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Fixation in slow learners, and sensitivity of Piagetian conservation scores to factors known to affect IQ scores

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Fixation in slow learners, and sensitivity of Piagetian conservation scores to factors known to affect IQ scores

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Content FIXATION IN SLOW LEARNERS, AND SENSITIVITY
OF PIAGETIAN CONSERVATION SCORES TO
FACTORS KNOWN TO AFFECT IQ SCORES
by
Mary Eselun Frankel
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Education)
January 1978
UMI Number: DP24272
All rights reserved
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a note will indicate the deletion.
Dissertation Pubi sh sng
UMI DP24272
Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author.
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UNIVERSITY OF SOUTHERN CALIFORNIA
THE GRADUATE SCHOOL
UNIVERSITY PARK
LOS ANGELES, CALIFORNIA 90007
This dissertation, written by
Mary Eselun Frankel
under the direction of h.-Q.V.. Dissertation Com
mittee, and approved by all its members, has
been presented to and accepted by The Graduate
School, in partial fulfillment of requirements of
the degree of
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TABLE OF CONTENTS
LIST OF TABLES.......... . . . ..........................iv
LIST OF ILLUSTRATIONS................................... viii
ABSTRACT................................................... ix
Chapter
I. INTRODUCTION AND REVIEW OF THE RESEARCH ............ 1
Fixation Hypothesis ............................. 1
Conventional versus Piagetian Tests ............ 4
Significant Variables............. 8
Ethnicity ........................................ 9
Class Program...................................... 10
CA, MA, and I Q ....................................12
II. ORGANIZATION OF THE PRESENT RESEARCH ............. 14
Variables...........................................14
Selection of Subjects............................ 17
Materials and Methods . . . 19
Scope and Limits..................................21
Hypotheses............................. 23
III. RESULTS................................................27
IV. DISCUSSION . . ...................................... 46
Fixation................. ^........................46
Intelligence As Intermediate Variable .......... 47
Use of IQ and Conservation Tests to
Classify........................................ 48
ii
Chapter
Limitations and Recommendations ............... 49
REFERENCES................................................. 51
APPENDIXES................................................. 64
A. LIST OF INDIVIDUAL SUBJECTS, TEST SCORES,
AND RELEVANT DATA..................................65
B. SUMMARIES OF ANOVAS OF GBKC SCORES.................67
C. SUMMARIES OF MULTIPLE REGRESSION OF INDEPENDENT
CONTINUOUS AND DICHOTOMOUS VARIABLES HAVING
SIGNIFICANT EFFECTS ON GBKC SCORES ........... 131
ill
LIST OP TABLES
1. Intercorrelations of All Dependent and
Independent Variables (Taken As Continuous) . . 30
2. Intercorrelations of All Dependent and
Independent Variables (Taken As Dichotomous
Variables)................. 31
3. Summary of All Two-Way Analyses of Variance
Found to Be Significant at a <_ .05
(Variables Dichotomized) ........................ 3^
4. Summary of Significant ANOVA Effects among
the Critical Variables of CA, MA, and IQ
(Variables Dichotomized) ........................ 37
5. Intercorrelations of CA, MA, and IQ, with
Dichotomous and "Continuous" Data Compared . . . 37
6. Multiple Regression Summary Table, "Continuous"
Data................................. 38
7. Multiple Regression Summary Table, Dichotomous
Data................................................. 39
8. List of Individual Subjects, Test Scores, and
Relevant D a t a ...................................... 66
9. ANOVA of GBKC Judgment Score: Program by SES . . 68
10. ANOVA of GBKC Judgment Score: Program by
Ethnicity...........................................69
11. ANOVA of GBKC Judgment Score: Program by Sex . . 70
12. ANOVA of GBKC Judgment Score: Program by IQ . . . 71
13. ANOVA of GBKC Judgment Score: Program by MA . . . 72
14. ANOVA of GBKC Judgment Score: 'Program by CA . . . 73
15. ANOVA of GBKC Judgment Score: SES by
Ethnicity...........................................7^
16. ANOVA of GBKC Judgment Score: SES by Sex .... 75
iv
17- ANOVA of GBKC Judgment Score: SES by I Q ........76
18. ANOVA of GBKC Judgment Score: SES by M A ........77
19. ANOVA of GBKC Judgment Score: SES by C A ........ 78
20. ANOVA of GBKC Judgment Score: Ethnicity by
S e x ................................................. 79
21. ANOVA of GBKC Judgment Score: Ethnicity by IQ . . 80
22. ANOVA of GBKC Judgment Score: Ethnicity by MA . . 8l
23. ANOVA of GBKC Judgment Score: Ethnicity by CA . . 82
24. ANOVA of GBKC Judgment Score: Sex by I Q ........ 83
25. ANOVA of GBKC Judgment Score: Sex by M A ........84
26. ANOVA of GBKC Judgment Score: Sex by C A ........ 85
27. ANOVA of GBKC Judgment Score: IQ by M A ............86
28. ANOVA of GBKC Judgment Score: IQ by CA ..... 87
29. ANOVA of GBKC Judgment Score: MA by C A ............88
30. ANOVA of GBKC Explanation Score: Program by
S E S ........................................ 89
31. ANOVA of GBKC Explanation Score: Program by
Ethnicity...........................................90
32. ANOVA of GBKC Explanation Score: Program by
S e x ................................................. 91
33. ANOVA of GBKC Explanation Score: Program by
I Q ....................................................92
34. ANOVA of GBKC Explanation Score: Program by
M A ....................................................93
35* ANOVA of GBKC Explanation Score: Program by
CA ' ............................. 94
36. ANOVA of GBKC Explanation Score: SES by
Ethnicity ............... -....................... 95
37. ANOVA of GBKC Explanation Score: SES by
Ethnicity . 96
38. ANOVA of GBKC Explanation Score: SES by IQ . . . 97
v
39. ANOVA of GBKC Explanation Score: SES by MA . . . 98
40. ANOVA of GBKC Explanation Score: SES by CA .. . 99
41. ANOVA of GBKC Explanation Score: Ethnicity by
S e x ................................................ 100
42. ANOVA of GBKC Explanation Score: Ethnicity by
I Q .................................................. 101
43* ANOVA of GBKC Explanation Score: Ethnicity by
M A .................................................. 102
44. ANOVA of GBKC Explanation Score: Ethnicity by
C A .................................................. 103
45. ANOVA of GBKC Explanation Score: Sex by IQ . . . 104
46. ANOVA of GBKC Explanation Score: Sex by MA . . . 105
47. ANOVA of GBKC Explanation Score: Sex by CA . . . 106
48. ANOVA of GBKC Explanation Score: IQ by MA .... 107
49. ANOVA of GBKC Explanation Score: IQ by CA . . . . 108
50. ANOVA of GBKC Explanation Score: MA by CA . . . . 109
51. ANOVA of GBKC Total Score: Program by SES .... 110
52. ANOVA of GBKC Total Score: Program by
Ethnicity..........................................Ill
53* ANOVA of GBKC Total Score: Program by Sex .... 112
54. ANOVA of GBKC Total Score: Program by IQ .... 113
55* ANOVA of GBKC Total Score: Program by MA .... 114
56. ANOVA of GBKC Total Score: Program by CA .... 115
57. ANOVA of GBKC Total Score: SESby Ethnicity . . . 116
58. ANOVA of GBKC Total Score: SES by Sex..............117
59. ANOVA of GBKC Total Score: SES by I Q ..............118
60. ANOVA of GBKC Total Score: SES by M A ..............119
61. ANOVA of GBKC Total Score: SES by C A ..............120
62. ANOVA of GBKC Total Score: Ethnicity by Sex . . . 121
63. ANOVA of GBKC Total Score: Ethnicity by IQ . . . 122
64:. ANOVA of GBKC Total Score: Ethnicity by MA . . . 123
65. ANOVA of GBKC Total Score: Ethnicity by CA . . . 124
66. ANOVA of GBKC Total Score: Sex by IQ ...... 125
67. ANOVA of GBKC Total Score: Sex by MA...........126
68. ANOVA of GBKC Total Score: Sex by C A .........127
69. ANOVA of GBKC Total Score: IQ by M A ........... 128
70. ANOVA of GBKC Total Score: IQ by C A ........... 129
71. ANOVA of GBKC Total Score: MA by C A ...........130
72. Summary of Multiple Regression of Independent
(Continuous) Variables Having Significant
Effects on Judgment Scores ....................... 132
73. Summary of Multiple Regression of Independent
(Dichotomous) Variables Having Significant
Effects on Judgment Scores ....................... 133
74. Summary of Multiple Regression on Independent
(Continuous) Variables Having Significant
Effects on Explanation Scores .................. 134
75- Summary of Multiple Regression of Independent
(Dichotomous) Variables Having Significant
Effects on Explanation Scores .................. 135
76. Summary of Multiple Regression of Independent
(Continuous) Variables Having Significant
Effects' on Total Scores.......................... 136
77- Summary of Multiple Regression of Independent
(Dichotomous) Variables Having Significant
Effects of Total Scores ......................... 137
vii
LIST OF ILLUSTRATIONS
1. Convergence of the Mean IQ Test Scores of
Chicano Children with the Standard Norms
As Sociocultural Factors Are Increasingly
Controlled...........................................11
2. Distribution of GBKC Partial and Total Scores . . . 28
3. Demonstration of Interaction Effects of
Program vs. SES on Explanation Scores..............33
4. Distribution of GBKC Total Scores by Mental Age
with Individual IQs Noted........................... 36
5. Scattergram of GBKC Judgment Scores by IQ,
Showing Ethnicity, SES, and Program for Each
Subject............................................... 42
6. Scattergram of GBKC Explanation Scores by IQ,
Showing Ethnicity, SES, and Program for Each
Subject .........................................43
7. Scattergram of GBKC Total Scores by IQ, Showing
Ethnicity, SES, and Program for Each Subject . . 44
viii
ABSTRACT
In questioning the validity of Inhelder’s assertion
that fixation prior to the formal operations level defines
mental retardation, and also questioning the common assump
tion that Piagetian intelligence and conventional Intelli
gence are the same thing, 68 "slow learner" school-age
children were selected, similar to the younger half of
Inhelder’s 19^3 study group in IQ, MA, CA, and sex, but all
attending public schools. Almost equal percentages were
selected to be similarly Chicano or Anglo, of middle or low
socioeconomic status (SES), and attending segregated or
integrated special education classes. Each of these vari
ables has been reported to affect both normative intelli
gence and Piagetian intelligence. The Goldschmid-Bentler
Kit— Conservation (GBKC) was used to assess Piagetian cog
nitive level in the conservation domain; Binet or similar
tests assessed the IQ and MA levels.
Analysis of variance was used with the independent
variables, taken two by two, to see if they affected the
variance of the judgment/explanation/total scores on the
GBKC, as would be expected if the two intelligences had
common factors. Except for the IQ, MA, and CA, they did
not. A slight interaction effect was seen between class
Ix
placement and SES. Both conventional psychometric measure
ments and objective Piagetian scores in this study thus
measure something related to age, both mental and chrono
logical, but do not show sensitivity, as do IQ tests, to
ethnicity, sex, socioeconomic status, or to whether the
children are taught in regular classes or segregated. It
is suggested that IQ scores and performance on conservation
tests overlap, rather than being closely related.
Stepwise multiple progression also failed to show any
large contribution after MA and IQ are taken into account.
SES, sex, and CA were found to have significant but very
small effects on the size of the multiple correlations.
In addition, InhelderTs description of mental retarda
tion as fixation is not supported by the distribution of
the GBKC scores against mental age. Passage of stage mile
stones appeared to be at normal MA levels rather than at
the expected delayed levels, and there was no marked tend
ency for low-IQ or low-MA children to fixate at low con
servation levels.
These results are not consistent with many reported
studies, and the work should be replicated. More cases (to
improve statistical analysis) and a wider CA range (to per
mit better assessment of fixation level) are recommended,
along with agreements among researchers as to operational
definitions of IQ, MA, mental retardation, and test pro
cedures .
x
I. INTRODUCTION AND REVIEW OF THE RESEARCH
This study is addressed in general to the theoretical
problems educators have in designing and using nomothetic
psychological tests in idiographically meaningful ways with
developmentally disadvantaged children (sometimes called
"borderline retarded," "educable retarded," "slow learn
ers," "morons," or "feebly gifted").
Fixation Hypothesis
In particular, an attempt is made to assess the appli
cability to American school children of Inhelder’s (1943/
1968) conclusion from her studies of Swiss "retardates"
that "to be retarded means, therefore: to be able to think
by concrete operations, but not by formal operations"
(p. 294). This translates into an approximate MA level
of up to 7 years for the adult "retardate" and from 7 to
11 years of MA for the adult "slow learner" (Inhelder,
1943/1968, pp. 292-293).
The use of fixation of reasoning processes as a defi
nition of mental retardation appears to make the definition
a circular one, and is essentially useless to educators in
predicting school performance and determining class place
ment (Murray, 1977). A child is not usually considered
retarded until he goes to school, and 12 years later he
often goes back into unnoticed normality in the world of
work. Had he been known at birth to be potentially fixated
at Piaget’s Level III, he might have been given the bene
fits of a Waisman Center Program like that at the Univer
sity of Wisconsin (Heber & Garber, 1971); newborn children
of mothers with IQs below 80 are being trained intensively,
achieving test IQs up to 50 points above expectation levels
in 5 years.
In addition, as Ross (1976) pointed out:
The question raised here . . . is not whether the men
tally retarded are incapable of formal thinking, but
that so many other people considered normal in intel
lectual functions, do not manifest formal thinking in
the Inhelder and Piaget tasks. Thus, if the "absence
of formal thinking = mental retardation" criterion
were applied with existing measuring devices, it would
be expected that at least one half of the population
would be classified mentally retarded. (p. 200)
Another argument against uncritical acceptance of
Inhelder’s definition of mental retardation includes the
observation that nobody, having achieved the formal reason
ing stage, reasons formally all of the time or in all con
tent areas; it means only that he is able to do so under
certain circumstances (Tanner & Inhelder, 1971).
There is also the possibility that, despite the con
siderable experimental support for the validity of Piaget’s
cognitive sequences as applied to slow learners, they may
not actually form Guttman scales, in which passage at any
level assumes passage at all earlier levels. Zeaman and
2
House (1963) pointed out that inability to focus attention
seriously affects a child’s performance on learning tasks.
Labeled borderline retardates have been shown just as cap
able of producing high quality test responses when they
perceive it to be to their advantage as do their brighter
schoolmates (Braginski & Braginski, 1972).
Experiments with children at moderate and severe
levels of intellectual functioning led Woodward (1961,
1963) to the conclusion that such subjects gave unreliable
scores, and could not properly be matched for MA with nor
mals for study purposes, because the MA apparently means
something different at different age levels. This also
suggests the impossibility of a Guttman scale, though she
felt that a Piagetian sequential developmental scale not
related to CA might yet be developed. For reasons not yet
known, language problems beset more labeled retardates than
they do normally developing children. The Piagetian
methode clinique from age 4 on depends largely on language
for assessment of the child’s cognitive level (Luria; 1961;
Milgram & Furth, 1963; W. E. Stephens, 1973; Vygotsky
(1939/1962). Thus there are built-in difficulties in any
normative statements (such as Inhelder’s) about develop-
mentally disabled persons (Hamel, 1975; Sigel, 197^0*
Although significant stage reversals only recently
began to appear in the literature, there is evidence that
skipped substages, quantitative shifts, and alternate
3
routes to formal thinking do take place, especially with
physically handicapped children, and especially the deaf
(Furth, 1970; Wohlhueter & Sindberg, 1975; Wolff, 1972).
Finally the relation of personality factors such as
"other-directedness" (Carlson & Michalson, 1973), and of
motivational and experiential factors (Goldschmid, 1968),
have been shown to interfere with reliably labeling chil
dren as mental retardates on the basis of their cognitive
performance. If this study can help cast doubt on
Inhelder’s definition of "true retardate," which is not
helpful to teachers and may not even represent a real vari
able, It will have served the children Involved.
Conventional versus Piagetian Tests
Another argument against uncritical acceptance of
assumption made by many laborers In the Piagetian fields
that the intervening variable known from days of old as
Intelligence is the same as the intervening variable hope
fully being measured In nomothetic (normative) tests by
more conventional psychometry (Elkind, 1969; Inhelder &
Piaget, 1958; Piaget, 1952/1963). The truth of this
assumption Is questioned In this study.
If the assumption is true, it seems likely that vari
ables known to affect performance In conventional tests
should also affect Piaget-type, essentially idiographic
tests of cognitive development.
This project Is not new. Similar inquiries have been
increasing quite rapidly for 15 years or more. Readers
need go no further than the daily newspaper and popular
journals to be aware of and often angry about the schools'
labeling of certain children as mentally retarded, segre
gating them from normal children, and providing a history
of failure experiences such that the children forever give
up trying to fit into society (MacMillan, 1971, 1973;
Mercer, 1970, 1973a, 1973b, 1973c; Meyers & Meyers, 1967)*
The impact of the 1977 federal Education for All
Handicapped Children Act will require even more replicative
studies with valid generalizable results to help schools
cope with a vastly increased number of pupils in special
education and with "put-upon" classes of normals being used
as models and motivators. In her introduction to the
Modgils' fifth volume of their monumental eight-volume com
pilation of Piagetian research, Inhelder (1976, pp. 7—8)
noted that already more than 3,700 references had been
covered. Yet the vast majority still fail to understand
Piaget's theoretical framework, Inhelder felt: Piaget's
theory is "constructivist" and "epigenetic," not "matura-
tional" or "innate"; also, it provides, not a list of
chronological-age milestones, but a limited series of be
havioral sequences. Why, then, are so many looking to
Piaget for guidance in relation to intelligence?
Piaget himself also feels that much of the research of
the 1960s misses his point. At the 1969 Monterey
5
conference on ordinal scales of cognitive development he
said,
I have no interest whatsoever in the individual. I
am very interested in general mechanisms, intelligence
and cognitive functions, but what makes one individual
different from another seems to me far less instruc
tive as regards the study of the human mind in gen
eral. (In Inhelder & Piaget, 1971* P- 211)
The question arises as to why so much research effort
is being poured into examination of the concept and testing
of intelligence, a word that gave both philosophers and lay
persons little trouble until the 20th century. The first
push was to refine and extend Binet1s school-ability test
battery, then to attack it with statistics and independent
variables so as to understand it better.
The second, and overlapping, push was to seek in
Piaget’s theory of the development of what he calls intel
ligence some less fractious concept and test for intelli
gence. Major programs to develop the desired objective
test battery have been undertaken since the early 1960s,
and are reported by Vinh-Bang (1959* cited in Inhelder,
19^3/1968); Laurendeau and Pinard (1962, 1970); Pinard and
Laurendeau (1970); Tuddenham (1970a, 1970b, 1971);
Warburton (1970); Vernon (1970); and many others. None has
been entirely satisfactory and each, as the standardization
process becomes more longitudinal, either finds or suggests
some variation from Piaget’s classical findings. One
should read the collections of essays edited by Elkind and
Flavell (1969); Dockrell (1970); and Green, Ford, and
6
Flamer (1971)- Fogelman (1970), Lavatelli (1970), and
Meyers, Ball, and Crutchfield (1973)3 among others, have
compiled Piagetian tests In usable form, but they lack the
standardization to provide norms.
The third attack on the Idea of Intelligence has been
progressing slowly but In the classical tradition of the
mind-body problem: we cannot really know if intelligence
is a genuine variable, or one or more real things^inside
the nervous system which can be measured or inferred better
than we can now. Hebb, since the early 1940s, and Luria,
until his recent death, have stayed closest to the body
end of the continuum of measurable links from anatomy to
physiology to psychophysics to cognitive psychology (Hebb,
19^9; Luria, 1973) in the effort to solve for good the
mind-body problem, about intelligence, at least.
The first of these approaches to understanding intel
ligence is now widely involved in breaking down the concept
by factor analysis (Dingman & Meyers, 1966; Guilford, 1967;
Meeker, 1969; Yoshida, Meyers, & Orpet, 1973; to name but
a few). Findings to date suggest that IQ-test factors are
relatively independent of Piaget-test factors, but the two
sets of factors are not inconsistent when the CA, MA, and
greatly variable behavior of the retarded subject are con
sidered. C. E. Meyers (1972) concluded that
Piagetian scaling . . . would have a more immediate
relation to educational programming than presently can
be secured from the essentially anomalous scores of
7
current measurement, which are interpreted only in
norms . . . [Y]ou will get a description of the
child’s state of coping ability having instant meaning
for him . . . .We’d have, in effect, criterion refer
enced measurement in mental development. (p. 15)
Significant Variables
The enormous difficulties in producing a true
Piagetian scale, and the possible loss of some of the wide
range of normative information available from current
tests, make it worthwhile to ask if Piaget's intelligence
is related to IQ-test intelligence by noting if such inde
pendent variables as sex, ethnicity (Anglo or Chicano),
socioeconomic status (SES), type of education program
(mainstreamed or segregated), CA, MA, and IQ affect the
variance in Piagetian conservation scores as they effect
the variance in IQ scores. Certainly, there are other
factors that could also be used--time in present class,
existence of stable IQ scores, assurance of good mental and
physical health, et cetera. The seven listed variables
were selected because they were typical of the factors
pointed to with heat during disagreements between parents
and school districts as to educational policy regarding
developmentally disabled children. People believe they
affect intelligence-test scores, and considerable research
supports this belief.
Sex
Binet-type intelligence tests are constructed from
8
items selected to balance those items easier for boys with
those items easier for girls; thus no sex-related total
scores are demonstrable. Other nomothetic tests, such as
factor tests and tests derived from theoretical models (as
in Meeker, 1969)* have generally shown that girls show an
early superiority in tests based on language factors, while
boys excel in spatial abilities (Anastasi, 195*0.
Piagetian tests which have been standardized or extensively
replicated have not produced evidence that sex differences
are significant, possibly because so few mention this vari
able as being tested (Tuddenham, 1970a).
Ethnicity
The deprived status of the Spanish-surname, Latin-
American child in the U.S. has been well documented:
Wheatley (1975), Sitkei (1966), Sitkei and Meyers (1969),
Palomares and Johnson (1970), Satler (1970), Padilla and
Ruiz (1973), and De Avila and Havassy (1975), have studied
the interrelationship of IQ scores and ethnic background
of both subject and experimenter, of both SES and Anglo/
Chicano status. Sitkei (1966) extended the dependent vari
able from one IQ score to a pattern of scores by using
Block, Levine, and McNemar’s (1951) useful statistics for
pattern evaluation. The same pattern analysis that aided
Sitkei (1966) also aided Lesser, Fifer, and Clark (1965)
and Stodolsky and Lesser (1967) in establishing the sig
nificance of different profiles of ability between several
9
"racial" groups, using nomothetic group tests.
Mercer’s (1973b) well-conceived and extensively docu
mented soci’ opsychological assessment of mental retardation,
however, has amply demonstrated that effects of SES and
sociocultural background cannot successfully be separated,
even using individual tests, when the subjects have been
matched on at least five sociocultural factors (Mercer,
1973a). See Figure 1.
Cross-cultural research, using Piagetian tasks has
been difficult to compare because of lack of experimental
comparability and methodological problems. Generally, the
sequence of Piagetian stages has been supported, while the
speed of development and ultimate (adult) level of cogni
tion reached appear to vary with the sophistication and
complexity of the culture (Fogelman, 1970; Furby, 1971;
Ginsburg, 1972; Greenfield, 1966).
A study by Sharp (1972) of conservation tasks by nor
mals, and by Anglo, Chicano, and black retardates found no
significant effect of ethnic group, but "conservation tasks
are no more culture fair than the psychometric measures"
(p. 62), since his educable mentally retarded (EMR) chil
dren were "actually limited in their intellectual poten
tial" (p. 62).
Class Program
Developmentally disabled children were once commonly
kept at home or institutionalized. By the last century,
10
Mean » 89.0 Children With 3
Modal Characteristics
100 120 140 160 40 60 80
Mean * ■ 90.4
!i » 598
Distribution With No
Control for Socio
cultural Factors
40 60 80 100 120 140 160
Mean " 95.5
N - 174
Children With 4
Modal Characteristics
100 120 140 160 60 40 80
Children With 0 or 1
Modal Characteristic
40 60 80 100 120 140 160
Mean m 104.4
Children With 5
Modal Characteristics
60 80 100 120 140 160
Children With 2
Modal Characteristics
Mean » 88.1
’ N - 146
80 60 40 100 120 140 160
Figure 1. Convergence of the Mean IQ Test Scores of Chicano Children with the
Standard Norms As Sociocultural Factors Are Increasingly Controlled
Source: Reprinted by permission of Dr. Jane R. Mercer, University of California, Riverside, Calif.
H
special education was being developed for them, and by the
1920s, public-school classes began to be available (Ellis,
1963; Kirk & Johnson, 1951; Robinson & Robinson, 1965).
Currently, there is great political pressure to provide
education for all who can be contained in regular classes.
This "mainstreaming" of the less than normally schoolable
child has not yet been evaluated, or even defined ade
quately in practice (MacMillan, Jones, & Meyers, 1976;
MacMillan & Semmel, 1977)* and there remains a good deal of
theoretical opposition to placing children with special
needs in nonspecial classes (Throne, 1975)- Evaluations to
date give variable results. The consensus is that main-
streaming, or some other way to avoid stigmatization of the
handicapped, is a good thing, but that we do not yet have
agreement on what practices constitute mainstreaming or on
how to do the evaluating or on how to separate behavioral
from ability problems (Gampel, Gottlieb, & Harrison, 197*0
Kaufman, Gottlieb, Agard, & Kukic, 1975; Lavatelli, 1970;
Wolinsky, 1970).
CA, MA, and IQ
Psychometric mental age and IQ have been shown to cor
relate at low levels with Piagetian task performance
(Horowitz, 1973a, 1973b), but the existence of attentional
perceptual and motivational factors, and of "basic temporal
governors" (Cardozo & Allen, 1975; Flavell, 1971; Furby,
197*0 may be obscuring any simple relation between time,
12
experience, and task scores. Most findings of Piagetian
researchers relate their results to chronological age; so
one would expect a correlation with CA to appear, with
mildly retarded children merely slower in following the
same sequences of concept achievement (Stephens, Manhaney,
& McLaughlin, 1972). Intercorrelations on conservation
tasks of MA with IQ and CA have shown various degrees of
association, depending on the number of tasks used, the
selection of subjects, and whether language is required in
responses (Fischer, 1977; McNary, 1977; McNary, Michael, &
Richards, 1973; and others).
13
II. ORGANIZATION OP THE PRESENT RESEARCH
Variables
Judgment, explanation, and total' scores on the
Goldschmid-Bentler Concept Assessment Kit— Conservation,
Form A (GBKC) were used as the dependent variable in this
study (Goldschmid & Bentler, 1968).
Seven independent variables were selected for evalua
tion because each has been asserted to have a significant
correlation with intelligence as measured by Binet-type
tests. They are IQ, MA, CA, sex, socioeconomic status
(SES), ethnicity (Latin-American or Anglo-American: Eth
nicity) and class placement (segregated, or partially or
wholly integrated into regular class: Program).
Efforts were made to select subjects similar to the
younger half of Inhelderrs (19^3/1968) study group in IQ,
MA, CA and sex. (See Appendix A.) On the other variables
there were no comparable data on Inhelder's group.
The IQ range used was 70-85, with the median at 8l, as
compared with InhelderTs similar median of 78 and 60-105
range. Her group of 75 included 20 rated "normal."
This 70-85 IQ range is increasingly significant to
American educators. Because of moot questions as to per
centage of children classifiable as mental retardates by
IQ and/or adaptive behavior, many states now use the Ameri
can Association on Mental Deficiency manual (Grossman,
1973) to forbid access to segregated classes for retardates
to all children who happen to get a score of 70 or above on
a standard individual IQ test. This often leads to serious
educational problems with the "slow learners" in this IQ
category, who cannot cope with regular classrooms but are
denied special help.
The median MA of the subjects of this study was 7-8,
with a range of 3-5 to 11-10, as established within 3 years
of the date of the experiment by a WISC, Binet, or Letter
test score.
Median CA of subjects fell at 10-1, with a range of
4-8 through 15-9. This is very close to Inhelder's 9-11
median CA. Her younger group's range is 7-8 to 11-11.
The effort to get equal comparison groups of boys and
girls resulted in 29 girls and 38 boys versus Inhelder's
32 girls and 43 boys. In each case the number of girls
was 74% of the number of boys, reflecting a predominance
of identified male slow learners as is usually found in
public schools and institutions (Luckey & Neman, 1976;
Mercer, 1973; Tarjan, Wright, Eyman, & Keeran, 1973).
The ethnicity variable has been dichotomized, and
refers to Chicano or Anglo. These groups were selected
because the school districts in which the study was made
have a changing population, now largely Caucasian, with
15
few Orientals, Indians or blacks, but do have 13-48% Latin-
origin residents. Criteria for labeling as Chicano in
cluded (a) Latin surname; (b) Spanish spoken by the child
or in the home; and (c) statement by the child or his
teacher that he considers himself to belong to a Latin cul
ture, usually Mexican in this area. Any two of these cri
teria were considered sufficient for purposes of this
study. Thus 40 Anglos and 28 Chicanos comprised the test
sample. The 4l% Chicano figure is within the actual popu
lation range but near the top.
SES was rated on a 6-point scale, using breadwinner’s
occupation, location of residence (census tract data), and
teacher’s opinion of educational level of parents. Only
7 children fell on the lowest level and 1 in the highest
three levels; so this category was usually treated dichoto-
mously as "middle" and "lower" SES, with 36 in the middle
class and 32 in the lower class.
The class placement variable is really a series of
categories of special classes, entry into which is not
always obviously related to its label. In accordance with
the actual practices in each school entered, the 4l pupils
classed as "integrated" were those in educationally handi
capped learning disability groups and supplementary educa
tion. These spent all or part of each day in regular
classrooms. The 27 pupils in truly segregated classes were
those labeled educable mentally retarded, aphasic, multiply
16
handicapped, multiply handicapped plus mild retardation,
or educationally handicapped self-contained class.
Selection of Subjects
Letters were sent to the superintendents of the 10
school districts (of 39 in the county) with the highest
Spanish-surname population. It was explained that the re
search would require testing pupils whose guidance files
showed recent individual IQ test scores between 70 and 85,
"slow learners", by current California standards; complete
confidentiality was guaranteed to pupils, schools, and
districts. Only 4 districts, 2 elementary, 1 union, and
1 unified, agreed to cooperate, and two of the four re
quired written parental permission for each child who might
be selected for study.
The remaining six districts either failed to answer
the letters or refused permission, mostly on the grounds
that any inquiries into the IQ, retardation or ethnic group
status of their pupils would be indiscreet in the present
climate of criticism of school practices.
This administrative reticence due to parental appre
hension probably ensured the presence of emotional, politi
cal and perhaps other pressures acting as uncontrolled
independent variables.
Other recognized but uncontrolled variables are likely
to be length of time in a special education class, percent
age of unidentified "slow learners" in regular classes, and
17
presence of enough evidence in child’s guidance folder to
identify him for this study.
Completely random selection of subjects from the guid
ance files of all children.of the appropriate age level who
had been individually tested was not possible. Ninety were
tested from those who met the following criteria: (a) ex
isting records of testing within the preceding 3 years on
the Binet3 WISC, WISC-R, or Leiter that yielded IQ scores
between 70 and 85; (b) obtained mental ages of 3 to 14;
(c) written permission on file, if required, to give this
test; (d) presence at school on the days the examiner was
there; (e) ability to demonstrate, as required in the GBKC,
a functional grasp of the concepts of more, less, bigger,
same; (f) were judged able to understand English, supple
mented, if necessary, by the somewhat limited Spanish of
the examiners; and (g) fitted the desired research pattern
of equality of sex, ethnic and SES groupings.
Of 90 protocols, 22 had to be discarded because of
insufficient identifying data, errors in test recording,
lack of cooperation by the child, or having been selected
without meeting all the requirements of the study. Those
chosen, in effect, exhausted the supply.
Extrapolations from this study may, therefore, be lim
ited to children in similar school districts, under similar
political and social pressures, and using similar educa
tional practices with their slower-learning children.
18
Comparisons of results with those reported by Inhelder
(1943/1968) should be valid, however, insofar as findings
regarding the sequence and any fixation of conservation
levels are concerned.
Materials and Methods
The GBKC test was selected because, as far as was
known, it was then the only standardized test on the market
using Piagetian conservation tasks, and because it was ob
jective in both administration and scoring.
Form A contains six subtests: two-dimensional space;
number; sequence; continuous quantity; discontinuous quan
tity; and weight. The use of Form C would have added sub
tests on conservation of area and length, but these were
rejected as unlikely to enable the examiners to diagnose
formal operational thinking (Level IV) since the test
standardization data indicate that normal children with MAs
of 8 years cannot pass them at a high level.
Each test item on the GBKC provides a training proce
dure to ensure that the child reacts appropriately to the
words: same, more, less, and equal for that item. The two
test questions asked for each item (e.g., "Is this more or
less?" and "Why?") yield a verbal or nonverbal judgment
score of 0-6, a verbal explanation score of 0-6, and a
total score of 0-12.
Although the test was standardized on normal 4-
through 8-year-olds, It was considered reasonable to use it
19
for low IQ children with a median MA of 7-8.
Each child was tested Individually with the GBKC at
his school by one of two testers, the author and an experi
enced school psychologist familiar with the county in which
the research was done. Approximately a month was spent
working together to ensure as near identical methods of
giving the test as possible. Prior to testing, each child
was interviewed to establish rapport and to obtain infor
mation necessary for the independent-variable categories
being examined. Each child either demonstrated, prior to
testing, that he had the concepts "equal,T T "different,"
"more," and "less," or he was taught them before he could
be tested. All scoring was done by the author from ver
batim protocols.
Statistical treatment of the data involved a limited
factorial pattern. It was to have included three-way
analysis of variance (ANOVA) of the seven independent vari
ables taken three at a time, but this proved impossible;
there were too many cells with no or too few entries; and
standard deviations were not matched well enough to satisfy
ANOVA assumptions.
ANOVA handling of the dichotomized independent vari
ables two at a time was then done, with more valid results.
(See Appendix B for detailed results.) In addition, multi
ple regression was then used to reexamine the original data
for evidence of relationships among the independent
20
variables which might have been missed by analysis of vari
ance (Kirk, 1968; Smillie, 1966). Stepwise multiple re
gression computation was expected to yield artificially
higher correlations for predicting conservation scores from
independent background variables than were obtained from
simple intercorrelations of all the variables, since the
number of subjects was less than 100 (Guilford, 1965).
The unexpectedly few variables for which the null
hypothesis could be rejected were then scanned visually,
and data were checked by desk computer.
Scope and Limits
Making arrangements with superintendents, principals,
parents, and teachers, then searching files, testing, and
scoring took about 8 months. A major deficiency in this
study was in additional time to increase the number of sub
jects to over 100. Statistical inference would then have
been more reliable.
Increasing the mental age range and including the
Goldschmid-Benter Form C would have permitted a more accu
rate picture of the growth of the concepts of conservation
at a more advanced level, e.g., area, which is usually
achieved by normals after age 11.
Assuming InhelderTs (19^3/1968) description of a re
tardate as one who "is able to think by concrete opera
tions, but not by formal operations" (p. 2 9*0* and assuming
that for the 4- to 8-year mental age level, the GBKC Form A
21
provides a reliable estimate of conservation level, then
one would expect to find evidence of conservation of two-
dimensional space, substance, and continuous and discon
tinuous quantity, but not of weight. Since the published
reliability coefficients (Goldschmid & Bentler, 1968) were
equaled in the current study, the choice of this test
should not be considered a limiting factor, provided gener
alizations are made only about conservation, not other cog
nitive schema.
Selection of subjects was as rigorous as possible both
for getting matched groups and for replicating Inhelder’s
group. Testing was done with great care for the GBKC
rules. Scoring would have been better cross checked by
another person, but it was at least all done by one scorer.
Spanish versus English language did not provide any prob
lems .
In general, the scope of the data is almost adequate
to make valid conclusions about most of the independent
variables and about the hypotheses, and to test Inhelder’s
statement about retardates.
Ideally, true conclusions about a developmental se
quence such as conservation concepts requires a longitudi
nal study, some of which have already been launched
(Heber & Garber, 1971; Laurendeau &'Pinard, 1970; Vinh-
Bang, cited in Inhelder, 19^3/1968; Watson, 197^; and
others).
22
Hypotheses
Null hypotheses for this study were stated as follows:
: No significant intercorrelations among the inde
pendent variables will be found. That is, none will be
above .25, approaching a predictive ability of more than 1%
(Isaac & Michael, 1971). Although ethnicity and SES have
been found Interrelated In many studies, as has sex, class
placement has produced variable effects. It was predicted
that the attempt to equalize numbers of cases In each of
these categories, plus the limited CA and IQ ranges used,
would be reflected In small, If any, Intercorrelations.
2
Hq: There will be no difference between Intercorre
lations of the independent along with the dependent vari
ables If they are computed with dichotomous data or with
continuous data used where possible (e.g., CA, MA, IQ, SES,
program category and GBKC scores continuous; and sex and
ethnicity necessarily dichotomous). This was predicted to
be not supported, since the wider ranges of continuous data
usually provide larger correlations than do two-choice
scores.
H : No significant main effects or interaction
o °
effects of any pair of Independent variables will be found.
The weight of cross-cultural Piagetian studies would
lead to a prediction that would not be supported, since
many show that minority or Immigrant or rural children get
lower conservation scores than do their opposites (GInsburg
23
& Opper, 1969; Green, Ford, & Flamer, 1971; Modgil &
Modgil, 1976). Other studies, Including one by Frankel
(1969) done in the same districts as was the present study,
and Mercer’s (1973a) summary of her pioneering pluralistic
approach, suggest that this hypothesis would be supported.
4
Hq: No multiple correlations derived by stepwise re
gression methods will be found to have predictive values
above 1% (R, 9 > + .30). Even if were to be
supported, it is still possible for several variables,
taken together, to yield higher predictive values; hence
this hypothesis was expected to fail (Guilford, 1965)-
: No children in the 70-80 IQ range ("dull”) will
achieve top scores (11 or 12) on the GBKC, and no children
in the 8O-85 IQ range ("slow learner”) will achieve very
low scores (0 or 1) on the GBKC. Inhelder’s findings
(19^3/1968; also Vinh-Bang, as cited by Piaget & Inhelder,
1962; and others) led to a prediction that would be sup-
ported--that children in the MA range represented here
would be fixated at Level III thinking.
5
If Hq is not supported, a doubt arises that relatively
short objective tests for Piagetian developmental level
will be reliable enough to warrant further efforts to de
velop such tests for slow-learner use (cf. Tuddenham,
1971)3 since conservation is a much-studied concept in cog
nitive development and seems to provide a sequence of age
levels for different types of conservation that covers the
24
whole of the traditional development period (2-16 years)
for intelligence (Fogelman, 1970). Also, the question of
whether fixation at concrete levels has occurred is
likely to become moot, contrary to current majority— and
Inhelder's--opinion about retarded or "developmentally dis
abled" children.
1 4
If Hq and Hq are supported, one must question whether
Piagetian stages of intellectual development represent the
same intermediate variable or variables, loosely called
intelligence, as we assume in nomothetic (psychometric)
theories and tests of intelligence, since variables long
recognized as affecting IQ test scores would not be affect
ing conservation acquisition.
2
If Hq is found to be supported, future studies can be
made half as laborious by omitting either continuous or
dichotomous variables from computations.
If is supported, perhaps some of the experimental
fishing expeditions may be foregone and attention centered
more on critical experiments and their replications. If
it is not supported, more reliance may be placed on multi
ple Rs, and we will know better how to control for related
variables. This hypothesis also serves as a partial rep
lication of studies of ethnicity, SES, sex, and program
effects, using subjects comparable to Inhelder's retar
dates .
The minimum probability of rejecting the null
25
hypothesis when it is right (a) was set at .05
26
III. RESULTS
Figure 2 provides a clear visual comparison of the
number of subjects making correct judgments on the six con
servation subtests of the GBKC (at the six possible score
levels) with the number of subjects giving explanations
considered at least Piaget Level II in quality, and with
the number of subjects achieving at each scoring level
(0-12) .
The total scores show a bimodal distribution, and ex
amination of the individual subject scores shows that no
subject got an explanation score higher than his judgment
score. The explanation score progresses downward fairly
regularly, with six subjects getting all of the explana
tions right. The judgment scores progress down from 10
cases at the 4 level, then soar to where 21 subjects get
all six judgments right.
Combining these scores to make the total-score figure
accounts for the latter’s bimodality and reflects an unex
pected marked support for Martin (1975)9 who found signifi
cant scoring differences depending on verbal response cri
teria versus nonverbal, and for Thorne (1975) and Wisener
(1975). Inhelder, Bovet, Sinclair, and Smock (1966)
claimed that "our evidence offers little, if any, support
27
20
12
12
10 10
10
10 12
GBKC Explanation Score GBKC Total Score GBKC Judgment Score
Figure 2. Distribution of GBKC Partial and.Total Scores
PO
co
for the contention that language learning per se contrib
utes to the integration and coordination of ’informational
units’ necessary for the achievement of conservation con
cepts” (p. 164). Yet in 1971, Inhelder felt it ’ ’highly
probable” that relation of performance and competence is
not exactly the same with her slow group as with others.
The evidence of this study would suggest that children
may understand a concept before they can explain it.
H^, the hypothesis predicting no significant inter
correlations among the independent variables, was not en
tirely supported if we use Isaac and Michael’s (1971) table
of levels of significance of r for variable df. This rates
as significant the low (c. + .35) correlations seen in
Tables 1 and 2 between program and SES, program and IQ,
ethnicity and sex, and ethnicity and MA. The correlations
between IQ and the dependent variables, MA and the depend
ent variables, and CA and the dependent variables were
higher than expected, but consistent with a common-
intelligence theory. Compared to other research the corre
lations between CA and MA appeared unusually high. The
GBKC score intercorrelations were high, but consistent
with Goldschmid and Bentler’s (1968) own findings.
The only interesting correlations are the positive one
between program and SES, and the negative one between pro
gram and IQ, which together suggest that selection for
segregated classes favors the higher-SES and the lower-IQ
29
Table 1
Intercorrelations of All Dependent and Independent Variables
(Taken As
Variable SES Eth. CA Sex
Program' 0.31 0.18 0.21 -0.03
SES -0.06 0.13 -0.03
Eth. 0.25 -0.30
CA 0.16
Sex
IQ
MA.
Judg.
Expl.
Continuous)
IQ MA Judg. Expl. Total
-O.36 0.11 -0.14 -0.10 -0.13
-0.15 0.13 -0.15 -0.23 -0.20
0.08 0.29
0.12 0.06 0.10
-0.06 O.96 0.46 0.42 0.46
-0.15 0.13 -o.o4 -o.o4 * -0.04
0.19
0.33
0.31 0.34
0*53
0.48
0.53
0.82 O.96
0.95
00
o
Table 2
Intercorrelations of All Dependent and Independent Variables
(Taken As Dichotomous Variables)
Variable SES
Eth.
CA Sex IQ MA Judg. Expl. Total
Program 0..^ 0.18 0.15 -0.03 -0A 3 O.lk -0.1^ -0.10 -0.13
SES -0.11 0.18 0.10 -0.20 0.18 -O.Oil- -0.11 -0.08
Eth.
0.2^ -0.3 0 0.08 0.17 0.12 0.06 0.10
. CA 0.21 -0.15
0.77
0A 5
O.39
0.A4
Sex 0.00 0.14 ~O.0k -O.Oif -0.04
IQ
0.09 0.27 0.26 0.28
MA O.kl 0 M O M
Judg. 0.82 O.96
Expl.
0.95
oo
H
■ » v
t ,
children. The same phenomenon appears in Figure 3 S and may
reflect the desire of higher-SES parents to get for their
children more individual attention and small classes, while
the lower-SES parents prefer anonymity over the high-
priced, segregated programs.
2
H , the hypothesis that dichotomizing the data from
this study for statistical purposes will not make any dif
ference, is apparently supported, as can be seen by inspec
tion of Table 1 and Appendix C, which consists of tables
paired for comparison. Continuous data yield slightly
higher correlations in some cases, but the range of SES and
program scores can be only slightly increased by using con
tinuous data; the dependent variables and IQ have a very
limited range by the conditions of the study, and CA and MA
are the only variables which can spread out and affect r
to any important extent.
3
H , the hypothesis of no significant ANOVA main or
interaction effects, is supported for all variables except
MA, CA, and IQ, and excepting one interaction effect which
is barely strong enough to meet the a <_ . 05 requirement for
rejecting the hypothesis. (See program versus SES.)
Appendix B contains the summaries of all 2 X 2 ANOVAs
that were done. It can be seen from Table 3 that, of
these, SES, sex, ethnicity, and program showed no siginifi-
cant main effects on the variances; only MA, IQ, and CA
were effective. A borderline interaction effect was
32
Mean GBKC Explanation Score
3.00-
2.75-
2.50-
2.25-
2.00-
1.75
1.50-
1.25-
1,00-
Middle
SES Group
Low SES Group
— 1 -
Integrated
Program
1 -----
Segregated
Program
Figure 3. Demonstration of Interaction Effects of
Program vs. SES on Explanation Scores
33
Table 3
Summary of All Two-way Analyses of Variance Found to Be Significant
at 01 < .05 (Variables Dichotomized)
Independent
Variables
Dependent Variables
Judgment Explanation Total
SES vs. MA** MA** MA**
vs. IQ* IQ*
vs. CA ** CA** CA**
Sex vs. MA** MA** MA**
vs. IQ* IQ* IQ*
vs. CA** CA** CA**
Eth. vs. MA** MA** MA**
vs. IQ* IQ* IQ*
vs. CA** CA** CA**
Prog. vs.
vs.
MA** MA** MA**
IQ*
vs. CA** CA**
SES* (Inter
action
only)
CA**
Note.* In none of these comparisons were SES, Sex, Ethnicity, or
Program variables shown to have significant.main effect on the
variances.
*a < .05.
**a < .01.
34
obtained for the program versus SES comparison, confirming
the evidence of the correlations between SES and program in
Tables 1 and 2.
In Table 4 the significant ANOVA main effects of the
critical MA, IQ, and CA on the three dependent variables
are seen not to include the MA versus CA for judgment or
total GBKC scores, while the MA versus CA for explanation
score gives only an MA main effect. Figure 4 displays
these relationships in scattergram form.
These results provide support for the findings of
Vinh-Bang, as cited by Piaget and Inhelder (1962), Boland
(1973)3 Brekke and Williams (1975)3 Stephens (1977)3 and
De Avila, Havassy, and Pascual-Leone (1976) in that vari
ables affecting conservation scores appear to be only those
related to maturation and intelligence (in both the psycho
metric and developmental senses of the word). These re
sults also fail to support Goldschmid’s (1967) conclusion
that SES may be significant within a culture; or Goldstein,
Moss, and Jordan’s (1965) finding that retardates do better
in a segregated program; or Beard (1964) and Nye (1969) on
the existence of significant sex effects.
4
H , hypothesizing that the independent variables,
applied in successively larger groups, will show no sig
nificant ability to predict the GBKC scores, is supported
for CA, sex, ethnicity, and program, as can be seen in
Tables 55 6, and 7. That MA and IQ account for most of the
35
CD
J i
O
O
CO
rH
a 3
-p
o
O
W
PQ
12
-
11
-
10
-
9 -
8 -
7 -
6 -
5
-
4
5 -
2
1 -
0
o = IQ 70-75
® = IQ 76-80
• = IQ 81-85
6
0
• •
0
o# o
9 0 0 0O 0
0
# ##000
o • ##
o
jTmrr \ 9 >TTTj^* , ~ n T ri'(ir|' (T h tttti ft jfi? 1 m 1 rn | , Tinn 1 n i 11 ^ 11111 ,rn't|»
J
" mri nTii T
11 12
Mental Age (Years)
uo
Figure 4. Distribution of GBCK Total Scores by Mental Age with Individual IQs Noted
Table 4
Summary of Significant ANOVA Effects among the Critical Variables
of CA, MA, and IQ (Variables Dichotomized)
Dependent Variables
Judgment Explanation Total
MA* vs. CA
MA** vs. IQ* MA** vs. IQ* MA** vs. IQ*
CA** vs. IQ** CA** vs. IQ** CA** vs. IQ**
Note. No interaction effects -were found to be significant among
these three variables.
*£ = <_ .05.
= _! •01*
Table 5
Intercorrelations of CA, MA, and IQ, with Dichotomous and
"Continuous" Data Compared
Tnrl
GBKC Scores
HiU.9
Data Var. CA MA IQ Judg. Expl. Total
CA 1.00 .77 -.15 .45 .39 .44
Dichotomous MA .09 .41 .Mi- A h
IQ .27 .26 .28
CA 1.00 .96 -.06 .46 .42 .46
"Continuous" MA .19 .53 • .48 .53
IQ ,-33 .31 .34
37
Table 6
Multiple Regression Summary Table., "Continuous" Data
0 }
CD
i —I
irO
' *H
-p
< L >
Ti
3
0
ft
C D
Q
Independent
Variables Step
Multiple
R
B?
Change
in R2
Simple
R
MA. 1
•53
.28 .28
•53
-P
IQ
2
• 58 • 3^
.05
•33
1 ^
Sh O
SES
3
.61
•37 .03 -.15
§ CD Sex 4 .61
• 39
.01 -.04
• “3
Ethnicity
5
.62
•39
.01 .12
Program 6 .62
•39
.00 -.14
p j
m 1 .48
•23 •23
.48
o
• r l
SES 2 .56
• 31 .09 - . 2 3
-P C D
ccJ ! h
« o IQ 3 • 59 •34 .03 •31
o 3 O
r —i CQ
S’
Ethnicity 4 .60 .36 .01 .06
w
Sex
5
.61
•37
.02 -.04
0
MA l
• 53
.28 .28
• 53
o
o
SES 2
• 59 • 35 .07
- .2 0
CQ
i—1
IQ 3
.62
• 39
.04
• 3^
ctJ
-P
o
Ethnicity 4
.63
.40 .01 .10
EH
Sex 5
.64 .41 .02
0
1
Note * Independent variables affecting R_ beyond the second decimal
place were omitted, though usually statistically significant.
38
Table 7
Multiple Regression Summary Table, Dichotomous Data
c n
O
i — 1
&
c t f
# 1 _1
* 1 1
1 h
>
_p
S
el i
Tj
S m
0
ft
e l i
Tj
S m
H
Independent
Variables Step
Multiple
R R2
Change
in r2
Simple
R
0
! h
O
CA 1
M
.20 .20
■ ^5
O
CO
IQ 2
• 57
.32 .12
.27
-P
S m
0
Sex 3 .59
.3k .02 -.oU
H I )
Ethnicity k .59 .35
.01 .12
Program
5
.60 .36 .00 -.lU
0
! h
o
MA 1 .kk .19 .19 .kk
O
m
IQ 2
.k9
,2k .05 .26
s
o
•H
CA
3 • 52 .27
.02
.39
3
SES k • 5U .29
.02 -.11
■A
Sex 5 • 55
.30 . 01 -.OU
&
Ethnicity 6
.57
.32 .02 -.06
MA 1 .kk .20 .20 .kk
0
! h
IQ
2
• 51
.26 .06 .28
O
o
CO
CA
3 .56 .32 .06 .kk
i—1
c t f
Sex k .53 .3k .02 -.ob
-P
O
Eh
Ethnicity 5 .59 .35
.01 .10
SES 6 .60 .36 .01 .08
Note. Independent variables affecting the multiple correlation (R)
beyond the second decimal place were omitted, though usually statis
tically significant.
39
variance change as the stepwise regression procedure is
applied is not now surprising. SES, however, appears to be
a significant variable in predicting all three GBKC scores,
when taken together with MA and IQ in a multiple correla
tion. Dichotomous data give slightly different results.
This finding is the only one In this study so far
which is supportive of the idea that psychometric and de
velopmental "Intelligence" scores In slow learners might be
shown to have significant Independent variables In common—
IQ score and socioeconomic status in this case. Since the
Interrelations of CA, MA, and IQ are so devious, however
(see Table 5)* it Is not profitable to speculate from these
data as to what might be the meaning of the obtained inter
correlations , or as to what might have happened had CA,
Instead of MA, been Inserted as the second or third vari
able In computing the Rs for continuous data.
5
H^, the hypothesis that fixation of conservation con
cepts at pre-formal-operations levels in this partial rep
lication of Inhelder's (1943/1968) study will not be demon
strable from the obtained data, appears supported. In
Figure 4, inspection of the MA levels represented at GBKC
scores of 0, 1, or 2 shows that l4 children with below-the-
median IQ scores apparently do not have conservation, while
six children with IQs above the median, and MAs up to
10-1/2 years also failed to achieve conservation. (The
criterion here is taken from Goldschmid & Bentler, 1968.)
40
At the high achieving end, we find nine children with IQs
above the median and six below scoring 10, 11, or 12, and
apparently having mastered conservation up through weight.
There is some thinning out of low-IQ subjects at the top-
scoring edge of the scattergram, but the expectation of
continuing development of these subjects, all of whom would
be educationally classified slow learners today (EMRs 5 or
10 years ago), is fully warranted.
Figures 5, 6, and 7 show, respectively, GBKC judgment
scores, explanation scores, and total scores by IQ, with
each subject identified as to ethnicity, SES, and program.
The most obvious trend is again the clustering of perfect
judgment scores along nearly, the whole IQ dimension, while
the clustering in Figure 6 (explanation scores) is toward
the bottom half of the distribution and equally spread out
in IQ. The total-score distribution appears saved from
complete diffusion by a cluster of mostly segregated chil
dren who are low on the IQ scale and show no evidence of
conservation.
Hand computation of the 21 perfect judgment scores in-
dicates complete support for the findings via analysis
of variance: almost exactly equal percentages of Chicanos
and Anglos, integrated and segregated pupils, and boys and
girls were able to score a 6; 36% of the middle SES group
and only 25% of the low SES group had operational conserva
tion; while imbalance showed in high versus low IQ (42%
41
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TO 1 2 3 4 75 6 T 8 9 80 1 2 3 h 85
IQ
LEGEND: Lower case letter: lower SES
Upper case letter: middle SES
0 = segregated class
C = Chicano (N = 28)
A = Anglo (N = h0)
Figure 5* Scattergram of GBKC Judgment Scores by IQ, Showing
Ethnicity, SES, and Program for Each Subject
42
Explanation Score
6 1
a A © a
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a
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TO 1 2 3 k 75 6 T 8 9 80 1 2 3 1 * 85
IQ
LEGEND: Lower case letter: lower SES
Upper case letter: middle SES
segregated class'
C = Chicano (N = 28)
A = Anglo (N = ho)
Figure 6. Scattergram of GBKC Explanation Scores by IQ,
Showing Ethnicity, SES, and Program for Each
Subject
43
12
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10
9
8
0
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TO 1 2 3 M 5 6 T 8 9 8 0 1 2 3 4 85
LEGEND: 0 = segregated class
a = lower class Anglo
A = middle class Anglo
c = lower class Chicano
C = middle class Chicano
c
Note. Median IQ is between 80 and 8l.
Figure 7. Scattergram of GBKC Total Scores by IQ, Showing
Ethnicity, SES, and Program for Each Subject
44
versus 20%), old versus young MA (53% versus 11%), and old
versus young CA (49% versus 12%).
Appendix A was examined with regard to the 19% of sub
jects who demonstrated conservation of weight to the extent
of passing that subtest In the GBKC. Only 1 of 11 errors
made by high total scores (10, 11, or 12) was on the weight
subtest. The 19% Is consonant with the findings of Brekke
and Williams (1975) and of Inhelder (1943/1968), but does
not support the Idea that weight conservation Is Inherently
more difficult than are conservation of substance, length,
and number, which are also listed by Piagetian theory as
being achieved during the concrete operations period.
Thus, the findings of this study join the hundreds of
Piaget-related efforts to clarify the nature and sequence
of learning conservation concepts In "slow learners" (as
defined currently In the AAMD manual; see Grossman, 1973)
and "mental retardates" (as presented In InhelderTs 1943/
1968 study).
It should finally be noted that the GBKC total conser
vation scores clustered at 7 years and at 10 years In terms
of mental age, milestones which would be expected from nor
mal children at those CAs rather than from developmentally
disabled children with those MAs.
45
IV. DISCUSSION
Current findings, in general, differ from many similar
investigations but support others. They find children with
IQs between 70 and 85 reaching conservations levels suit
able more to their MAs than did Inhelder. They do not
offer sufficient evidence to label low scorers on the GBKC
as cognitively fixated. They do suggest the existence of a
few commonalities between Binet intelligence and Piaget
intelligence.
Fixation
InhelderTs (1943/1968) group of subjects had a re
ported median IQ of 78 (for the youngest 75, matched on
number, IQ, age, and sex to the subjects of the present
study). However, inspection of her list of cases yields an
extraordinary range of class placements and behavior prob
lems. Also to be noted is that a cognitive level of II,
not oscillating or fixated, is labeled as normal in reason
ing, despite an IQ below 80, while an 11-year-old, fixated
at Level II, is labeled as a slow learner, despite his IQ
of 92. This highly subjective evaluation would appear to
be circular: if fixated in his handling of Piagetian
tasks, he is retarded; if retarded, he is either fixated or
suffering from oscillation, retrogression, decalage or some
46
other abnormality of problem solving.
From the evidence of this study, admittedly limited by
the MA range of the standardized Piagetian battery of con
servation tests used (the GBKC), we have seen that already
31$ of the subjects understood all the subtests correctly
(passed all judgment items), and presumably will continue
to grow in their cognitive skills. The fact that they are
now labeled with the special education "tar brush"
(Edgerton, 1967) is not necessarily going to keep them from
functioning 5 or 10 years from now just as other adults do.
Lovell (1971) and Arlin (1976), among many others, have
pointed out that Level IV--formal operational thought— is
rare even with IQs above 140, and probably only half the
adult population ever attains that level. There may even
be levels beyond IV attained by a select few (Riegel,
1973). A person is cognitively fixated until he moves up a
level, and thus he cannot truly be labeled until he is
grown and settled into a life pattern.
Intelligence As Intermediate Variable
For the convenience of educators and parents, and in
line with age-old tradition, it may be assumed that both
psychometric and developmental theorists are talking about
something real when they distinguish fast from slow learn
ers. We may expect that sooner or later men like Luria
(1973) may be able to tell us more than that left temporal-
47
lobe lesions affect audio-verbal memory; left parieto
occipital areas control space and number syntheses; and
that inability to "see the problem" is associated with
frontal-lobe trouble. Meanwhile we must make do with nomo
thetic (psychometric) tests that were so constructed as to
yield a Gaussian distribution (Morrison, 1975) and thereby
lead us into believing that whatever is being tested is
relevant to individual assessment, which requires basically
idiopathic (developmental or clinical) data (Elkind, 1974;
Throne, 1972).
Prom the ANOVA and regression analysis data of this
study, we may tentatively conclude (prior to a longitudinal
study) that psychometric and developmental test batteries
probably overlap but are not coterminous. Even at present,
Mercer can say with some confidence:
For every child it is possible to determine, on the
basis of the information gained from the mother about
the family background, what the average IQ would be
for a child from precisely his background. (Cited in
Soeffing, 1975, p. 114)
This study showed that IQ does in fact correlate with the
development of conservation. Hence it is concluded that
they at least have something in common.
Use of IQ and Conservation Tests to Classify
While each of the dimensions of the definition of men-
tar retardation has specific dangers associated with
it, there is one danger more pervasive than the rest.
That is the reification, or attribution of existence
to a fictional entity. Considering the present state
of understanding, mental retardation is a fictional
48
construction, and one definition is potentially as
good as the next. (Detterman, 197^3 p. 28)
Bosma (1973) and Fischer (1974) have gone so far as to
propose a moratorium on IQ testing for special-class place
ment, a step which has been taken already in California.
Haywood (1971) and Riscolla (197*0 prefer the use of
achievement, personality, and clinical tests to either
Piagetian or Binet-type tests for EMR identification, and
Kolstoe (1971) wrote:
Until such time as test developers are able to provide
an instrument which combines the virtues of the Piaget
levels and the IQ distribution, the accurate detection
of mental retardation must wait until the child grows
up. (p. 94)
Limitations and Recommendations
The primary limitation on this research has' been its
cross-sectional design. A longitudinal study is the. most
illuminating way to learn about a developmental process
like the growth of intelligence,,as was made clear by Fels,
by Terman, and others. Sharp’s 1972 study also stressed
this point.
Agreement among researchers as to definitions and cri
teria for mental retardation is also lacking in this study
(Luckey & Neman, 1976), along with objective test proce
dures, replicable experimental designs (Hoffman, 1974), and
opening up the concept of intelligence to include the pos
sibility that it may not be strictly cumulative and incre
mental (Bower, 1976); that it may not develop synchronously
49
in all areas (Siegel, 1977); that it is undoubtedly quali
tatively different along the bright-to-dull and age dimen
sions (Coker, 1976; Nivette, 1971); and that it may be much
more variable than has been assumed (Hunt, 1969)*
The next step in the current study should be to in
crease the number of subjects to provide at least 30 in
each dichotomized variable category, to extend the MA range
to 15 years, and to use Form C of the GBKC, plus some of
the Berkeley area and volume tests (Tuddenham, 1970a,
1970b).
Now that sex, ethnicity, SES, and program can be at
least theoretically fairly well controlled, it would be
helpful to ask again if EMR pupils suffer from fixation or
from a slow-down in the development of cognitive abilities.
Finally, replication of the identical test format
should be requested by other researchers so as to get com
parable data on the dimensions being tested, whatever they
may be.
50
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51
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63
APPENDIXES
64
APPENDIX A
LIST OF INDIVIDUAL SUBJECTS, TEST SCORES,
AND RELEVANT DATA
65
Table 8
List of Individual Subjects, Test Scores, and Relevant Data3 ,
Case Ho,
&
Ethnic
Background SEX PROGRAM SES
GA
(Yr.-Mo.)
MA
(Yr.-Mo.)
IQ
GBK-C Test Sc:ores
JUDG. EXPL. TOTAL
Anglo-1 M Seg-AFH UL 6 -1 4-9 73 0 0 0
Anglo-2 M Int-SupEd UM 8 -0
5-7
70 0 0 0
Anglo-3 M Int-SupEd UL 8-5
7-1 85 6 6 12
Anglo-4 M Seg-MH UL 9-6 6 -2 72 0 0 0
Anglo-5 M Int-EHLD UL 9-6 . 7 -6 82
5
4
9
Anglo-6 M Int-SupEd UL 9-8 7-4
77
2 2 4
Anglo-7 M Int-SupEd LL 10 -10 6-1 1.
77
4
3 7
Anglo-8 M Int-EHLD •LM 11-9 9-0 74 6
C .
J
11
Anglo-9 M
Seg-AFH LM 1 2-2
9-3 76 6 6 12
Anglo-10 F Int-SupEd LM 1 2 -11 9-0 70 0 0 0
Anglo-11 F Seg-MH LM 6 -7 4-8
71
0 0 0
Anglo-12 F Int-EHT I) LL 1 1 -8
9-5 81
5 4
9
Anglo-13 F . Int-SupEd UL 1 2 -8 10-5 82 1 7 1 2
Anglo-l4 F Seg-MH LM 1 0 -1 8 -2 81 0 0 0
Anglo-15 F Int-EHLD LM 9-0 6 -9 75
2 1
3
Anglo-l6 F Int-EHT ,D LM 11-10 9-8 83 6
3 9
Anglo-17 F Int-EHLD UL 1 2 -7 9 -10 78 6
5
11
Anglo-l8 F Seg-EMR LM 14-1 10-0
71
2 l
3
Anglo-19 F Seg-EMR LL
13-7 9 -6 70 6
5
11
Anglo-20 F Seg-EMR LM i4-o 1 0 -6 .
75
6 6 12
Anglo-21 F Seg-EMR LM 1 2 -8 10-2 80 6
3 9
Anglo-22 F Int-EHLD LM 6 -8 5-6
83
1 1 2
Anglo-23 F Int-EHLD UL 8-4
7-1 85
2
0 2
Anglo-2k M Int-EHLD LM
9-5 7-8 81 5
1
6
Anglo-25 F . Int-EHLD UL 8 -6
7-3 85
1 1 2
Anglo-26 M Int-EHLD LM 7-6 5 -11 79 3
0
3
Anglo-27 F Int-EHLD •UL 8 -1 6 -8
83 3
1 4
Anglo-28 F ■ Int-EHLD LM
9-1 7-6 83
2 0 2
Anglo-29 M Int-EHLD LM 6 -1 4-10 80 0 0 0
Anglo-30 M Int-EHLD LL
6-7 5-6 84 2 2 4
Anglo-31 M Int-EHLD LM 6 -1 0 5-8
83
4 2 6
Anglo-32 M Int-EHLD UL 7-10 6-4 81
5 5
10
Anglo-33
F Int-EHLD LL 8 -8 6 -1 1 81 6 O 12
Anglo-34 i ‘ ‘ Seg-EMR LM 12-5 74
j
1
3
Anglo-35
F Int-EHLD LM 7-6 5 -8 76
2 1
- L .
3
Anglo-3 6 M Int-EHLD LM 8-5 6 -1 0 81 6
3 9
Anglo-3 7 M Seg-EMR LM 1 2-6 1. 0 -0 80
5 4
9
Anglo-3 8 F Seg-EMR LM 1 1 -8 8-2 70 0 0 0
Anglo-39 F Int-EHT,D LM 11-9 9-5
82 6 6 12
Anglo—40 M Seg-MH UL 4-8
3-5 73 3
0
3
Mex. Bkg.-l M Int-EHLD UL 8-4 6 -1 0 82 2 2 4
Mex. Bkg.-2 M Seg-APH LM 8-6
7 -1
84 1 1 2
Mex. Bkg. -3 M Int-EHLD UL 8-8 6 -1
71
0 0 0
Mex. Bkg.-4 M Int-EHLD UL
9-H 8-2 82
3
7 .
6
Mex. Bkg.-5 M Seg-APH III 10-7 7-10 74
3 2
5
Mex. Bkg.-6 M Int-SupEd UL 12-0 10-2 85 2 2 A
Mex. Bkg.-7 M .Seg-MH LM 12-0
9-1 76 1 1 2
Mex. Bkg.-8 F Int-EHLD LL 12-0 10-2
85 ■ 6
5
11
Mex. Bkg.— 9 F Int-EHLD UL 11-10 9-10
83 5
4
9
Mex.. Bkg.-10
?
Int-EHLD UL 10-2
7-3 71
4 1
5
Mex. Bkg.-11 F Int-SupEd LL
7-7 5-8 74 4
3 7
Mex. Bkg.-12 M Seg-EMR LM
1 3 -7
10-5
77
6
3 9
Mex. Bkg.-13 M Seg-EMR LM 1 5 -9 11-10
75 5 3
8
Mex. Bkg.-l4 F Seg-EMR LM 12-6 1 0 -7
85 6
5 11
Max- Bkg.-15 M Seg-EMR' LM. 13-10 11-6
33
6 _ 6 12
Mex. Bkg.-16 M Int-EHLD ' LM 12-5 io-4
83
6
5
11
Mex. Bkg,-17 M Int-EHLD LM
13-9
1 1 -8
85 6 1
r 7
t
Mex. Bkg.-18 M Int-EHLD UL 1 0 -7 8 -1 1 84 • 6 4 10
Mex. Bkg.-19 F Seg-EMR LM
11-3 7-io
70 0 0 0
Mex. Bkg.-20 M Seg-EHDC UL 9-10
7-1 85
6
3 9
Mex. Bkg.-21 M Seg-EHDC UL 8-4
5-6 75
1 0 1
Mex. Bkg.-22 F Seg-EMR LM 10-3 7-4 72
5
1 6
Mex. Bkg.-23 M Seg-EHDC LM 8-8
7-1
80 1 1 2
Mex. Bkg.-24 M Seg-EMR UL 8 -9 6 -7 75
1 1 2
Mex. Bkg.-2p M Seg-EHDC LM 9-6 8-1
85 3
*
>
6
Mex. Bkg.-26 . M ■Int-EHLD UL 11-0 8-1 74 6
5
11
Mex. Bkg.-27 M Int-SupEd UL 1 0 -9 8-10 82 • 4 2 6
Mex. Bkg.-28 M Int-EHLD UL 14-6 11-10 81 6 2 8
Abbreviations: PROGRAM includes as "segregated class placement" multiply handicapped
(MH), aphasic (APR), educationally handicapped day class (EHDC), and educable mentally
retarded (EMR)j "integrated class placement" includes educationally handicapped learning
disability groups (EHLD) and supplementary educational groups (SupEd). Statistical treat
ment of socioeconomic status (SES) combines upper middle (UM) and lower middle (111) together
and combines upper lower (UL) and lover lower (LL) together.
APPENDIX B
SUMMARIES OP ANOVAS OP GBKC SCORES
67
Table 9
AUOVA of GBKC Judgment Score: Program by SES
Source SS df MS F a
Program 6.13 1 6.13 1.18 US
SES .007 1 O
O
—- J
.001
us
P X S
5.07
1
5.07 •97
us
Error
332.76 64
5.19
Total 344.63
67
5.14
SES
Program
Low
Middle
X 3.84
3.43
SD 1.90 2.44
U
25
16
X 2.42 3.25
SD 2.63 2.44
U
17
20
68
Table 10
ANOVA of GBKC Judgment Score: Program by Ethnicity
Source SS df MS F a
. Program 9.28 1 9.28 1.80 NS
Ethnicity
7^7
1
7-^7
1.^5 NS
P X E 1.66 1 1.66 .22 NS
Error 329.20 64 5.14
Total 344.63 67
5 .14
Ethnicity
Program
Anglo Chi cano
4.28 X
3.37
SD 2.16
1.93
N 27 3.4
2.84 X 3.21
SD 2.67
2.35
N
13-
Table 11
ANOVA of GBKC Judgment Score: Program by Sex
Source SS df MS
F
a
Program
6.93
1
6.93
1.32 NS
Sex .82 1 .82
.15 NS
P X S 1.05. 1 1.05 .20 NS
Error 335-96 6k 5.2^
Total 3M+.63
67
$.lk
Sex
Program
Male Female
X
3.87
3. M i -
SD
2.13
2.12
N
23
18
X 3.00
3.09
SD
2.33 2.77
N 16
- ' 11
70
Table 12
ANOVA of GBKC Judgment; Score: Program by IQ
Source SS df MS F a
Program
.23
1
.23
.04 NS
IQ
19.22 1 19.22
3.87 NS
P X I .94 1
• 9^ .19
NS
Error 317.66 64 4.96
Total 344.63
67
5.14
IQ
Program
Low High
X 2.78 4.14
SD 2.29
1.89
N 14
27
X 2.85 3.66
SD 2.43
2.73
N 21
6
71
Table 13
ANOVA of GBKC- Judgment Score: Program by MA
Source SS df MS F a
Program 13 .64 1 13.64 3.21 NS
MA 64.87 1
64.87
15.28 < .01
P X M I.29 1
1.29 .30 NS
Error 271.66 64 4.24
Total 344.63
67
5.14
MA
Program
Low
High
X 2.95 4.70
SD 1.92
1.99
N 14
17
X
1-75
4.06
SD 2-. 05 2.34
N 12
15
72
Table l4
ANOVA of GBKC Judgment Score: Program "by CA
Source SS df MS F a
Program 15.27
1
15.27
3.08 NS
CA 78.49 1 78.49
19.57
< .01
P X C 2.64 1 2.64 .66 NS
Error 256.69 64 4.01
Total 344.63
6?
5.14
CA
Program
Young Old
X 2.87 4.72
SD
1*93
I.90
N
23
18
X 1.45
4.12
SD 1.86 2.27
N 11 16
73
Table 15
ANOVA of GBKC Judgment Score: SES by Ethnicity
Source SS df MS F a
* SES
• 33
1 .44 .06
NS
Ethnicity 4.64 1 4.64 .87 NS
S X E
-37-
1
*37
.07 NS
Error 538*94 64
5*29
Total 34- 4- . 63
67
5.14
Low
SES
Middle
Ethnicity
Anglo Chicano
X
3*35 3*73
SD 2.17 2.12
N
17 15
X 3.08 3.76
SD 2.46
2.35
N
23 13
74
Table 16
ANOVA of GBKC Judgment Score: SES by Sex
Source SS df MS F a
SES • 54 1 • 54 .10. NS
Sex .56 1 .56 .11 NS
S X S
15-70
1
15.70
5.06 NS
Error 327.70 64 5.12
Total. 344.63
67
5.14
Sex
Low
SES
Middle
Male Female
,
X 3.20 4.08
SD 2.21 1.92
N 20 12
3.84 X 2.76
SD 2.26
2.51
N
19 17
75
Table IT
ANOVA of GBKC Judgment Score: SES by IQ
Source SS df MS F a
SES .05 1
.05
.01
NS
IQ
25.17 1
25.17 5.05
A
0
\ s \
S X I .11 1 .11 .02
NS
Error
518.67
64
k.91
Total 544.6}
67
5.14
IQ
Low
SES
Middle
Low High
X 2.84 4.00
SD 2.54 1.88
N
15 19
X ' 2.81 4.l4
SD 2.40 2.28
N 22 14
76
Table 18
ANOVA of GBKC Judgment Score: SES by MA
Source SS df MS F a
SES
k.95
1
k.95
1.12 NS
MA
62.31
1 62.31 1^.17 < .01
S X M .2k 1 ,2k
.05 NS
Error 28l.*K) 6k
k.39
Total 3kk.63
67
5.1k
MA
Low
SES
Middle
Low
High
X 2.85
if.66
SD 2.05
1.77
N 20 12
X 2.18 If.23
SD
1.97
2.38
N 16 20
Table 19
ANOVA of GBKC Judgment Score: SES by CA
Source SS df MS F a
SES
5-43
1
5.^3
1.29 NS
CA 74.78 1 74.78 17.80 < .01
S X c .44 1 .44 .10 NS
Error 268.73 64 4.19
Total 344.63
67
5.14
CA
Low
SES
Middle
Young Old
X 2.73
4.69
SD 2.07
1.65
N
19 13
X 2.00 4.28
SD 1.89
03
NO
C v l
N
15
_____ ___ _ . ...... . _
21
78
Table 20
ANOVA of GBKC Judgment Score: Ethnicity by Sex
Source SS df MS F a
Ethnicity i f . 32 1 if. 32 .82
NS
Sex .02 1 .02 .005
NS
E X S if.60. 1 if.60 .88 NS
Error 355-01 6k
5.23
Total jkk.63 61 3.lif
Sex
M ale Female
.Anglo SD
E t h n i c i t y
Chicano ■ SD
79
Table 21
ANOVA of GBKC Judgment Score: Ethnicity by IQ
Source SS df MS F a
Ethnicity
3-27
1
3.27 .67 NS
IQ
24.07 1 24.07 4.92 < .05
E X I 2.87 1
2.87 •58 NS
Error 312.69 64 4.88
Total 344.63
67
5.14
IQ
Anglo
Ethnicity
Low High
X 2.81 3.66
SD 2.44 2.14
N 22 18
X 2.84
^•53
SD 2.26 1.84
N
13
- ‘15
80
Tat>le 22
ANOVA of GBKC Judgment Score: Ethnicity "by MA
S o u r c e SS df MS F a
Ethnicity •91
1
•91
.21 NS
MA 53.96 1 53.96 12.31 < .01
E X M
5.25
1
5.25
1.19 NS,
Error 280.1+3 64 4.38
T o t a l 344.63
67
5.14
MA
A n g lo
Ethnicity
Low H ig h
2.66 4.00 X
SD 2.05
2.53
N 24 16
X
2-33
4.81
SD 2.01 1.68
N 12 . 16
81
Table 23
ANOVA of GBKC Judgment Score: Ethnicity by CA
Source SS df MS F a
Ethnicity
.05 1 .05 .01
NS
CA 65.08 1 65.08 15.26 A
0
H
E X C 1.68 1 1.68
.39
NS
Error 272.87 64 4.26
Total 344.63
67
5.14
CA
Anglo
Ethnicity.
Young Old
X 2.50 4.25
SD 2.10 2.29
N 24 16
X 2.20 4.61
SD 1.81 1.91
N 10 18
82
Table 2k
ANOVA of GBKC Judgment - Score: Sex by IQ
Source SS df MS F CL
Sex . 6k 1 . 6k
.13
NS
IQ
25. 7k 1 25. 7k 5.28 < .05
S X I
6.66
1 6.66 I.36 NS
Error 311.5k 6k if.86
Total 3^4.63
67
5. 1k
Male
Sex
Female
Low
IQ
High
X 2.65
k.k2
SD 2.3if 1. 7k
N 20
X 3.06
3-57
SD 2. ifO 2.3if
N
15
lif
83
Table 25
ANOVA o f G BKC Judgm ent S c o r e : S e x b y M A
S o u rce SS df MS F a
S ex
3.65 1
3-65
.82 NS
M A 61.00 1 61.00 13.88 < .01
S X M 1.80 1 1.80 .41 NS
E r r o r 281.14 64
4.39
T o t a l 344.63
67
5.14
M A .
Low H igh
X 2.60 4.81
SD 2.14 1.68
N
23
16
X 2.46 4.00
SD 1.85
2.53
N
13
16
84
Table 26
ANOVA of GBKC Judgment Score: Sex by CA
Source
SS
df
MS
F a
CA 76.22 1 76.22 18.25 < .01
Sex
6.89
1
6.89 1.65 NS
C X S
.1*7
1
.47 .11 NS
Error 267.25 64 4.17
Total 344.63
67
5-14
Sex
Male Female
X 2.56
2.09
Young SD 2.12
1.75
CA
N
23
11
X 4.87 4.05
Old SD 1.62 2.38
N 16 '
. 18
85
Table 27
ANOVA of GBKC Judgment Score: .IQ by MA
S o u r c e SS df M S F a
IQ
19.66 1 19.66 4 .8 9 < .05
M A 51.90
T
-L 51.90 1 2.95 < .01
I X M 10.09 1 10.09 2 .5 1 NS
E r r o r 256.85 64 4.01
T o t a l 544.63
67
5.14
M A
Low
IQ
H igh
Low H igh
X
1-75
4.2 6
SD 1.68
2.57
N 20
15
X : 5.56 4.52
SD
1.99
2.00
N 16
17
86
Table 28
ANOVA o f G BKC Judgm ent S c o r e : IQ by CA
S o u r c e SS d f MS F a
CA 84.91 1 84.91 23.63 < .01
IQ
40.68 1 40.68 11.32 < .01
C X I
3-97
1
3.97
1.10
E r r o r 229.96 ' 64
3.59
T o t a l 344.63
67
5.14
IQ
Low H igh .....
X 1.26
3.31
SD
1.33
2.00
N
15 19
X 4.00
5.07
SD 2.27 I.63
N 20 14
87
Table 29
ANOVA of GBKC Judgment Score: MA by CA
Source SS df MS F a
CA 15.52 1 15.52 3.74 NS
MA
3-53
1
3-53 .85
NS
C X M 6.05 1 6.05 1.46 NS
Error 265.02 64 4.14
Total 344.63 67
5.14
MA
Young
CA
Old
Low High
X 2.45 2.00
SD 2.04
1-73
N
31 3
X 3.20
4.65
SD 1.92
2.95
N
5 29
88
Table 30
ANOVA of* GBKC Explanation Score: Program by SES
Source SS df MS F a
Program 1.20 1 1.20
.31 NS
SES 1.87 1 I.87 .48
NS
P X S 15.96 1 15.96 4.15 < .05
Error 246.25 64 3.84
Total 266.81 67
3.98
SES
Program
Low Middle
X 2.92 1.81
SD 1.80 2.00
N
25
16
X 1.28
2.35
SD
1-97
2.11
N
7
20
89
Table 31
ANOVA of GBKC Explanation Score: Program by Ethnicity
Source SS d f MS F a
Program 3-^9 1 3.^9 .85 NS
Ethnicity 1.65 1 1.65 .40 NS
P X E
•37 1 .37 -09 NS
Error 262.07 6k 4.09
Total 266.81 67 3-98
Ethnicity
Anglo Chieano
X
2.33
2.78
Integrated SD 2.09 1.62
N 27 l4
Program
-
X 2.00 2.1k
Segregated SD 2.44
1.79
N
13
. 14
90
Table 32
, ANOVA of GBKC Explanation Score: Program, by Sex
Source SS df MS F a
Program
2.85 1 2.85 .69 NS
Sex A o 1 .ko .09 NS
P X S .o r 1 .01 .003 NS
Error
263.67 64 4.10
Total 266.88 67 3.98
Sex
Male Female
X 2.56 2.38
Integrated SD 1.83 2.11
N
23
18
p-rngram
X 2.12 2.00
Segregated SD
1.99
2.32
N 16 -11
.
91
Table 33
ANOVA of GBKC Explanation Score: Program by IQ
Source SS df MS F
a
Program .01 1 .01 .005 NS
IQ
14-90 1 14.90
3.83 NS
P X I .16 1 .16 .04 NS
Error 249.02 64
3.89
Total 266.88 67 3.98
IQ
Program
Low High
X 1.85
2.81
SD
1.99
1.86
N 14 27
X 1.81 3.00
SD 2.01 2.28
N 21 6
92
Table 34
ANOVA of-GBKC -Explanation Score: Program by- MA
Source SS df MS F a
Program 7.23
1 7.23 2.2 6 NS
MA
56.33
1
56.33 17.63 < .01
P X M 3.27
1 3.27
1.02 NS
Error 204 .49 64
3-19
Total 266.88
67
3.98
MA
Program
Low High
I.87 X
3.35
SD 1.84 I.76
N 24
17
X
• 75 3.13
SD .96 2.16
N 12
15
93
Table 35
ANOVA of GBKC Explanation Score: Program by- CA
Source SS df MS F a
Program 7.00 1 7.00 2.06
NS
CA 4-3.98 1 43.98 12.94 < .01
P X C 2.60- 1 2.60
.7 6
NS
Error 217.51 64
5.39
Total 266.88
67 3.98
CA
Program
Young
Old
X
1.91
3.22
SD 1.88 1.80
N
23
18
X .81
2.93
SD 1.16 2.17
N 11 16
94
Table 36
ANOVA of GBKC Explanation Score: SES by Ethnicity
Source SS df MS F a
SES ' 3.10 ■ 1 3.10 .76 NS
Ethnicity
•59
1
•59
.14
NS
S X E 2.16 1 2.16
•55
NS
Error 260.67 64
if.07
Total 266.88
67 5-98
Ethnicity
Low
SES
Middle
Anglo Chicano
X 2.64 2.46
SD 2.23
1-59
N
17 15
X
1.91
2.46
SD 2.15 1.89
N
25 13
95
Table 37
/ ANOVA of GBKC Explanation Score: SES by Sex
Source SS df MS F a
SES 3.27 1 3.27 .82 NS
Sex .16 1 .16 . 0^ NS
S X s 8.8Q 1 8.80 2.21 NS
Error 25A.k6 6k
3.97
Total 266.88 67 3.98
Sex
Male Female
X 2.30 3.00
Low SD I.83 2.08
N 20 12
SES . ,
X 2 .kj 1.70
Middle SD 1.98 2.11
N
19
. 17
96
Table 38
ANOVA of GBKC Explanation Score: SES by IQ
Source SS df MS f OL
SES 1.03 1 1.03 .26 NS
IQ 15.25 1
15.25 3.93 NS
S X I
.17. 1
.17 .04 NS
Error 248.00 64 3.87
Total 266.88 67 3.98
IQ
Low
High
X 1.92 3.00
Low SD 2.06 1.76
N
13 19
,SKQ
X
1.77
2.64
Middle SD
1-97
2.13
N 22 14
97
Table 39
ANOVA of GBKG Explanation Score: SES by MA
Source SS df MS F a
SES
10.31
1 10.31 3.25 NS
MA 58.74 1 58.74 18.56 < .01
S X M
2.13 1 2.13
.67 NS
Error 202.54 64
■3.16
Total 266.88
67
5.93
MA
Low
SES
Middle
Low High
X 2.00 3.50
SD 2.00 1.44
N 20 12
X
00
3.10
SD .88 2.19
N 16 20
98
Table 40
ANOVA of GBKC Explanation Score: SES "by CA
Source SS df MS F a
SES 9.12 1 9.12 2.70 MS
CA 45.43 1 45.43 13.48 < .01
C X A 2.39 1 2.39 .71 NS
Error 215.60 64
3.36
Total 266.88 67
3.98
CA
Young Old
X 2.05 3.30
Low SD 2.04 1.54 '
N
19 13
RES
X
• 93 2.95
Middle SD 1.03 2.02
N
15
21
99
Table kl
ANOVA of GBKC Explanation Score: Ethnicity by Sex
Source SS df MS F a
Ethnicity •69
1
.69
.16 NS
Sex .09
1
.09
.02 NS
E X S I.36 1 I.36
•33
NS
Error 26b.bj 6b k .13
Total 266.81
67
3.98
Sex
Anglo
Ethnicity-
Male Female
X 2.38 2.09
SD 2.20 2.22
N 18 22
-
X 2.38 2.71
SD 1.62 2.05
N 21
■ ~ ' 7
100
Table U2
ANOVA of GBKC Explanation Score: Ethnicity by IQ
Source
SS
df MS
F
a
Ethnicity .38 1 .38 .10
NS
IQ
17.10 1 17.10 4.47 < .05
E X I
3.95-
1
3-95
1.03
NS
Error
244.87
64 3.82
Total 266.88
67
3.98
IQ
Anglo
Ethnicity
Low High
X
1.95
2.56
SD 2.23 2.14
N 22
18
X 1.61 3.20
SD I.50 1.56
N
13 '15
101
Table k3
ANOVA of GBKC Explanation Score: Ethnicity by MA
Source SS df MS F a
‘Ethnicity .0 6 1 .06 .01 NS
MA 51.00 1 51.00
15.29
< .01
E X M
1.56 1 1.56 .k6 NS
Error
213.57
6k
505
Total 266.88
67
3.98
MA
Low
High
X 1.62 3.12
.Anglo SD 1.92 2.30
N 2k 16
Ethnicity.. - -
X 1.25 3.37
Chicano SD 1.05
1.5^
N
12 .16
102
Table UU
>
S 3
o
$
o
GBKC Explanation Score: .Ethnicity by CA
Source SS df MS F a
Ethnicity
.30 1
.30 .08 NS
CA
39.12
1 59.12 11.11 < .01
E X C 1.^9 ' 1 1.49 .b2 NS
Error
225.31
6b 3.52
Total 266.88
67 3.98
CA
Anglo
Ethnicity
Old Young
X 1.50
3.31
SD
1-93 2.15
N 2b 16
X 1.70 2.88
SD 1.25 1.81
N 10 . 18
103
Table 45
AITOVA of GBKC Explanation Score: Sex by IQ
S o u r c e SS d f MS F a
S e x .32
1
.32
.08 NS
IQ 17.64 1 17.64
4.55
< .05
S X I
.74 1 .74
.19 NS
E r r o r 248.14 64
3.87
T o t a l 2 6 6 .8 8
67 3.98
IQ
M ale
S ex
F em ale
Low High
X 1.80 ^.OO
SD 1.98
1-59
N 20
x9
X 1.86 2.64
SD 2.03 2.30
N
15
14
10 4
Table k6
ANOVA of GBKC Explanation Score: Sex by MA
'
Source SS df MS F a
Sex
2.59 1 2.59 .78 NS
M A
5^.13 1
5^.13 I6.3I < .01
S X M .009 1 .009 .003 NS
E r r o r 212.39 6k
3.31
T o t a l 266.88 67 3.98
M A
Low
H igh
X 1.65
3 M
• Male SD 1.72 1.63
N
23
16
J "
X 1.23 3.06
Female SD 1.6k 2.23
N
13 -
' 16
*
105
Table 1+7
ANOVA of GBKC Explanation Score: Sex by CA
Source SS df MS F a
CA 1+3.18 1 1+3.18 12.37 < .01
Sex
3.76
1
3.76 1.07 NS
C X S
.05 1 .05 .01 NS
Error 222.30 61+ 3.1+8
Total 266.88
67 3.98
Sex
Young
CA
Old
Male Female
X
1.69
1.27
SD I.7I +
1.79
N
23
11
X
3.37
2.83
SD 1.66 2.20
N 16
' . 18
106
Table 48
ANOVA-of GBKC Explanation Score: IQ by MA
Source
SS df MS F a
IQ 12.90 1 12.90 4.28 < .05
MA ^7.12 1 47.12
15.63
< .01
I X M 9.21 1 9.21
3.05 NS
Error
192.87
64 3.01
Total 266.88
67
3.98
MA
Low_______ High
X .80 3.20
Low SD 1.00 2.14
IQ
N 20
15
X 2.37
3.29
High
SD I.96
1.79
N 16
17
107
Table 1+9
ANOVA of GBKC Explanation Score: IQ by CA
Source
SS
df MS F a
CA 1+9.00 1 49.00
15.93
< .01
IQ
26.91 1
26.91 8.7^
< .01
c x i
3-32
1 3.32 1.08 NS
Error 196.88 64 3.07
Total 266.88
67
3.98
IQ
Young
CA
Old
X
SD
N
X
SD
N
Low High
. 60 2.31
1
•91
1.88
15 19
2.75 3.57
2.07 1.74
20 l4
108
Table 50
ANOVA o-f GBKC Explanation Score: MA by CA
Source SS df MS F a
CA 1.50 1 1.50
.^5 NS
MA 13.62 1 13.62 4.15 < .05
C X M 3.72 1 3.72 1.13 NS
Error 209.76 6k
3.27
Total 266.88
67
3.98
M A
Young
CA
O ld
Low H igh
X
1.51
2.00
SD 1.76 1-73
N
31 3
X
i.ko
3.37
SD 1.1k
1.93
N
5
29
109
Table 51
ANOVA of GBKG Total Score: Program by SES
Source SS df MS P a
Program
12.77
1
12.77
•
00
NS
SES 1.64 1 1.64 .10 NS
P X S 39.04 1 39.04 2.38 NS
Error 1051.78 64 16.43
Total 1110.74
67 16.57
SES
Program
Low Middle
X 6.76 5-25
SD
3.55
4.18
N
25
16
X
3*71
5.60
SD 4.46
4.59
N
7
20
110
Table 52
^ ANOVA of GBKC Total Score: Program by Ethnicity
Source SS df MS F a
Program 24.16 1 24.16 1.44 NS
Ethni c ity 16.l4 1 16.14
.96 NS
P X E 2.85 1 2.85
.17
NS
Error
1073.^5
64
16.77
Total IIIO.74
67 16.57
Program
Ethnicity
Anglo Chicano
X
5.70 7.07
SD 4.09 5.22
N 27
14
X 4.84
5-35
SD
4.99 3.95
N
13
l4
111
Table 53
ANOVA of GBKC Total Score: Program by SEX
Source S'S
df MS F a
Program
18.67
1 18.76 1.09 NS
Sex 2.38 1 2.58 .14 NS
P X S 1.27 1 1.27
.07 NS
Error 1088.80 64 17.01
Total 1110.74
67 16.57
SEX
P rogram
Male Female
6.43 X
5.83
SD 3.66 4.12
N 23 18
X 5.12 5.09
SD 4.17 4.92
N 16 11
112
Table 54
ANOVA of GBKC Total Score: Program by IQ
Source SS df MS F a
Program .11 1
.11
.007
NS
IQ 67-97
1
67.97
4.24 < .05
P x I
.31
1
.31
.02
NS
Error 1024.17 64 16.00
Total 1110.74
67 16.57
Program
Low
IQ
High
X 4.64 6.96
SD 4.18 3.45
N 14
27
X 4.66 6.66
SD 4.28 4.88
N 21 6
113
Table 55
ANOVA o f GBKC T o t a l S c o r e : Program b y M A
S o u r c e SS df MS F a
Program
40.75
1
40.75 5.09 NS
M A 242.11 1 242.11 18.4l < .01
P X M 8.68 1 8.68 .66 NS
E r r o r 84l.66 64
15.15
Total 1110.74
67 16.57
M A
I n t e g r a t e d
Program
S e g r e g a te d
Low
Higfa
X 4.83 8.05
SD
5.55 3.47
N 24
17
X 2.5O 7.20
SD 2.84
4.37
N 12
15
114
Table 56
ANOVA of GBKC Total Score: Program by CA
Source SS df MS F a
Program 42.96 1 42.96 3.26
NS
CA 239.99 1
239.99
18.24 < .01
P X C 10.49 1 10.49
1.79 NS
Error 841.97 64
13.15
Total 1110.74
67 16.57
CA
Program
Young Old
X 4.78 7.94
SD 3-61 3.42
N
23
18
X 2.27 7.06
SD 2.86 4.26
N 11 16
115
Table 57
ANOVA of GBKC Total Score: SES by Ethnicity
Source SS df MS F a
SES 5.46 1 5.46
.32 NS
Ethnicity 8.57 1
8.57
.50
NS
S X E 4.32 1 4.32
.25 NS
Error 1090.70 64 17.04
Total 1110.74 67 16.57
Ethnicity
• Low
SES
Middle
Anglo Chicano
X 6.00 6.20
SD 4.31 3.52
N
17 15
X 5.00 6.23
SD 4.44
3.91
N
23 ' 13
116
Table 58
ANOVA of GBKC Total Score; SES by Sex
Source SS df
MS F a
SES 6.48 1 6.48
•39
NS
Sex
1.33
1
1.33
.08 NS
S x s ' 48.02 1 48.02 2.91
NS
Error 1054.25 64 16.47
Total 1110.74
67 16.57
Sex
Low
SES
Middle
Male Female
X 5.50 7.08
SD
3.87 3.91
N 20 12
X 6 .5 I 4.47
SD
3-95
4.46
N
19
* ' ^
117
Table 59
ANOVA of GBKC Total Score: SES by IQ
Source SS df MS F a
SES .62 1 .62
.03 NS
IQ
79.61 1 79.61
4.97
< .05
S X I .005 1 .005 .001 NS
Error 1023.97 64 16.00
Total 1110.74
67 16.57
IQ
Low
SES
Middle
Low High
X 4.76 7.00
SD 4.28 3.44
N
13 19
X
4.59
6.78
SD 4.21 4.08
N 22 14
118
Table 60
ANOVA of GBKC Total Score: SES by MA
Source SS df MS F a
SES
29-57
1
29.57
2.20
NS
M A 242.07 1 242.07 18.06 < .01
S X M
5.83
1
5.83
.28
NS
Error
857.69
64 13.40
Total 1110.74
67 16.57
MA
Low High
X 4.85 8.16
SD
3.89
3.04
N 20 12
X 3.06
7-35
SD 2.67
^•35
N 16 20
119
Table 6l
ANOVA of GBKC Total Score: SES "by CA
S o u r c e SS
df MS F a
SES 28.63 1 28.63 2.12 NS
CA
236.79
1
236.79 17.58 < .01
S X C 4.91 1 4.91 .36 NS
E r r o r
861.89
64 13.46
T o t a l 1110.74
67 16.57
CA
Low
SES
Middle
Young O ld
X 4.78 8.00
SD 3.98 3.00
N
19 15
X
2.93
7.23
SD 2.71 4.27
N
15
21
120
Table 62
ANOVA of GBKC Total Score: Ethnicity by Sex
Source SS df
MS F a
Ethnicity 8.49
1
8.49 .49 NS
Sex
.22 1 .22 .01
NS
E X S
10.99
1
10.99
.64 NS
Error 1 0 8 9 .2 6 64 1 7 .0 2
Total IIIO.7 4
67 16.57
Sex
Anglo
Ethnicity
Chicano
Male Female
X
5.85 5.09
SD 4.27 4.50
N 18 22
X
5.95
7.00
SD 5.62
3.87
N 21
, -7
121
Table 63
ANOVA OF GBKC Total Score: Ethnicity by
IQ
Source SS df MS F
a
Ethnicity
5-89
1
5.89 •37 NS
IQ 81.77
1
’ 81.77
5.20 < .05
E X I
13.57
1
13.57
.86 NS
Error 1005.13 64
15.70
Total 1110.74 61 16.57
IQ
Anglo
Ethnicity
Chicano
Low High
4.77
X 6.22
SD 4.56 k.oQ
N 22 18
X 4.46
7.73
SD
3.59
3.03
N
13 15
122
Table 6k
AH OVA OF GBKG Total Score: Ethnicity by.MA
Source SS df MS F a
Ethnicity . 50 1 .50 .03
NS
MA 209.88 1 209.88 15.29 < . 01
E X M 12.5^ 1 12.54
•91
NS
Error 878.05 64 13.72
Total 1110.74
67 16.57
MA
Low High
if.29
7.12
SD Anglo
Ethnicity
8.18
2.85 Chicano SD
12
123
Table 65
ANOVA of GBKC Total Score: Ethnicity by CA
Source SS df MS F a
Ethnicity .09
1
.09 .007 ~ NS
CA 205.14 1 205.14 14.66 < .01
E x C .005 1 .005 .001 NS
Error
895.33
64
13.-99
Total 1110.74
67 16.57
CA
Anglo
Ethnicity
Chicano
Young Old
X 4.00 7.56
SD 3.83 4-33
N 24 16 ’
X 3.90 7.50
SD 2.96 3.40
N 10
. 18
124
Table 66
ANQVA of GBKC Total Score: Sex by IQ
Source SS df MS F a
Sex 1.87 1 I.87 .11 NS
IQ
86.02 1 86.02 5.44 <
.05
S X I 11.86 1 11.86
•75
NS
Error 1010.86 64
15.79
Total 1110.74
67 16.57
IQ
Male
Sex
Female
Low High
X 4.45 7.42
SD 4.21 2.89
N 20
19
A
X 4.93 6.21
SD 4.26 4.54
N
15
, • l4
125
Table 67
ANOVA of GBKC Total Score: Sex by MA
Source SS
df
MS F
a
Sex
12 .40 1 12.4o .90 NS
MA 230.06 1 230.06 16.78 < .01
S X M I.56 1 1.56 .11 NS
Error
877.13
64 13.70
Total 1110.7^
67 16.57
MA
Male
Sex
Female
Lov High
X 4.26 8.25
SD
3.65 2.93
N
23
16
X 3.69
7.06
SD
5.25
4.66
N
15
- '16
126
Table 68
ANOVA of GBKC Total Score: Sex by CA
Source SS df MS F a
C A 23^ .Ik 1 23^-.15 17.15 < .01
Sex 2 0 .8 3 1 2 0 .8 3 1 .5 2 NS
C X s
•85 .
1
.85 .06
NS
Error
873.75
6k
15.65
Total 1 1 1 0 .7 4
67 16.57
Sex
Male Female
SD
11
6.88 8 .2 5
k.kl SD
-18
127
Table 69
ANOVA of GBKC Total Score: IQ by MA
Source SS df MS F a
IQ
64.42 1 64.42
5.23
< .03
MA. 197.92 1 197.92 16.07
H
O
V
I X M
38.59
1
38.59 3.13
NS
Error 788.08 64 12.31
Total 1110.74
67 16.57
MA.
Low
IQ
High
Low High
X 2.55
7.46
SD 2.46 4.4o
N 20
15
X
5.93
7.82
SD
3.71
3.48
N 16
17
128
Table 70
ANOVA of GBKC Total Score: IQ by CA
S o u r c e SS df MS F a
CA 262.93
1
2 6 2 .9 3 2 2 . 5 2 < .01
IQ 133.76
1
133.76 ■11.1*5 < .01
C X I
1^-55
1
lif.55
1.21* NS
E r r o r 7V7.ll 64 11.67
Total 1110.71* 67
16.57
IQ
Young
CA
Old
Low H igh
X 1.86
5.63
SD 2.03
3.65
N
15 19
X
6.75
8.64
SD 4.17 3.00
N 20 l4
129
Table 71
ANOVA of GBKC Total Score: MA by CA
S o u r c e SS
df MS F a
CA 2 6.68 1 26.68 2.02 NS
M A 31.01 1 31.OI 2.34
NS
C X M 19.29
1
19.29 1.46 NS
E r r o r 845.12 64 13.20
T o t a l 1110.74
67 16.57
M A
Low High
X 3.96 4.00
SD 3.61 3.46
N
31 3
V
JTL 4.60 8.03
SD 2.70
3.77
N
5 29
130
APPENDIX C
SUMMARIES OF M ULTIPLE REGRESSION OF INDEPENDENT
CONTINUOUS AND DICHOTOMOUS VARIABLES HAVING
S IG N IF IC A N T EFFECTS ON GBKC SCORES
131
T a b le 72
Summary o f M u ltip le R e g r e s s io n o f In d ep en d en t
(C o n tin u o u s) V a r ia b le s H aving S i g n i f i c a n t
E f f e c t s on Judgm ent S c o r e s
V a r ia b le S te p
M u ltip le
R H2
Change
in R^
S im p le
R
M A 1
0.53 0.28 0.28 0.53
IQ 2 0.58 0.3U 0.05 0.33
SES 3 0.6l
0.37 0.03 -0.15
S ex k 0.6l 0.38 0.01 -0.0U
E t h n i c it y
5
0.62
0.39
0.01 0.12
Program 6 0.62
0.39
0.00 -O.lU
C A
7 0.63 0.39
0.00 0.U6
132
Table 73
Summary o f M u ltip le R e g r e s s io n o f In d ep en d en t
(D ic h o to m o u s) V a r ia b le s H avin g S i g n i f i c a n t
E f f e c t s on Judgm ent S c o r e s
M u ltip le ^ Change S im p le
V a r ia b le S te p R _ R in _ R
C A 1 0.U5 0.20 0.20 0.U5
IQ
2
0.57
C \ l
00
O
0.12 0.27
Sex 3 0.59 0.3^ 0.02 -o.ol
E t h n i c it y k 0.59 0.35
0.01 0.12
Program
5 0.60 0.36 0.00 -0.1U
SES 6 0.60 0.36 0.00 -0.0k
133
Tat>le jk
Summary o f M u ltip le R e g r e s s io n on In d ep en d en t
(C o n tin u o u s) V a r ia b le s H avin g S i g n i f i c a n t
E f f e c t s on E x p la n a tio n S c o r e s
M u ltip le ^ Change S im p le
V a r ia b le S te p R _ R _ in R^ R
M A 1 0.U8
0.23 0.23 O.hQ
SES 2 0.56 0.31 0.09 -0.23
IQ 3 0.59 0.3^ 0.03 0.31
E t h n i c it y h 0.60 0.3.6 0.01 0.06
S ex
5
O.61
0.37
0.02 -0.0U
C A 6 O.61 0.38 0.00 0.U2
13^
T a b le 75
Summary o f M u ltip le R e g r e s s io n o f In d ep en d en t
(D ic h o to m o u s) V a r ia b le s H avin g S i g n i f i c a n t
E f f e c t s on E x p la n a tio n S c o r e s
V a r ia b le S te p
M u ltip le
R R2
Change
in R^
S im p le
R
M A 1 o.i+U 0 .1 9 0 .1 9 0 . 1 + 1 +
IQ
2 0.1+9 0.21+ 0 .0 5 0 .2 6
C A
3 0 .5 2 0 .2 7 0 .0 2
0 .3 9
SES 1 + o . 51+ 0 .2 9 0 .0 2
1
0
H
H
S ex
5 0 .5 5 0 .3 0 0 .0 1 -0.01+
E t h n i c it y 6
0 .5 7
OJ
00
0
0 .0 2 0 .0 6
135
T a b le 76
Summary o f M u lt ip le R e g r e s s io n o f In d ep en d en t
(C o n tin u o u s) V a r ia b le s H aving S i g n i f i c a n t
E f f e c t s on T o t a l S c o r e s
M u ltip le p Change S im p le
V a r ia b le S te p R R in R^ R
M A 1 0 .5 3
0 .2 8 0 .2 8 0 .5 3
SES 2
0 .5 9 0 .3 5 0 .0 7
0
C \l
O
1
IQ 3 0 .6 2
0 .3 9 o.oi* 0 . 3 U
ETH k
O.63 o.U o 0 .0 1 0 .1 0
S ex
5
0 . 6 U 0 .U1 0 .0 2 - 0 . 0 U
CA 6 0.6k 0 .U2 0 .0 0 0 .U6
Program 7 0 .6 5 O.k 2 0 .0 0 - 0 .1 3
136
Table 77
Summary of Multiple Regression of Independent
(Dichotomous) Variables Having Significant
Effects on Total Scores
Multiple Change Simple
Variable Step R_ R in Rp
MA 1 O.UU 0.20 0.20 O.kk
IQ
2
0.51
0.26 0.06 0.28
CA
3 0.56 0.32 0.06 . O.kk
Sex k 0.58 0.3b 0.02 -0.0k
Ethnicity
5 0.59 0.35
0.01 0.10
SES 6 0.60 0.36 0.01 -0.08
Program
7
0.60 0.36 0.00 -0.13
137

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Asset Metadata

Creator Frankel, Mary Eselun (author)

Core Title Fixation in slow learners, and sensitivity of Piagetian conservation scores to factors known to affect IQ scores

Degree Doctor of Philosophy

Degree Program Education

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

Tag education, tests and measurements,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c26-466115

Unique identifier UC11245628

Identifier usctheses-c26-466115 (legacy record id)

Legacy Identifier DP24272.pdf

Dmrecord 466115

Document Type Dissertation

Rights Frankel, Mary Eselun

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