what extent predictive value could be improved
by including additional factors and 2) the factor sequence
which might yield the strongest combined factor relation
ship. Multiple correlation and stepwise regression analy
sis were utilized in developing the multiple factor data.
Findings were reviewed and synthesized into a form
from which conclusions and recommendations were drawn.
Delimitations of the Study
Appraisal of factors was limited to information
available for San Diego County from 1970 census reports.
7
Organization of the Study
Chapter I has defined the purpose and significance
of the study, the basic assumptions, terminology, the pro
cedure, the delimitations, and organization of the study.
Chapter II reports a review of the literature and
research related to school enrollment projections and to
the influence of housing unit and housing occupant factors
on pupil yield.
Chapter III concerns the procedures utilized in
gathering, preparing and processing the data, an explana
tion of the treatment and the rationale for the methodology
employed.
Chapter IV contains the findings of the study and
an analysis of the most significant factors.
Chapter V presents a resume of the study, the find
ings, conclusions and recommendations resulting from the
investigation.
CHAPTER II
REVIEW OF THE LITERATURE
The review of the literature is divided into three
sections. Selected references were examined relating to
1) population and school enrollment projecting, 2) factors
relating to pupil yield, and 3) pupil yield examples.
Population and Enrollment Projecting
Current population estimates can be developed from
a number of different methods. A common practice involves
using a combination of techniques. The State Department of
Finance^ utilizes six approaches: three component methods,
a ratio-correlation method, a housing unit method and a
composite method.
The three components of change involving the
civilian population include: 1) natural increase (births
minus deaths), 2) natural migration ("in" migrants minus
"out" migrants), and 3) net movement of civilians into
military service. Recorded data can provide the source of
information for natural Increase and movement into the
armed forces, but Indirect sources are utilized to estimate
net migration. The Department of Finance has developed two
1 California, Department of Finance, California Pop
ulation 1971. pp. 46-47.
8
regression equations using 1) changes in the number of
households as measured from the increase or decrease in
residential users of electricity and 2) changes in school
enrollment as measured from the comparison of current
enrollment (grades 3 through 8) with prior year enrollment
(grades 2 through 7). An additional procedure designated
as Census Bureau Method II was utilized to yield another
estimate of net migration for school age children seven
through fifteen to use in developing migration estimates
for the total population. The total population estimate
comes from the sum of the three components applied to the
base.
p
The ratio-correlation method uses a regression
technique, but differs from the component method in that it
yields a direct estimate of population. Such factors as
births, deaths, elementary school enrollment, reported
employment, automobile registrations, state personal income
tax returns, registered voters and taxable retail sales are
used as the independent variables.
The housing unit method relates directly to this
study. It is employed by the State Department of Finance
to estimate city and county populations used in the dis
tribution of funds under the streets and highways and
revenue and taxation codes.3 This method requires an esti
mate of 1) occupied housing units of average household size
2Ibid., pp. 47-48. 3lbid.. pp. 48-49.
10
and 2) the number of persons not residing in household
units (group quarters). Again electric meter counts, with
suitable adjustments, are utilized to determine occupied
households. Average household size comes directly from
published census reports. Population in groups quarters is
difficult to estimate, significant only where that portion
of the population is relatively large.
L .
The composite method develops independent esti
mates for the civilian population by age groups, using the
method and base data considered most appropriate for each
age range. Births by age of mother are used to estimate
populations under 5 and 18-44. School enrollments are used
to estimate children 5-1?• Deaths by age of decedent are
used to estimate population 45-64 and social security re
cipients to estimate the population 65 and over. The total
population estimate for the area is derived by summing the
age group projections.
The relationship between school enrollment predic
tion and population forecasting has been recognized for
many years. A 1925 citation indicated:
The school population is an element of the total
population and bears a definite relationship to it.
Because of this relationship, future total population -
estimates may be used in forecasting school population.
While population estimation efforts require periodic
Ibid.. p.49.
^Fred Englehardt, Forecasting School Population.
Contributions to Education, No. 171 (New York: Columbia
University, Teachers' College, 1925), p.22.
adjustments in order to account for changes in birth, death
and migration rates, the ratio of actual to potential en
rollment projected is further influenced by the existence
of compulsory attendance laws, local promotion-retention
policies, holding power to drop out rate, and the avail
ability of private and parochial schools.
Several studies have compared pupil forecasting
methods. One study^ which investigated selected community
factors thought to affect accuracy of projections concluded:
1) that survival ratio techniques utilizing projection
ratios for predicting school enrollments were more reliable
than other methods tested, but 2) that survival ratio tech
niques are not accurate when a change in the rate of in
crease or decrease in school enrollment occurs and 3) that
data needed for making reliable compensatory changes are
not obtainable from school enrollment statistics.
A Wayne University study^ suggested that four en
rollment procedures were Indicated to correspond to the
four prediction patterns which were identified. A stand
ard procedure was considered applicable when houses are
^Donald Lee Peterson, "An Investigation of Tech
niques for Predicting School District Enrollments in
Florida" (unpublished Ed.D. dissertation, University of
Florida, 1959)» Dissertation Abstracts. Vol. XX, No. 7
(i960), pp. 2662-63.
^Norman S. Wheeler, "Techniques Used for Predicting
Public School Enrollments in Detroit, Michigan, Using the
Elementary School Service Area as a Base for All Units"
(unpublished Ed.D. dissertation, Wayne University, 1955),
Dissertation Abstracts. Vol. XV, No. 9, (1955), P. 1538.
12
being built and occupied at an average rate. A ratio
method was suitable when homes are constructed very rapidly
and large numbers of younger families simultaneously move
into an area. An interpolation method was suggested when
limited amount of rapid home building is occurring and where
the rate of building and occupancy may dwindle to a point
where the standard procedure may be used. Finally, a birth
trend method was indicated where practically no home build
ing can occur and where older families are being replaced
by newer families.
O
One investigation which sought to develop an en
rollment projection method for Texas Public Junior Colleges
examined standard ratio methods including cohort survival
methods, census class estimates and total population pro
jecting. Hunt indicated that ratio methods vary widely in
their usefulness from time to time and community to com
munity? they make limited use of known relationships
between enrollment and community characteristics and re
quire acceptance of assumptions difficult to justify except
on the basis of extensive local experience. This study
concluded that a multiple linear regression analysis was
better suited for prediction rather than projection.
A 195^ enrollment study analyzed six representative
Q
David Glen Hunt, "The Development of Enrollment
Projection and Prediction Methods for Texas Public Junior
Colleges" (unpublished Ph.D. dissertation, University of
Texas, 1962), Dissertation Abstracts, Vol. XXIII. No. 9.
1963, P. 320^.
enrollment forecasting methods.9 Three methods derived
enrollment projection from population forecasts— linear
extrapolation, multiple factor and logtatlc curve. Three
methods forecast enrollment directly from vital statistics
and past enrollment data— Wilson1s method, survival rates
were found to forecast with the greatest accuracy. A
recommended procedure involved a variation of the cohort
survival method adjusted by assumptions regarding the
future course of births, migration and holding power.
Factors Relating to Pupil Yield
Several combinations of factors have been examined
in prior studies concerned with pupil yield. Driscoll^0
examined four characteristics: 1) number of rooms, 2)
zoning, 3) building permit valuation and 4) location of
the home. Weak but significant relationships were found
between the four characteristics. In addition, the ratio
of secondary pupils to elementary pupils was found to in
crease with an Increase in room size and the percent of
homes producing school age children were found to increase
as room size increased.
^William Henry Strand, "Forecasting Enrollment in
the Public Schools" (unpublished Ph.D. dissertation, Uni
versity of Minnesota, 1954). Dissertation Abstracts. Vol.
XIV, No. 12, 1954, p. 2258.
l0William Norman Driscoll, "The Prediction of
School Enrollment from New Home Developments" (unpublished
Ed.E. dissertation, Colorado State College, 1965), Disser
tation Abstracts, Vol. XXVI, No. 5» 1966, p. 2558.
14
A University of Maryland investigation^1 examined
five factors: 1) type of dwelling, 2) number of bedrooms,
3) number and ages of children, 4) assessed value of
monthly rent, and 5) location by election districts. The
findings in this study indicated that: 1) significant
differences existed between school levels, 2) pupil yield
increased with increases in the number of bedrooms, 3)
except for semi-detached units, the election district was
the deciding factor in the prediction of pupil yield,
Glbbs1^ selected the following factors: 1) build
ing type, 2) building value, 3) number of bedrooms, and 4)
building age. Included in his major findings was 1) that
as single family residences and townhouses age, children
tend to be older and when these units become approximately
eight years old fewer children remained in residence, 2)
that new apartments yield few children, but as these
buildings age the number of children increases, 3) that
lower value units have fewer and younger children than
higher value, units, 4) that a positive correlation exists
between the number of bedrooms and the number of children
in residence, 5) that single family and townhouse units
1^William John Ellena, "A Technique for Predicting
Pupil Yield by Types of Dwelling Units" (unpublished Ed.D,
dissertation, University of Maryland, 1959), Dissertation
Abstracts, Vol. XX, No. 8, 1960, p. 3150.
^Wesley Payette Gibbs, "Development of a System
for Predicting School Enrollment Using Selected Housing
Factors" (unpublished Ph.D. dissertation, Northwestern
University, 1966), pp. 35-51*
15
were found to be similar in the number and ages of children
yielded, while new apartments had significantly fewer
children.
A Bureau of School Planning 1970 publication1.3
suggested that the relationship between migration and
transiency is important in projecting pupil yield. In
areas where the transiency rate is high the area generally
will not age. The characteristics of the family moving
into the community will be much the same as that of the
family moving out in terms of family size, age levels,
racial and economic level. Conversely, migration is iden
tified by home ownership and stability. A community ex
periencing a migration pattern is more likely to age and
witness a progression of pupil yield age levels.
While land use and zoning influences are often
mentioned in relationship to pupil yield, an interesting
conclusion comes from one recent school community study:
A change in the mix of new housing units will have
little effect, assuming no change in projected student/
ratios unit. While dwelling units per acre may rise
from seven single family units to about thirty multiple
family units (under R-4 zoning), the ratio of school age
children per unit declines . . . from about 1.0 for R-1
to .25 for R-4. The end result is a near constant of
seven to none students per regardless of the
density of the development.1^
13California State Department of Education, Bureau
of School Planning, Demographic Analysis— A Basis for Pro-
jecting School Population tfrends (Sscramento: California
5 ta t6 DgpgrtiBfeRT 'g r 'E g T X SgC reffr 'T 9 7 0 ), p. 14.
^Financial Planning Committee and Sites and
Facilities Planning Committee, Joint Report, Master Plan
16
Pupil Yield
Until replaced by a modified cohort survival tech
nique, enrollment justifications for state school building
aid projects were based on a pupil progression method
adjusted by a house count for new residential construction.
These house count factors were:
Kindergarten .16 Grade Three .15 Grade Six .12
Grade One .15 Grade Four .14 Grade Seven .11
Grade Two .15 Grade Five .13 Grade Eight .10
Grade Nine .10 Grade Eleven .08
Grade Ten .07 Grade Twelve .06
K-6 1.00 9-12 ,33ie
7-8 .21 K-12 1.5415
These factors based on the relatively uniform
growth pattern following World War II had proved inappro
priate for many growth situations in recent years as the
factors produced higher pupil yield projections than the
actual number of school age children realized.
Cajon Valley Union School District reported the
following pupil yield figures for 1972:
Grade Houses Apartments Mobile Homes
T3" “ 35“ ' — —
7 .09
K-8(projected) .74 .20 .15
While 3 of 107 study areaB exceeded a factor of
1.00, only 5 of 36 study areas with 1.00 or more K-6 pupils
for Sites and Facilities and Capital Financing (Alameda,
Ca: Alameda Unified School District, 1972), p. 28.
^California State Department of Education., Bureau
of School Planning, Forms SP-1E, SP-1S, SP-SE, "Projected
Average Daily Attendance," Revised 8/68.
generated a factor of .85 or more.^
Carlsbad Unified School District developed average
annual student growth factors based on three types of
single unit dwelling units— three and four bedroom units,
two bedroom condominiums and townhouses, and random in
dividual homes.17 The factors:
Grades K-6 = .44
Grades 7-8 = .16
Grades 9-12 = .22
Total K-12 = .82
Yield factors are cited that Involve more than the
dimension of structural type. A 1972 study^8 for Alameda
Unified School District developed the following K-12 pupil
yield factors:
Estimated School Age
Zoning Children/Housing Unit*
R-1 (New tract— first 10 years) 1.00-1.20
R-1 (After 10 years) .70- ,80
R-2 (and townhouses) .35- .60
R-3 (and condominiums) .30- .50
R-4 .10- .^5
R-5 and R-6 .05- .25
♦Not Indicative of ASUD enrollment. Reduction required
for parochial and non-student factors.
^Rex T. Dahms, compiler. Long Range Development
Plan (San Diego, Ca.: Cajon Valley Union School District,
T$72), pp. IHB3-B7.
^Carlsbad Unified School District, Report A-57,
"Student Enrollment Projections in Summary by Grades," 1972,
18
Alameda Unified School District Financial Plan
ning Committee and Sites and Facility Planning Committee,
Joint Report, Master Plan for Sites and Facilities and
Capital Financing, p. T % \
18
Only in two of sixteen census tracts did actual K-8
19
school age population exceed a factor of 1.00. 7 Examina
tion of block group data for each census tract revealed a
lower ratio of school age children per multiple family
20
dwelling unit than per single family dwelling unit.
The previously cited Bureau of School Planning
21
publication indicated the following 1970 relationships
between the cost of housing and pupil yields
Middle Secondary
Cost of Housing (New) Primary Grades Grades Grades
$12,000 to $16,000 Heavy Moderate Low
17.000 to 24,000 Moderate Heavy Moderate
25.000 to 32,000 Moderate Mod.-H. Mod.-H.
33»000 to 40,000 Low Low -M. Moderate
40.000 up Very low Very low-Low-Mod.
low
Very Low = Less than ,50
Low = .50 to ,75
Moderate = .75 to 1.00
Heavy = 1.00 to 1,24
(Implied) Very Heavy = More than 1,24
With the advent of environmental impact reports,
many developers are now citing pupil yield factors. One
22
recent proposal projected that the proposed single housing
units would generate school age children on the basis of the
following formula: K-6 = ,55
Jr. High = ,18
Sr. High = .33
K-12 = 1.06
19Ibid., p. 1 3. 20Ibid.. p.14.
21
California State Department of Education, Bureau
of School Planning, Demographic Analysis, p. 13.
22
Mercury Construction Co., Panorama Hills. Private
Development Plan, 1972, pp. 28-29.
19
Chapter Summary
A combination of techniques are utilized in con
temporary population forecasting. The California State
Department of Finance uses component methods, a ratio cor
relation process, a housing unit approach, and a composite
procedure in its projecting efforts. Because school popu
lation can be viewed as part of total population, pupil
enrollment can be projected from it, but the potential
number of school age children to actual enrollment realized
is affected by factors unique to pupil projecting. Gen
erally the studies support some form of a cohort survival
technique as yielding the most accurate projections.
Many of the same pupil factors have bsen reported
rather consistently in prior studies. Factors most often
cited because of their positive correlation with pupil
yield have been: 1) the number of bedrooms (three or more),
2) the type of structure (single unit, R-1), 3) the relative
value (higher), 4) the relative age (newer houses).
Selected examples of current pupil yield factors
indicated a declining yield from the amounts previously
used in the state school building program. In addition,
many of the current models develop more than a single di
mension factor.
CHAPTER III
METHODOLOGY
Included in the examination of methodology will be
a description of factor development, a review of the pro
cedures utilized, and a discussion of the rationale sup
porting the judgments involved.
Factor Development
Evaluation of the literature reviewed and consid
eration of the availability of data led to the selection of
four housing unit and four housing occupant variables as
the independent variables. Housing unit variables in
cluded the type of structure, the number of bedrooms, the
age of the dwelling, and the value or rent of the housing
unit. Housing occupant variables included date of occu-
panoy, family income, race or ethnic classification, and
owner/renter status. A description of the source and use
of the independent variables and the dependent variable
(pupil yield) follows:
Type of Structure.— Three factors were developed
from type of structure census data: single unit, multiple
unit, and mobile homes. The percentage of each factor to
total occupied housing units was reported.
Number of Bedrooms.— Four factors were developed
20
21
relative to the number of bedrooms. These factors were
reported by the percentage of no bedroom units, one bed
room units, two bedrooms units, and three and more bedrooms
units to the total number of occupied units.
Year Structure Built.— Three factors were developed
by combining reporting periods utilized in census tables.
Factors of under five years (1965-1970), five to twenty
years (1950-1964), and over twenty years (1939 or earlier-
19^9) were developed by the percentage of each to the totals
reported for year structure built.
Value/Rent.-- The index of housing values and rent
was utilized as the value/rent factor. This factor was
utilized as reported and represents the proportion of owner
occupied units valued at $25,000 or more to all owner oc
cupied units reported; added to the proportion of renter
occupied units times the percentage of renter occupied units
with gross rent of $120.00 or more to all renter occupied
units reported.
Year Moved Into Unit.--Four factors were developed
by combining reporting periods from the census category
"Year Moved Into Present Living Quarters," Factors of
under two years (1969-1970), two to three years (1967-
1968), four to ten years (1960-1966), and over ten years
(19^9 and earlier-1959) were indicated by the percentage of
each to the totals reported for year moved into present
living quarters excluding those reported as always lived in
present quarters.
Tenure.--Two factors were developed from the census ;
category "Tenure." The percentage of owner occupied and
renter occupied to all occupied units was reported.
Race/Ethnic.— Four factors were developed from cen
sus data race and Spanish American tabulations. The per
centage of white, black and "other" populations to the total
population was reported. The Spanish indicator utilized was
the percentage of Spanish American to total population.
Family Income.— The mean family income per census
tract in the single family income factor reported.
Pupil Yield.— Four pupil yield factors were re
ported. They were developed by dividing the number of
occupied housing units into the number of school age chil
dren aged five through seventeenj five through eleven,
twelve and thirteen; and fourteen through seventeen. These
age groupings were intended to relate to grades kindergarten
through twelve, K through six, seven and eight, and nine
through twelve respectively.
A total of twenty-six factors result from the com
bination of nine variables.
All factors were derived from population and housing
data obtained from 1970 census reports for San Diego County.
This information was gathered from various public agencies
which distributed data generated from second and fourth
count census summary tapes.
Some of the data utilized were based on 100$ cen
sus tabulations; others were based on census samples.
Pupil yield, type of structure, value/rent, owner/renter
status, and race categories were developed from total
enumeration reports. The year structure built, family in
come and Spanish ethnic factors were generated from 20$
samples; the year moved into present unit came from a 15$
sample and the number of bedroom factors were based on a
5$ sample.
Procedure
The factors selected were gathered and/or devel
oped, grouped into twenty-six items by census tract and
recorded on eighty column coding sheets. All of the 304
census tract groupings utilized were key punched into IBM
cards which were processed to yield an ascending order sort
and print out of the twenty-six items identified.
Separate pupil yield expectancy tables were devel
oped for the housing unit and housing occupant factors.
Along with factor correlation coefficients the expectancy
tables were used to identify the individual independent
variable factors bearing the strongest relationship to the
dependent variable. Expectancy table reporting was selected
because of the advantage it provides in presenting existing
relationships between factors in a manner suitable for
practical utilization.
Additional statistical treatment was required to
24
obtain the formula data necessary to develop the pupil
yield model. Answers to the following questions were
needed: 1) To what extent could predictive values be in
creased by the addition of selected factors? 2) In what
order should the factors be added? Computer analysis re
sulting in multiple correlation and stepwise regressions
computations was utilized to gain the needed information,
and was obtained through the use of the SPSS (Statistical
Package for Social Sciences) regression program available
at the university computer center.
Rationale
Several types of housing unit and housing occupant
factors were considered to be suitable for use in this
study. Final selections involved evaluation of answers to
the following questions! 1) Which factors had been iden
tified in previous studies? 2) What factors were available
or could be developed from 1970 census data? 3) Which
factors could be eliminated because of suspected duplica
tion— e.g., family income and level of adult education?
4) How difficult would a factor be to obtain in the future
from local reporting sources? 5) Is there any advantage to
exceeding the number of factors which could be reported on
one IBM card?
The rationale supporting the use of procedures
utilized in this study involved a basic assumption. That
assumption states that a similar relationship exists
between pupil yield factors developed from a census tract
base and pupil yield factors developed from individual
housing reports. Acceptance of this assumption does not
rest on the relationship being identical, only similar.
One might expect the range in pupil yield from smaller than
census tract enumeration efforts to exceed the range devel
oped on a census tract base. However, it would be reason
able to expect pupil yield parameters established on a
census tract base to be sufficient for any contiguous group
of occupied housing units approximating census tract size.^
If true, statistical treatment by multiple correlation and
stepwise regression analysis appears justified.
/
Chapter Summary
Eight independent variables were selected for in
vestigation— four housing unit and four housing occupant.
The specific factors included: type of structure, number
of bedrooms, year structure built, index of value/rent,
year moved into present unit, tenure, race/ethnic status,
family income and population density. Together with pupil
yield, the dependent variable, the nine variables generate
a total of twenty-six factors for Investigation.
^The approximate mean acreage and mean total popu
lation for the 304 census tracts is 3»270 acres and 4,200
population.
26
The factors were key punched into IBM cards, proc
essed to yield an ascending order print out, and placed on
expectancy tables. Information obtained from the expect
ancy tables was utilized in the additional statistical
treatment by multiple correlation and stepwise regression
analysis.
Practical considerations were involved in the
selection of factors including reducing the number to one
IBM card per case. The rationale supporting the statis
tical treatment Involved the assumption that census tract
based data would yield similar relationships to that data
based on smaller numbers of housing units.
1
I
CHAPTER IV
REPORT AND INTERPRETAION OF FINDINGS
Findings will be reported and interpreted relative
to three major categories: 1) basic considerations, 2) de
velopment of a pupil yield model, and 3) suggested implica
tions. Within this context, questions inherent to the
study will be examined.
Basic Considerations
The dependent variable was represented by four
pupil yield factors. These factors and their correspond
ing values from grouped and ungrouped data are reported in
the following chart:
Pupil Yield Factors
Pupil Yield
Factor
Group Data
Mean Value
Ungrouped Data
Mean Value
5-17
.7898 .7534
5-11 .4316 .4130
12-13
.1226 .1178
14-17 .2337
.2228
Grouped data are based on combined pupil yield
values from 304 census tracts; ungrouped data are based on
the total number of children per age range divided by the
total number of housing units contained within the same
27
census tracts. Unless otherwise Indicated, all informa
tion reported is based on computations developed from
grouped data.
The independent variables were represented by
twenty-two factors. These factors which were described in
greater detail in Chapter III are reported in Table 1.
TABLE 1
INDEPENDENT VARIABLES/FACTORS
Independent Variable
Factors Mean Standard Deviation
Structure Single
.7075 .2283
Multiple .2374 .2214
Mobile .0590
.1219
Year Built
<5
.1688 .1478
5-20
.5143 .2204
>20 .3100
.2533
Index of Value/Rent
----
.3979 .2276
Number of Bedrooms 0 .0336 .0874
1 .1796
.1571
2 .3358 .1528
>2 .4387 .2663
Tenure Owner .5886
.2477
Renter .4114 . 2480
Family Income
----
#11,328. 03,916.
Race/Ethnic White
.9295 .1391
Black .0382 .1267
"Other” .0307 .0308
"Spanish" .1294 .1025
Year Moved Into
Unit <2 .3452
.1213
2-3
.2200
.0537
4-10
.2699 .0882
>10 .1578 .0842
29
Ascending order listings of factors provided in
formation about the distribution of these indices. Rela
tively normal distributions were indicated from all but two
of the variables. However, both structure type and race/
ethnic variables included factors with skewed distribu
tions. Conversion to Z scores was not attempted because
little improvement in dispersion was likely to result. In
spite of the expectancy that the factors "mobile homes,"
"white," "black," and"other" would yield lower correla
tions, they were retained for treatment in multiple cor
relation and stepwise regression analysis.
Housing Unit Factors.— One of the questions in
herent to the study was, "which housing unit factors are
related to school age children?" An examination of the ex
pectancy tables developed for each of the independent vari
ables revealed the strongest pupil yield relationship to
exist with "number of bedrooms" and specifically the factor
"Thrfee or more bedrooms." Table 2 presents this relation
ship in expectancy table form.
Another view of the relationship between housing
unit factors and pupil yield can be obtained by examining
correlation coefficients. The highest correlating housing
factors are reported in Table 3. Of note is the fact that
the same five housing unit factors were found to rank high
est with each of the dependent variable factors, and that
except for high school age pupil yield (14-17), the ranking
TABLE 2
HOUSING- UNIT/PUPIL YIELD EXPECTANCY TABLE
Census Tract
Percentage
of Bedrooms
>2
Pupil Yield
Low
(<•250)
Below Avg.
(.250-.499)
Average
(.500-.999)
Above Avg.
(1.000-1.249)
High
(>1.250)
Frequency
>90$ 1(06$) 17(94$) 18
80-89 1(06$) 4(22$) 13(72$) 18
70-79 3(13$) 14(58$) 7(29$) 24
60-69 2(06$) 10(28$) 13(36$) 11(30$) 36
50-59 1(03$) 23(77$) 4(13$) 2(07$) 30
40-49 4(13$)
21(70$) 3('10$) 2(07$) 30
30-39 8(20$) 32(78#) 1(02$) 41
20-29 5(13$) 12(31$) 19(49$)
3(07$) 39
10-19 13(34$) 19(50$) 6(16$) 38
*9 22(73$)
3(10$) 3(10$)
2(07$) 30
Frequency 40
49
118
43
54
304 vu
0
31
is identical. Furthermore, the strength of number of bed
rooms >2 is apparent.
TABLE 3
RANKED HOUSING UNIT FACTORS
Pupil Yield
Factors
Rank Housing Unit
Variable
Factor r
5-17
1 Number of bedrooms >2 .8246
2 Number of bedrooms 1
-.7097
3
Structure Single
.6715
4 Structure Multiple -.6 4 9 3
5
Year Built >20 -.5747
5-11 1 Number of bedrooms >2 .7764.
2 Number of bedrooms 1
-.6 6 0 9
3
Structure Single .5956:
4 Structure Multiple -.5758
5
Year Built >20
-.5377
12-13 1 Number of bedrooms >2 .8637
2 Number of bedrooms 1
-.7025
3
Structure S ingle
.6837
4 Structure Multiple -.6682
5
Year Buiit >20
-.5753
14-1? 1 Number of bedrooms > 2 .7800
2 Structure Single .7223
3
Number of bedrooms 1
-.7115
4 Structure Multiple
-.6953
5
Year Built >20 -.5858
Housing Occupant Factors.— Another question in
herent to the study was, "Which housing occupant factors
are related to school age children?" One of the housing
occupant factor expectancy tables which indicated a posi
tive relationship was "year moved into unit— 4 to 1 0,"
Table 4 presents this relationship in expectancy table form.
TABLE 4
HOUSING OCCUPANT/PUPIL YIELD EXPECTANCY TABLE
Census Tract
Percentage
of Year
Mbved in
(4-10)
Pupil Yield
Low
U.250)
Below Avg.
(.250-. i ' 9 9)
Average
(.500*.999)
Above Avg.
(1.000-1.249)
High Frequency
( > 1.250)
50$ 3(100$)
3
45-49$
1(20$) 1(20$) 3( 60$) 5
40-44$ 4(19$0 8(38$) 9(43$) 21
35-39$ 2(08$) 6(22$) 6(22$) 13(48$)
27
30-34$
3(05$) 3(05$) 24(42$) 18(32$) 9(16$)
57
25-29$ 4(06$) 12(16$) 44(60$) 5(07$) 8(11$) 73
20-24$ 6(10$)
20(35$) 22(39$) 4(07$) 5(09$) 57
15-19$ 18(45$) 7(17$) 12(30$) 1(03$) 2(05$) 40
10-14$ 7(44$)
5(31$) 3(19$) 1(06$) 16
<9$ 1(33$) 2(67$) 3
Frequency
39 49
118
43 53 302 v .
r >
33
Correlation coefficients for the highest ranking
housing occupant factors are indicated in Table 5. Of
note is the fact that except for high school age pupil
yield (14-17), the same five factors were found with each
of the dependent variable factors, but not necessarily in
the same rank order. Furthermore, the strength of the
correlations generally were weaker than was indicated for
the housing unit factors.
TABLE 5
RANKED HOUSING OCCUPANT FACTORS
Pupil Yield
Factors
Rank Housing Occupant
Variable
Factor r
5-17
1 Tenure Owner .6698
2 Tenure Renter -.6 6 8 8
3 Moved into Unit 4-10 .5450
4 Moved into Unit <2 -.4248
5 Moved into Unit
2-3 .4054
5-11
1 Tenure Owner
.5923
2 Tenure Renter -.5910
3 Moved into Unit 4-10
.4947
4 Moved into Unit
2-3 .4235
5 Moved into Unit < 2 -.3341
12-13
1 Tenure Owner
.6993
2 Tenure Renter -.6986
3 Moved into Unit 4-10 .6124
4 Moved into Unit <2 -.4414
5 Moved into Unit 2-3
.4373
14-17
1 Tenure Owner .7142
2 Tenure Renter -.7138
3 Moved into Unit <2
-.5379
4 Moved into Unit 4-10 .5366
5 Family Income — —
.2957
3k
A Pupil Yield Model
Two of the principal questions inherent to the
study were, "Can school enrollment estimates he made by
using certain housing unit and housing occupant factors and
if so, what grouping of factors is most predictive of pupil
enrollment?" Treatment of factors by multiple correlation
and stepwise regression analysis was intended to yield
answers to these questions.
Computations were obtained for each of the four
dependent variable factors. The treatment utilized data
from the total number of cases, forced the use of "Year
Built /5" on the first step and entered the remaining in
dependent variable factors in a sequence intended to maxi
mize correlation with pupil yield. Twenty-one independent
variable factors were loaded into the regression equation
for the basic pupil yield indicator--"Pupil Yield 5“17»"
A listing of the loading sequence appears in the appendix.
With twenty-one factors loaded the values obtained were:
2
for multiple R .950, for R .903 and for standard error
.136. An F ratio of 125.01 was indicated based on 21 and
282 degrees of freedom. This value is significant at the
i . 01 level.
Practical considerations mediate against the use of
twenty-one factors in the application of a prediction equa
tion. "F" ratios for all pupil yield factors reach signif
icance levels of <.01 following the second step as indicated
by Table 8. Table 7 shows the first five factors loaded
TABLE 6
PUPIL YIELD 5-17 PREDICTION EQUATIONS
Step
*1
Constant x2
X3
x4
X5 X6
3
X1
= .542 + .505(X2 ) + 1.373(X3 ) - 1. 71i( x 4 )
4
X1
.636 + .247(X2)
1
><
VO
*
+
1.607(X4 ) - ,467(X5 )
5
X1
= .460 - .217(X2) + 1.128(X3) - 1.859(X4 ) - .485(X5 ) + .505(X6 )
VjJ
vxi
TABLE 7
STEPWISE REGRESSION ANALYSIS FOR PUPIL YIELD FACTORS
Pupil Yield Step Variable-Factor r R R2
5-17
1 Year Built <5 .130 .130
.017
2 # of Bedrooms >2 .825 .825 .680
3
Year Moved Into Unit>10 -.207 .872 .762
4 Index of Value/Rent -.031 .903 .815
5
Structure Type-Single .672
.919 .845
5-11 1 Year Built <5 .139 .139 .019
2 # of Bedrooms >2 .776 .777 .604
3
Year Moved Into Unit>10 -.277
.854 .730
4 Index of Value/Rent -.099 .903 .815
5
# of Bedrooms (1) -.6 61 .913 .834
12-13
1 Year Built <5 .159 .159 .025
2 # of Bedrooms >2 .864 .864
.747
3
Index of Value/Rent -.0 0 2 .897 .804
4 Year Moved Into Unit>10 -.149 .916 .838
5
Structure Type-Multiple -.6 6 8
.927 .859
14-17
1 Year Built <5 .082 .082 .007
2 # of Bedrooms >2 .780 .780 .609
3
Structure Type-Multiple
-.695
.816
.665
4 Year Moved Into Unit >10 -.0 8 2 .840
.705
5
Year Built >20 -.5 8 6 .852
.725
o^
37
for each pupil yield indicator. The prediction yield
formulas for Pupil Yield 5-17» steps three through five are
indicated in Table 6.
Minimum prediction computations would involve
utilization of the first two independent variable factors.
Information relating to use of these factors is found in
Tables 8 and 9.
One common application for pupil yield prediction
equations involves projecting school age children from
newly constructed housing units. To investigate new hous
ing, the fifteen census tracts were examined in which a
plurality percentage of structures had been constructed
during the four years prior to 1970. In twelve of the fif
teen census tracts a majority of new structures were single
units; in two of the census tracts a majority of new struc
tures were multiple units; and in one census tract a
majority of structures were mobile homes.
The actual pupil yield (5-17) was compared with the
pupil yield (5-17) developed from the two factor prediction
equation (Appendix B). Findings indicated an actual pupil
yield mean of 1.053 for the twelve single unit census
tracts and a formula pupil yield mean of 1.069 for the same
twelve single unit census tracts. Multiple unit formula
values were higher than actual pupil yield for the two
multiple unit census tracts and the predicted formula pupil
yield for the mobile home census tract was very close to
TABLE 8
TWO FACTOR ANALYSIS OF VARIANCE TABLES
Pupil
Yield
Source of Variance Stun of
Squares
DF Mean
Square
F
5-17 Step Two Regression 36.781 2 18.390 320.044
Residual 17.296 301
.057 '
5-11 Step Two Regression 11.568 2 5.784
229.167
Residual 7.597 301 .025
12-13
Step Two Regression 1.109 2 .554 444.934
Residual
.375
301 .001
14-17 Step Two Regression 2.560 2 1.280
234.817
Residual 1.641 301 .005
oo
TABLE 9
TWO FACTOR PUPIL YIELD PREDICTION EQUATIONS
*1
Pupil Yield
X2
Year Built <5
X3
# Bedrooms >2 Constant S.E.
5-17 = ,0330(X2) + 1.3057(X3)
+
.21141 .23971
5-11 = .0481(X2)
+ ,7294(X3)
+
.10351 .15887
12-13
= ,0167(X2) + ,2257(X3) +
.02081 .03530
14-17 = -.0244(X2) + .3467(X3) +
.08571 .07383
VjJ
V O
40
the actual pupil yield. One standard error was exceeded in
three of the single unit and one of the multiple unit cases.
A single factor prediction equation was developed using the
number of bedrooms >2. Application of this formula—
X = 1.564Y + .051--resulted in a more accurate predicted
pupil yield for each of the structure type factors. Ob
viously, caution must be exercised in drawing any conclu
sions relative to which formula is more accurate for
general use because of the small sample size.
Another consideration in the application of pupil
yield predictions equations relates to the trend of declin
ing school enrollments. A reduction in the number of
school age children can be anticipated. Annual changes in
dicated from ungrouped 1970 census data are reported in
Table 10.
TABLE 10
ANNUAL CHANGES IN PUPIL YIELD
School Year Children (5-17) Mean Pupil Yield Change
1969-70 316,552 .7534
______
1970-71 315,505 .7509 (.0025)
1971-72 312,494 .7438 (.0071)
1972-73 308,645 .7346 (.0092)
1973-74 305,696 .7276 (.0070)
1974-75
304,080
.7237 (.0039)
If the assumption is made that 1970 pupil yield re
lationships will be influenced little by migration activ
ity, an annual adjustment to pupil yield formula could be
' 41
considered which would reflect the changes Indicated in
Table 11.
Suggested Implications
Several possible relationships were indicated from
the findings; others were suggested in the review of the
literature. Implications relative to both categories of
relationships were considered worthy of reporting and are
discussed in this section.
A correlation coefficient matrix was developed in
dicating the relationship between all twenty-six factors
utilized. This matrix is presented in Appendix B and
Appendix C.
What are some of the implications indicated between
the dependent and independent variables?^
Number of Bedrooms.— One of the most frequently
cited factors relating to pupil yield is the number of bed
rooms per unit; the greater the number of bedrooms, the
higher the pupil yield. The strength of this relationship
is reaffirmed by this study.
Building Type.— A significantly higher pupil yield
for single units over multiple units generally has been re
ported. Current findings support the position that single
units do generate higher pupil yield values than either
multiple units or mobile homes, and that mobile homes gen-
^Unless otherwise Indicated, implications are based
on reported statistical treatments.
TABLE 11
SCHOOL AGE BY PUPIL YIELD FOR YEAR OF BIRTH
Birth Date Pupil Yield
1969
1970
1970
1971
1971
1972
1972
1973
1973
1974
1974
1975
1970 .0542 0 1 2
3
4
5
1969 .0509
1 2
3
4
5
6
1968
.0475
2
3
4
5
6
7
1967 .0478 3
4
5 6
7
8
1966 .0507 4
5
6
7 8
9
1965 .0548 5
6
7
8
9
10
1964
.0585
6
7
8
9
10 11
1963 .0586 7
8
9
10 11 12
1962
.0595
8
9
10 11 12
13
1961 .0605 9
10 11 12
13
14
1960 .0618 10 11 12
13
14
15
1959 .0592
11 12
13
14
15
16
1958 .0597
12
13
14
15
16
17
1957 .0580
13
14
15
16
17
1956 .0579
14
15 16
17
1955 .0567 15
16 17
1954 .0550 16
17
1953 .0532 17
M = .0558
ro
43
erate slightly higher pupil yield values than multiple
units. In addition, a positive relationship between mobile
homes and high school age pupils was suggested.2
Building Age.— The relationship between building
age and pupil yield is somewhat curvilinear in nature. In
1970 pupil yield for single and multiple units peaked for
buildings between five and twenty years of age, was
slightly lower for structures of under five years of age,
and lowest for structures over twenty years in age. Be
cause of the small number of census tracts in which a
plurality of mobile homes exists, no implications are
warranted.
Value.— In comparison to other studies, the rela
tionship between pupil yield and cost of housing was dis
appointing, but not unexpected. Probably the use of the
census tract base and the index of value/rent as the value
unit contributed to the weak relationship. However, some
suggestion exists that more elementary age children (5-11)
may be expected from new single units of lower value than
from similar units of higher value, and that more high
school age pupils (14-17) can be expected from new single
units of higher value than from similar units of lower
value.^
Year Moved Into Unit.— Among the four factors used
^Indicated from ascending order factor listings.
3
Indicated from ascending order factor listings.
44
to indicate this variable, "moved in 4-10" ranked highest
ahead of "moved in 2-3"; "moved in >10" ranked third and
"moved in <2" showed the lowest relationship to pupil yield.
The same relationship held constant for all four of the
dependent variable factors. However, pupil yield (12-13)
was relatively stronger in "moved in 2-3" and "moved in
4-10"; whereas pupil yield (14-17) was relatively stronger
in "moved in >10."
When "year moved into" unit factors are grouped with
"year built" (5-20), a transiency indicator can be developed
to determine high and low mobility census tracts,
4
Pupil Density. — An earlier reference indicated
that, while multiple units may not generate pupil yield
values as high as single units, ultimately multiple units
produce as many school age children per acre. To examine
this possibility, high percentage multiple unit census
tracts of similar size and of near equal development and
value were compared for similarity in pupil density. No
conclusive trend was indicated either to support or reject
the theory. This failure may involve the fact that several
differences exist between the San Diego area and the com
munity on which the judgment was based. Alameda is a rel
atively flat, more densely populated, urban-adjacent com
munity. Metropolitan San Diego characteristically is
alternating mesa-canyon terrain, less densely populated and
4
School age children (5-17) per acre.
^ 45
mixed urban-suburban communities. Continued interest re
mains to determine the validity of the concept to specific
areas.
Chapter Summary
Relationships between the twenty-two independent
variable factors and the four dependent variable factors
were reported by housing unit and housing occupant class
ifications.
Number of. bedrooms >2 ranked highest among housing
unit factors, followed by number of bedrooms 1, structure -
single unit, structure - multiple, and year built >20.
Relationships between occupant factors and the de
pendent variable were not as strong with tenure-owner rank
ing highest, followed generally by tenure-renter, year
moved into unit 4-10, year moved into unit <2, year moved
into unit 2-3. Rank order differences were noted for pupil
yield 14-17.
A pupil yield model was developed based on a step
wise regression procedure which forced the loading of "year
built <5h as the first step. Prediction equations were
provided using from one to five independent variables and
various applications and adjustments were suggested.
Questions inherent to the study were answered and
implications relating to the findings were indicated.
CHAPTER V
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
The topics covered in this chapter include a sum
mary, conclusions and recommendations.
Summary
The summary section is intended to fulfill the dual
purpose of reviewing the preceding chapters and abstracting
the entire study.
Title. "Pupil Yield— The Relationships Between Selected
Housing Unit and Housing Occupant Factors and the Number of
School Age Children."
Problem. Accurate pupil projecting remains an essential
prerequisite for implementation of educational program,
fiscal and facility plans. One method of estimating school
enrollment involves pupil projections based on the number
of housing units. Pupil yield is the term used to refer to
the number of school age children per housing unit. The
purpose of this study was 1) to investigate the relation
ship between pupil yield and selected housing units and
housing occupant variables and 2) to develop a pupil yield
model.
Procedures. 1970 census reports for San Diego County were
46
47
utilized. From this data were developed four dependent
variable factors and twenty-two independent variable fac
tors. The dependent variable factors included pupil yield
for ages 5-17, 5-11, 12-13, and 14-17; whereas the inde
pendent variables from which factors were developed in
cluded type of structure, number of bedrooms, year struc
ture built, value/rent index, year moved into unit, tenure,
race/ethnic, and family income.
Information covering each of the twenty-six factors
was gathered from 304 census tracts and placed on IBM
cards. Processing included the development of ascending
order listings, expectancy tables, multiple correlation and
stepwise regression analysis.
Findings. Rank order housing units relating to pupil yield
5-17 included number of bedrooms— three or more, number of
bedrooms - one, structure type - single units, structure
type - multiple units, and year built - over twenty. Rank
order occupant units relating to pupil yield 5-17 included
tenure - owner, tenure - renter, year moved into unit -
5-10, year moved into unit - less than two, year moved into
unit - 2-3. Except for pupil yield 14-17, rank orders for
housing and occupant factors were consistent.
Prediction equations for each pupil yield factor
utilizing year built - less than five, and number of bed
rooms - three or more, generated F scores sufficient to
yield significance below the .01 level.
48
Conclusions. Generally, maximum pupil yield values are
realized from housing units between five and twenty years
of age, where occupants have resided for between four and
ten years. Both the strongest positive and negative cor
relations for all pupil yield factors were from the same
independent variable, number of bedrooms. Number of bed
rooms >2 was positively correlated and number of bedrooms -
1 was negatively correlated.
Repeated utilization of enrollment projections from
pupil yield prediction equations should yield relatively
accurate results. However, periodic enumeration efforts
are required in order to re-evaluate pupil yield prediction
formulas.
Conclusions
The following conclusions are based on information
compiled and reported in this study:
1. Repeated utilization of enrollment projections from
pupil yield prediction equations should yield rela
tively accurate results.
Both satisfactory practical and statistical enroll
ment estimates are obtainable from the regression equations
developed in this study provided that the character of the
area to be studied is similar to the San Diego County
census tracts from which the factors were developed.
2. Both the strongest positive and negative correla
tions for all pupil yield factors were with the
independent variable, number of bedrooms; "three or
more being positively correlated and "one" being
negatively correlated.
49
This conclusion corresponds to similar statements
from previously cited studies which identified the positive
relationship between the number of bedrooms and the number
of school age children.
Practical application of this variable might be
enhanced through the utilization of an average number of
bedrooms factor developed by dividing the sample total num
ber of bedrooms by the sample total number of housing units.
3* Generally maximum pupil yield is realized from
housing between five and twenty years of age where
occupants have been residents between four and ten
years.
The current study, in addition to reaffirming a
previously identified conclusion that older structures
generate fewer school age children, supports the common
sense position that through the first ten years a positive
relationship exists between the length of residence in the
same location and the ages and number of school age chil
dren.
To some extent this conclusion serves to support
the policy position taken by some larger school districts
that permenant neighborhood school facilities should be
constructed for an enrollment capacity of less than would
be generated from peak pupil yield projections with re
locatable classrooms to be utilized during the high en
rollment periods.
4. Expectations are higher for pupil yield pattern
consistency than for pupil yield numerical con
sistency.
50;
A corollary conclusion to the previous statement
suggests that while pupil yield values may be expected to
vary over a period of time, a predictable pupil yield pat
tern occurs whether or not the area is relatively stable or
highly transient in nature.
5. Exceptions to the pupil yield peaking at "year
moved in, four to ten" seems to be indicated for
high percentage "other and Spanish" tracts.
The correlation coefficient matrix suggests that a
higher degree of mobility exists for racial/ethnic "other
and Spanish," which is likely to result in an earlier pupil
yield peak.
6. Relatively lower high school age pupil yield (14-17)
values occur in census tracts with a high percent
age of lower value, single units where occupants
moved into units within three years prior to 1970.
This conclusion suggested by the correlation co
efficient matrix corresponds to statements from previous
studies indicating that younger families tend to buy newer
homes of lesser value.
7. Movement to higher value housing usually means a
relative increase in upper grade (12-1 7) pupil
yield.
This conclusion suggested from the correlation co
efficient matrix is associated with earlier statements in
dicating that older families tend to buy newer homes of
greater value.
Recommendations
The following recommendations are based on the con-
51
elusions and data reported in the study:
1. Enrollment projections from pupil prediction equa
tions should he considered appropriate only as an
alternative when the opportunity for direct enumera
tion is not possible or practical.
Because of the time dimension influence on pupil
yield values, in addition to other less predictable in
fluences, the use of pupil yield prediction equations
should not be considered a substitute for direct pupil cen
sus activities.
2. Periodic enumeration efforts are required in order
to reevaluate pupil yield prediction formulas.
If pupil yield figures are to have value in pro
jection computations, school districts should consider
annual conduct of selected census activities, involving
newly occupied and special category housing.
3. Special enumeration activities should be accom
plished to determine the Impact of pupil yield
generated for special structure types, such as
condominiums, town houses, federal housing, vaca
tion units, institutions and others.
This recommendation has particular significance
because of the Increasing number of new condominiums being
constructed. One might speculate that new condominiums
would generate a pupil yield smaller than for single units,
but larger than for multiple units.
4. Until proven to the contrary, school district ad
ministrators should consider the possibility that
over a period of time pupil yield per acre may be
relatively similar irrespective of the type of
buildings constructed.
While this study could not offer conclusive proof
52
either to confirm or discount the concept, some suggestion
exists that it may have validity in urban areas.
5. Identification of migration-transient patterns from
housing unit and occupant data appears feasible and
should be Investigated.
One approach for obtaining migration-transiency
information in the absence of longitudinal data suggests
that housing units of comparable type and age can be com
pared with "year moved into" unit data to determine the
degree of current mobility.
APPENDIXES
APPENDIX A
PUPIL YIELD 5-17 STEPWISE REGRESSION ANALYSIS
Step Variable Factor Factor # r R R2
1 Year Built <5
11
.13 .13 .02
2 Number of Bedrooms >2 26 .82 .82 .68
5 Year Moved Into Unit >10 22 -.20 .87 .76
4 Value/Rent 14 -.03
.90 .81
5
Structure Type Single
5 .67
.92 .84
6 Year Built >20
13 -.57 .93 .86
7 Race/Ethnic White
15
-.16
.93 .87
8 Race/Ethnic Spanish 18 .05 .94 .88
9 Year Built 5-20 12 .53 .94 .89
10 Number of Bedrooms 1 24
-.71 .94 .89
11 Number of Bedrooms 0
23 -.37 .94 .89
12 Number of Bedrooms 2
25 -.49 .94 .89
13 Year Moved Into Unit
2-3
20 .40
.95 .90
14 Family Income 10 .18 .95 .90
15
Tenure Owner 8 .66 .95 .90
16 Year Moved Into Unit <2
19
-.42 .95 .90
17 Year Moved Into Unit 4-10 21 .54 .95 .90
18 Structure Type Multiple 6 -.65 .95 .90
19 Race/Ethnic Black 16
.15 .95 .90
20 Race/Ethnic Other 17 .11 .95 .90
21 Structure Type Mobile
7 -.06 .95 .90
Not Loaded Tenure Renter 9
54
APPENDIX B
MULTIPLE REGRESSION FACTORS
Variables Factors Factor #
Structure Single
5
Multiple 6
Mobile
7
Year Built <5
11
5-20 12
>20
13
Index of Value/Rent 14
Number of Bedrooms 0
23
1 24
2
25
72 26
Tenure Owner 8
Renter
9
Family Income 10
Race/Ethnic White
15
Black 16
"Other"
17
"Spanish" 18
Year Moved Into Unit <2
19
2-3 20
4-10 21
>10 22
Pupil Yield
5-17 1
5-11 2
12-13 3
14-17 4
55
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
APPENDIX C
MULTIPLE REGRESSION RUN
1 2
3
4
5
6
7 8
>
9
1.00 0.98 0.96 0.91 0.67 -0.64 -0.06 0.66 -0.66
0.98 1.00
0.93 0.83 0.59 -0.57
-0.04
0.59 -0.59
0.96
0.93
1.00
0.87 0.68 -0.66
-0.05 0.69 -0.69
0.91 0.83 0.87
1.00 0.72 -0.69 -0.08
0.71 -0.71
0.67 0.59 0.68 0.72 1.00
-0.85 -0.31 0.77 -0.77
-0.64
-0.57 -0.66
-0.69 -0.85 1.00
-0.15 -0.88 0.88
-0.06 -0.04 -0.05 -0.08
-0.31 -0.15 1.00 0.14 -0.14
0.66
0.59 0.69 0.71 0.77 -0.88 o;i4 1.00
-0.99
-0.66
-0.59 -0.69 -0.71 -0.77 0.88 -0.14
-0.99 1.00
0.18 0.10
0.23 0.29 0.44
-0.37 -0.16
0.49 -0.49
0.12
0.13 0.15 0.08 -0.01
-0.17 0.33 0.28 -0.28
0.53 0.49 0.57
0.54 0.40 -0.44
0.05 0.48 -0.48
-0.57 -0.53 -0.57
-0.58 -0.36 0.50
-0.23 -0.59 0.59
-0.03 -0.09 -0.00
0.09 0.18
-0.17 -0.06
0.25 -0.25
-0.16 -0.20 -0.12 -0.07 0.02 -0.05 -0.04 0.16 -0.16
0.15 0.18 0.11 0.08 0.01 0.01
0.05 -0.11 0.11
0.10
0.17 0.07 -0.01 -0.16
0.17 -0.00 -0.24 0.24
0.05 0.09 0.02 -0.02
-0.13
0.11
0.05 -0.23 0.23
-0.42
-0.33
-0.44
-0.53 -0.65 0.62 0.09 -0.61 0.61
0.40 0.42 0.43 0.28 0.21
-0.25 0.06 0.28 -0.2'8
0.54
0.49 0.61
0.53 0.47 -0.55
0.11
0.63 -0.63
-0.20
-0.27 -0.14 -0.08
0.23 -0.08
-0.27
0.10 -0.10
-0.37 -0.35 -0.36
-0.37 -0.50 0.54 -0.05 -0.46 0.46
-0.70 -0.66 -0.70
-0.71 -0.75 0.67 0.17 -0.74 0.74
-0.49 -0.45 -0.50 -0.50 -0.30 0.22 0.18
-0.31 0.31
0.82
0.77 0.86 0.78 0.74
-0.67 -0.18
0.77 -0.77
#
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
APPENDIX C— Continued
11 12
13
14
15
16
17
18
19
0.12
0.53 -0.57 -0.03 -0.16
0.15
0.10 0.05 -0.42
0.13 0.49 -0.53 -0.09 -0.20 0.18
0.17 0.09 -0.33
0.15 0.57 -0.57
-0.00 -0.12 0.11
0.07 0.02 -0.44
0.08 0.54 -0.58 0.09 -0.07 0.08 -0.01 -0.02
-0.53
-0.01 0.40 -0.36 0.18 0.02 0.01 -0.16
-0.13 -0.65
-0.17 -0.44 0.50
-0.17 -0.05 0.01
0.17
0.11 0.62
0.33 0.05 -0.23
-0.06 -0.04
0.05 -0.00 0.05 0.09
0.28 0.48
-0.59 0.25 0.16 -0.11 -0.24
-0.23 -0.61
-0.28 -0.48
0.59 -0.25 -0.16 0.11 0.24
0.23 0.61
0.18
0.23 -0.30 0.71 0.28
-0.23 -0.33
-0.41
-0.35
1.00 -0.06 -0.50 0.34 0.22 -0.21 -0.12 -0.21 0.22
-0.06 1.00 -0.78 0,12 0.07 -0.04 -0.16 -0.25 -0.40
-0.50 -0.78 1.00 -0.32 -0.19 0.16 0.21
0.33 0.24
0.34 0.12 -0.32 1.00 0.40
-0.35 -0.36 -0.50 -0.12
0.22
0.07 -0.19 0.40 1.00
-0.97 -0.49 -0.31 -0.02
-0.21 -0.04 0.16
-0.35 -0.97
1.00
0.29 0.22 -0.01
-0.12 -0.16 0.21 -0.36 -0.49 0.29 1.00 0.50 0.16
-0.21
-0.25 0.33
-0.50
-0.31 0.22 0.50 1.00 0.07
0.22 -0.40 0.24 -0.12 -0.02 -0.01 0.16 0.07 1.00
0.32 0.14 -0.26 0.06 -0.03 0.02 0.07 -0.00 -0.14
0.08
0.45 -0.34 0.05 -0.01
0.03 -0.05 0.02 -0.66
-0.53
0.01 0.32 -0.10 0.05 -0.01
-0.17 -0.03 -0.42
-0.16
-0.39 0.45 -0.15
-0.10
0.05 0.24 0.10 0.2 6
-0.10
-0.49 0.50 -0.21 -0.07 0.06
0.05 0.25 0.50
-0.07 -0.24
0.29 -0.26 -0.04 0.04 0.02 0.10 0.26
0.14 0.56 -0.56 0.23 0.08 -0.06 -0.10 -0.19 -0.53
APPENDIX C— Continued
.ctor
#
21 22
23
24
1 0.54 -0.20
-0.37
-0.70
2 0.49 -0.27 -0.35
-0.66
3 0.61 -0.14 -0.36 -0.70
4
0.53
-0.08
-0.37 -0.71
5 0.47 0.23
-0.50
-0.75
6
-0.55
-0.08 0.54
0.67
7
0.11
-0.27 -0.05 0.17
8
0.63
0.10 -0.46 -0.74
9 -0.63
-0.10 0.46 0.74
10 0.22 0.13 -0.19 -0.45
11 0.08
-0.53
-0.16 -0.10
12 0.45 0.01
-0.39 -0.49
13 -0.39 0.32 0.45 0.50
14 0.05 -0.10
-0.15
-0.21
15 -0.01 0.05 -0.10
-0.07
16 0.03 -0.01 0.05 0.06
17 -0.05 -0.17
0.24 0.05
18 0.02 -0.03 0.10
0.25
19 -0.66 -0.42 0.26 0.58
20
0.23 -0.35 -0.17
-0.24
21 1.00 -0.00 -0.18 -0.46
22 -0.00 1.00 -0.04 -0.10
23
-0.18 -0.04 1.00
0.25
24 -0.46 -0.10
0.25 1.00
25 -0.30 0.18
-0.17
0.28
26 0.60 0.04
-0.35 -0.78
25 26
-0.49 0.82
-0.45 0.77
-0.50 0.86
-0.50 0.78
-0.30 0.74
0.22 -0.67
0.18 -0.18
-0.31 0.77
0.31 -0.77
-0.38 0.45
-0.07 0.14
-0.24 0.56
0.29 -0.56
-0.26
0.23
-0.04 0.08
0.04 -0.06
0.02 -0.10
0.10
-0.19
0.26
-0.53
-0.12 0.34
-0.30 0.60
0.18 0.04
-0.18 -0.36
0.29 -0.79
1.00 -0.60
-0.60 1.00
ui
00
i
BIBLIOGRAPHY
i
59
BIBLIOGRAPHY
BOOKS s
Bent, Dale H. ; Hull, C. Handlaij and Nie, Norman J. Statis
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McGraw-Hill Book Co,, 1970.
Driscoll, William Norman. "The Prediction of School En
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Ed.D. dissertation, Colorado State College, 1965.
Dissertation Abstracts International, Vol. XXVI, No. 5»
Ann Arbor, Michigan: Xerox University Microfilms, 1966
Ellena, William John. "A Technique for Predicting Pupil
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Englehardt, Fred. Forecasting School Population. Contribu
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Gibbs, Wesley Fayette. "Development of a System for Pre
dicting School Enrollment Using Selected Housing Fac
tors." Unpublished Ph.D. dissertation, Northwestern
University, 1966.
Griffith, William Jess. "Variables Affecting Public School
Enrollment Change." Unpublished Ph.D. dissertation,
Ohio State University, 196^. Dissertation Abstracts
International, Vol. XXV, No. 11. Ann Arbor, Michigan:
Xerox University Microfilms, 1965.
Guilford, J. P. Fundamental Statistics in Psychology and
Education. New York: McGraw-Hill Book Co., 19°5.
Hunt, David Glen. "The Development of Enrollment Projec
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of Texas, 1962. Dissertation Abstracts International,
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Jacoby, E.G. Methods of School Enrollment Projections.
Educational Studies" and Documents, Vol. XXXII. Paris:
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UNESCO, 1959.
Laugesen, Roy Milton. "An Evaluation of Population Pro
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Peterson, Donald Lee. "An Investigation of Techniques for
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Sax, Gilbert. Empirical Foundations of Educational Re-
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Strand, William Henry. "Forecasting Enrollment in the
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Xerox University Microfilms, 195^.
Wheeler, Norman S. "Techniques Used for Predicting Public
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Dissertation Abstract International, Vol. XV, No. 9.
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REPORTS AND ARTICLES:
Bureau of School Planning. Guide for the Development of a
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Sacramento, Ca.: California State Department of Educa
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Bureau of School Planning. Demographic Analysis— A Basis
for Projecting School Population Trends. Sacramento,
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Carlsbad Unified School District. Student Enrollment
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Conlisk, John. Determinants of School Enrollment and
School Performance. Madison, Wis: Wisconsin Univer
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62
Dahms, Rex T., compiler. Long Range Development Plan. San
Diego, Ca.: Cajon Valley Union School District, 1972.
Financial Planning Committee and Sites and Facilities Plan
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School District, 1972.
Mercury Construction Company. Panorama Hills. Private
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Office of the Legislative Analyst. Enrollment Projection
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Sacramento,- Ca. : State of California, 1970.
"Prediction." Encyclopedia of Educational Research, ^th
ed. , 1969.
U. S. Bureau of Census. 1970 Census User's Guide. Wash
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Asset Metadata

Creator Westwater, David Leo (author)

Core Title Pupil Yield--The Relationships Between Selected Housing Unit And Housing Occupant Factors And The Number Of School Age Children

Degree Doctor of Education

Degree Program Education

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

Tag education, administration,Education, general,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Muelder, Wallace R. (committee chair), Wilbur, Leslie (committee member), Wulf, Katherine M. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-869715

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