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Figural And Symbolic Divergent-Production Abilities In Adults And Adolescents

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Figural And Symbolic Divergent-Production Abilities In Adults And Adolescents

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Content This dissertation has been 64—3097
microfilmed exactly as received :
GERSHON, Arthur, 1923-
FIGURAL. AND SYMBOLIC DIVERGENT—PRODUC
TION ABILITIES IN ADULTS AND ADOLESCENTS.
University of Southern California, Ph.D., 1963
Psychology, experimental
University Microfilms, Inc., Ann Arbor, Michigan
PXGURAL AND SYMBOLIC DIVERGENT*"PRODUCTION
ABILITIES IN ADULTS AND ADOLESCENTS
by
Arthur Gershon
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
' (Psychology)
June 1963
UNIVERSITY O F S O U T H E R N CA LIFORNIA
GRADUATE SCH O O L
UNIVERSITY PARK
LO S ANG ELES 7 . CA LIFO RN IA
This dissertation, written by
Arthur Gershon
under the direction of h~.f....Dissertation Com
mittee, and approved by all its members, has
been presented to and accepted by the Graduate
School, in partial fulfillment of requirements
for the degree of
D O C T O R OF P H I L O S O P H Y
DIS££RT£npN COMMITTEE
t —4—^2^0— ^
ACKNOWLEDGMENTS
As much of experimental psychology had its origins
in Germany so did much of what this dissertation represents
derive its impetus from European origins. First and fore
most through the kind and thoughtful inspiration of the
!late Karl Altenhain of Hasslinghausen and his wonderful
daughter Monica Ella? then to Franklin J, Potter* whom
Wundt might also have described as "ganz amerikanisch";
i 1
|two persons* Dorothy and Joseph, ?jhom only the writer can
|know the debt of gratitude owed to them for their help and-
i
i l
|kindness over a lifetime, and for their dedication to the j
|concept of the learned man. j
i i
! To Professor Guilford, no words of appreciation are j
i I
; i
iadequate. The writer can only further dedicate himself |
i ' i
I to attempt to continue the pursuit of scientific inquiry
i
I
I so superbly demonstrated by this teacher and friend. To
| *
!two other students of this wise master who also helped
1
train the writer-- Professor William B. Michael and Doctor
Philip R. Merrifield, these words of appreciation are also j
j
|extended. i
TABLE OF CONTENTS
i
i
I
| acknowlrbgmemts
LIST OF TABLES
|
\
LIST OF FIGURES
I. THE PROBLEM . . ...................
Statement of the Problem
Importance of the Study
Some Further Logical Considerations
Organization of the Dissertation
II. REVIEW OF THE LITERATURE ...........
Aptitudes Project studies antedating
the structure of intellect
The organization of human abilities
Other studies, influenced by structure-
of-intellect theory
Factorial invariance
Factorial structure and growth of
intelligence
Summary
III. THE HYPOTHESES ... ...............
»
Statement of the Hypotheses
Current Status of the Theoretical
Model
Hypothesized Test Measures
Alternative Hypotheses
I CHAPTER
I
! IV. P R O C E D U R E S ...................
i
i
; The Samples
\ Administration of the Test Batteries
; Scoring
i Statistical Treatment of the Score
I Data
Eellabilities
! V. TEE FACTOR ANALYSES.............
Intercorrelations
Extraction of Factors
Rotation of Axes
; Computational Checks on Rotations
| Comparison of Factor Patterns
Factorial Invariance in Analytical
Orthogonal Relations
VI. INTERPRETATION OF FACTORS .......
VII. DISCUSSION............. .
Relation of the Results to the
| Hypothesised Operation
Relation of the Results to the
i Hypothesised Contents
| Relation of the Results to the
i Hypothesised Products
Relation of the Results to Other
Bivergent-Froduction Factors
Relation of the Results to the
I Other Hypotheses
j Recommended Tests for Newly Discovered
Factors
Implications for Future Research
VIII,. SUMARY .............
! REFERENCES . . , .......................
Page
109
131
163
202
228
237
APPENDICES
A. DESCRIPTION OF THE STRUCTURE-OF-INTELLECT
C O D E ..................
B. THE HYPOTHESIZED FACTOR STRUCTURE OF
THE TEST BATTERY................
C. DESCRIPTION OF TESTS ..............
D. ORIENTATION TALK TO STUDENTS........
E. VARXMAX ROTATED FACTOR MATRIX, ADULTS .
F. VARIMAX ROTATED FACTOR MATRIX,
ADOLESCENTS......... ......... ' . .
LIST OF TABLES
| TABLE
|
| 1. The Test Bettery ...................
! 2. Comparison of Means and Variabilities. .
| Mult and Adolescent Samples .....
! ' 3, Reliabilities of the Test Scores . . . .
I
4. Correlation'Matrix, Adults..........
■
5. Correlation Matrix, Adolescents . . . .
!
• 6. Unrotated Factor Matrix, Adults ....
7. Unrotated Factor Matrix, Adolescents . .
• e
8. Rotated Factor Matrix, Adults .......
9. Rotated Factor Matrix, Adolescents . . .
10. Coefficients of Congruence (0r) Computed
for the Two Graphic Orthogonal Rotated
Solutions; Adult Matrix lg; Adolescent
Matrix, 2g ......................
j
i
j 11. Coefficients of Congruence (0r) Computed
| for the Tro Varimax Orthogonal Rotated
I Solutions; Adult Matrix lv; Adolescent
| Matrix 2 u ......................
i
12. Comparison of Factor Patterns in the Two
Graphic Orthogonal Rotated Solutions .
i
vi
Page
96 I
I
125 I
128
132
i
|
135 :
139
141
149
151
i
155 !
I
159 i
j
j
207
F
i
LIST OF FIGURES
FIGURE
1.
2 .
Divergent-production matrix showing
positions of factors under
investigation in this study ........
Divergent-produetion matrix showing
factors confirmed in each sample . .
Page
55
212
CHAPTER I
!
THE PROBLEM
Among the contributions of psychometrics to the
i ‘ ' !
explanation and prediction of human behavior are its
!
inquiries into basic human intellectual capacities. For j
;
the most part, such primary abilities or aptitude© have
; I
derived their identities through factor-analytical and |
other multivariate procedures applied to measurement© from j
paper-and-pencil tests. The fruitfulness of this explore- i
i i
! tion in the domain of aptitudes has been largely dependent I
; \
upon basic theoretical considerations in psychology con-
; I
coming the existence or organization of ” traits** of human
I behavior.
i • i
' i
Spearman (1927) had called for research endeavors
• - :
i that would be
|
1 ... nothing less than a general survey of the entire
range of possible operations of knowing. To execute
this gigantic task, there appears to be only one i
effective means. It consists in an appeal to the
| complete system of ultimate laws that govern all j
j cognition (p. 162).
i - : . . ' j
I It remained for Thurstone (1947) to provide the |
methodology if not the psychological design for a compre- j
I ' |
ihensiv© theory of mental abilities. His concepts of
: primary mental abilities and the methods of multiple- I
|factor analysis haw had their logical extension in j
I ' *
i
Guilford®s (1955,* 1956j 1959) unified theory of toman '
!
labilities. This theoretical model has classified the !
! !
1 i
separate facets of the thinking processes into the single I
I
descriptive system which Guilford terms the nstructure of
I - ' i
| intellect. 6 5 !
Ttorstonc®s (1947) foresight in this matter was
! . ;
iexemplified by his explanation that:
In factorial investigations of mentality, us i
proceed on the assumption that mind is structured j
; somehow, that mind is not a patternless mosaic of
, | an infinite number of elements without functional |
groupings. The extreme opposite view would he to j
hold that mind has no structure at all (p. 57). j
i He believed that multiple-factor analysis would |
i i
■ i
[help structure certain domains of interest where ! 5 basic and:
i
!
fruitful concepts are essentially lacking and where era-
i
sial experiments have been difficult to conceive” (Ttorstone,
| _ ;
1 1947, p. 58). It remained for Guilford, however, to pro- j
vide parsimony and a logical basis for a concordance to !
account for intellectual functions that were being
increasingly reported by trait-oriented investigators.
Trait theories, however, had been a source of
!
debate among philosophers and scientists well before the
|
emergence of nineteenth-century experimental psychology.
Although the annals of psychological literature abound
i
i
with empirical studies and treatises concerning the nature
of behavioral traits, there continues to be sparse general
agreement about the form, name, description, or inter- I
!
relationship of such constructs. !
Despite the lack of resolution among conflicting
theories, a number of investigators have been making
attempts to clarify the situation (Cattel, 1953; Eysenck,
I
1951; French, 1951; Guilford, 1959). It is the consensus
among behavioral scientists such as these that a science
of psychology has its own methodology for inquiry info
!
' i
those facets of personality that are amenable to
|
experimental analysis. i
!
In the present study, it is assumed that empiri
cally based trait theory can be fruitfully applied to the |
■ ' ‘ . !
study of the organization of mental functions in general. j
More specifically, it is assumed that factor theory and
factor-analytical methodology can be fruitfully applied to
the measures of intellectual behavior. If follows from j
this9 that test measures, as behavior samples (Loevinger,
! :
| 1957 ) provide the basis for the inferences concerning the
| existence and nature of such traits. Primary reliance is, j
j therefore9 placed upon factor analysis as a theory and as j
i :
; a method upon which to base conclusions concerning
| behavioral constructs which underlie mental functioning. ■
i - ;
j It is'not this writer's contention that abilities I
I consistently isolated by factor^analytical technique
I necessarily correspond to particular neural patterns in
the human nervous system. Such an assumption is not
I
: necessary for the prediction of behavior. Ilhat is pre*»
supposed in trait theory is that human beings act in
i certain logical, consistent ways. Factor“analytical theory:
proposes to define such relatively stable traits by the
! !
I use of statistically derived evidence. Evidence is |
: usually manifested by the responses of subjects to items
!
| in psychological tests. The determination of what kinds
| of tests and which factors they measure is the setting in I
; which the psychometric drama unfolds.
In postulating the structure of intellect, !
‘ i Guilford (1956^) has indicated at which level fruitful
| research can be conducted. He points out that; j
In view of the great variety of thinking abilities
(and functions) revealed by factor analysis, the
time honored concepts of reasoning, induction, j
deduction, and so forth appear even more inadequate
than before . . . the factors, instead have generated ;
their own categories . . . essentially operational
concepts, since, like factors, they refer back to the
kinds of tests from which factor definitions were
inferred (p. 287).
The value of a theoretical system such as Guilford'sj
or a methodological theory such as Thurstone's multiple- |
; - j
! factor analysis is enhanced if it can be demonstrated that !
! . i
■ i
it is logically consistent in all respects and no major
• ■ I
flaws can be demonstrated in the system. The latter is
more often an ideal to be achieved rather than a reality
I j
and it can be rarely shown that models conceived by human© I
i
have attained such perfection. j
In order to obtain the relationships between
; • 1
' ■ j
concepts that lead to explanation and prediction, however,
|the behavioral scientist will continue to employ his
! •
imperfect theoretical models. Spence (1948) has indicated
i ‘
! -
j that in psychology
| ... theories serve primarily as a device to aid in j
the formulation of empirical laws. They consist in
guesses as to how the uncontrolled or unknown factors j
in the system under study are related to the !
experimentally-known variables. To these hypotheti
cal constructs Tolman has applied, the very appropriate
term 'intervening variable1 because they are assumed
to intervene between the measurable environmental i
6
and organic variables, on the one hand, and the
i measurable-behavior properties on the other (p. 67).
In the physical sciences,theories are viewed as
i !
". . . constructions which serve primarily to integrate ;
or organise into a single deductive system sets of empiri-
| cal laws which previously were unrelated** (Marx, 1948,
| p. 66)« There is value in 8 8 fallacious8 8 models, even in
! * 1
! the world ©f physical sciences. The impact of the
i
Coperaiean concept of a heliocentric universe did not
i
j completely dispell the efficacy of using the sphere' of
j Ptolemy as a model ©f the universe„ In what geocentric
: universe, all celestial bodies were conceived as orbiting
about Earth as the epicenter. Navigators today, as well
I as for a number of centuries past, have used this model as .
! the basis for obtaining a series of celestial fixes in
; . |
; order to pin-point the position of a ship or plane in j
; relation to the surface of the earth. Few today would
| dispute the fallacy of a Ptolemie cosmology; few, however, :
S j
jwould dispute its practicality. One might contend that
j
the geocentric universe concept is merely a relative con-
l |
j ♦ i
j eept subject to the point of view of an observer, and that 1
i I
| the model could fee incorporated into the more universal j
i !
| scheme of celestial mechanics. Not to beg the questions, ' J
7
; \
however, the point to be made here is that even "false”
i
models in science have utilitarian value.
• 1 i
Poincare was certain Euclidean geometry and
Newtonian mechanics would not be displaced. Even with
Einstein’s General Theory and the New Geometry, we con-
i i
tinue the centuries-old theorems of the straight line, the
■ . I
square, and the compass. The theoretical model of the
: structure of intellect, like all scientific models, can.
: ' i
only be adequately tested in the crucible of rigorous
I
research. The question posed for psychology is not
whether the model will hold universally true, but whether
our knowledge and prediction of human behavior can be
; advanced by the application of ideas deduced from it.
I
Statement of the Problem
Although 120 primary abilities (or factors) were !
I defined by the model at the time this study was initiated
! in 1953, more than half still required empirical verifi- [
! ■ !
j cation. The category of abilities selected for investi
gation, the operation of divergent production, derived its j
i
i
operational specification from a structure-of-intell@ct 1
theory. Where Wertheimer (1959) had discussed in general
| terms what ha called ^productive thinking,8 8 Guilford had
|found that such abilities seem to separate into two dig-
|tinet categories. Convergent-production abilities are
!
I measured by tests that emphasise tasks that require a
i :
; unique, best, or conventionally accepted solution. j
I ' :
; Bivergent-production abilities, by contrast, are measured
j
jby teste that emphasise a variety of solutions to each j
|
I task item. It is the latter set of abilities that are of
i :
primary interest in this investigation.
I ;
The divergent-production factors held specific
pertinence for early investigation because of their seem-
j ing relationship to the identification of creative talent. ;
; * y
j Creativity has been an area of interest transcending a
j * i
j number of academic disciplines and it is of current socio- |
I i
logical importance in an evolving technological era. Of j
| the 24 cells in the divergent-production matrix of the j
S strueture-of-intellect model, previous studies had left I
i
i
for future exploration a number of the factors-of figural j
and symbolic content.
Figural factors have been identified with tasks of
a concrete or perceptual nature, in particular, where form
and perceived structure are involved, as in designs and
drawings. In a sense, such content can be described as
[
"tangible8 ® information. The symbolic factors are identic
fiable by tasks that require the manipulation of abstract
signs or symbols such as letters and numerals. Both of
these content areas have been generally categorised as
' i
"non-verbal" as distinct from the semantic factors, which
: !
are concerned with tasks involving verbal material or con- !
!
ceptual operations where knowledge or meaning of words is
- j
a prerequisite. A substantial degree of evidence concern
ing several of the divergent-production factors of semantic !
content has become increasingly available as a result of
‘ * '
a series of parallel studies (Guilford, Merrifield, and
I
Cos, 1961), but no data concerning the social-intelligened9
. 1 » ’ * ' j
: . * * j
or behavioral-content factors have been obtained, where j
r
' - I
; non-verbal information, different from figural or symbolic j
information may also be involved. • j
|
The divergent-production cells of the model chosen j
I ' ^
for investigation are for the factors of:
; |
; Divergent production of figural units (BFU)
I ' i
| Divergent production of figural classes (BEG)
j Divergent production of figural systems (DFS) j
| |
! Divergent production of systolic classes (DSC)
Divergent production of symbolic relations (DS&)
Divergent production of symbolic IraplIcations(DSI)l;
Although the divergent production of figural relations i
(DFE) and the divergent production of symbolic transforms- :
felons (BST) also still required demonstration, practical
considerations required a concentration of" research effort ;
upon those factors for which promising measures could be
readily developed.
\
In addition, further clarification was needed for.
one factor previously Identified, the divergent production ’
of figural transformations which had also been Included
In an investigation (Guilford et al., 1961), to be called
the "ereative-adolescent study9 8 in the following chapters. ;
That study, with ninth-grade boys and girls, had identi- :
fled the sis semantic, two figural, and two syndic
I
factors which compose the balance of cells in the ;
divergent-production maferix, except for the behavioral j
i
■ !
A second problem of this study, of theoretical ■
and of methodological importance, pertains to the problem I
^The alphabetical code designations of factors is
outlined in. Appendix A.
i of factorial invariance; the identification of common
factors under changed conditions from one study to
: another. The changed condition was age level of the
i population of subjects. The same battery of tests was
analyzed for a ninth'**grade sample as well as a young ,
: adult male sample.
Thurstone (1947) has maintained that the concept
of rotating axes to a simple structure provides the
solution to the problem of achieving invariant results.
Other investigators have indicated difficulties with this
approach, have attacked its “subjective1 1 or "intuitional**
nature, and have suggested more “objective” techniques for
identifying factors across different studies. Since much
of the evidence heretofore obtained in support of the
factors of intellect in the Guilford model have stemmed
from studies with superior, young, male, adult samples in
the military service or young men and women from college-
campus samples, it is a question of theoretical importance
to determine whether the number and apparent organization
of human abilities is restricted to adult populations.
A somewhat popular position heretofore has been
that intellectual ability In children is less
! 12 i
! ■ i
I differentiated than in adults and that development follows |
I 1
"a mass-to-specific tendency®® with increasing age
j (Garrett s 194-6). The evidence on this point has been
; equivocal. It appears that this conception of intellect
; tual development may require revision as conflicting
evidence emerges from structure«*o£“ intellect and other
i * .
J multivariate research. Although the exploration of a
| psychological, domain' transcends in importance the lesser
issue of cross-identification of abilities at different :
| age levels, the implications for educational research may
be far-reaching. It would remain for the test constructor ;
; to overcome a paucity in test ideas once the parallels in
; intellectual organisation can be demonstrated at various
: age levels.
Importance of the Study
One importance of this study is that it represents i
new attempts to validate the Guilford model as a fruitful
I source of hypotheses for isolating and defining the
: factors of human intellect. If it can be shown that the :
; model continues to suggest the operational designs of
! appropriate test measures of unique abilities, then its
contribution to explanation and prediction in a psychology
of thinking will be substantiated. Guilford had (1960a)
specified that:
!
For the structure-of-infellect model to he
supported as theory requires two types of verifies- |
tion. First, previously found factors must be
confirmed as distinct from each other, when
interpreted in terms of their location in the model.
Second, new factors must be hypothesised from the j
model, and their separate existences verified (p. 13). |
The exploratory type of verification that first j
|
deduces the existence of "new factors" from the model Beerasi
t
to imply a hierarchy of hypotheses in which the existence
of a factor within the model is first postulated, and
secondary hypotheses are then generated concerning the typej
i
of test© requisite to demonstrating the existence of the
factor. I
r
|
Another aspect of this same problem is concerned
i
I
with the adequacy of trait indicators or test measures of
these hypothesised factors. Such test ideas derive their
|
operational specifications from the model. If if turns oufj
that existing tests meet these specifications, much
developmental effort can be conserved. It has generally
been the case, however, that known tests are factorially
i
complex, or have been too often restricted to measuring
I ' 1
I 14 !
! i
| ■ |
I factors of cognition or of convergent production. There-
I |
i ]
I fore, in attempting to verify aspects of the structure-of-
| |
intellect theory by the procedure outlined above, new I
l tests were needed to demonstrate new factors.
j . !
| Mother consideration -of importance posed by this
; ;
j I
: study concerned factorial invariance as a function of age. j
; i
! Heretofore, factor theory had not sufficiently clarified !
!
| . ;
! conflicting theories concerning the development of |
:
| abilities. It had been suggested by the work of Guilford
!
I
i and his associates (Gardnerj 1963; Guilford et al.. 1961;
Merrifield, Guilford, Gershon, 1S53) and by others that
certain human intellectual functions' that are observed and
: measured in adults are observable and measurable in ■
j children as well. Additional evidence of the same kind
, would contribute much to ■ further research on the education ;
j and training of young. persons in preparation for their
I !
! future roles in the adult community.
i
I ■ ;
| The value of using the primary-mental-afeilities
1 :
! * * |
I'concept for educational counseling, for employment selec-
! ■ ■ i
I tion, and for the prediction of vocational success has had I
I
! an increasing degree of support. If the fruits of primary-:
| ability research can be extended to young persons, then a i
* *
i considerable expenditure in time and effort can be con-
-
served in developing vocational plans. Young adolescents
! can begin to plan more realistically their futures based
i
upon an assessment of their intellectual capacities. If
I identification of the dimensions of intellect important
l
i
j to adult careers must await physiological maturation in
[ the child, however, then little can be done to fight
j Nature. Such an extension of the "readiness" concept to
: intellectual metamorphosis is inconsistent with the
evidence evoked by other research in primary mental
abilities.
If was considered possible from a methodological
point of view that the basic intellectual capacities of
pre-adults might be more clearly measurable since test"
score results might be less confounded from the effect© of
| education, experience, and training than in the case of
i
I adults. If it could be demonstrated that intellectual
I
i
! traits found in adults are similarly measurable in
! literate children, then considerable economy of research
effort and resources in experimental programs could be
effected; school-age populations have been generally more
available for group-test experimentation, in larger
16
I
| numbers, than have college or adult populations. The !
! |
j exception to this in the past had been the availability of j
[ i
i ;
| military personnel. In such samples, however, there i
i i
:
| assisted a number of undesirable experimental biases which
| i
| made f i 5 less°eaptiveM groups of examinees more desirable,
j In the constellation of £actor~analytical studies of apti- j •
fcudes of hlgk~level personnel (Guilford, lf62), of which
| the present study is part, examinees had been superior I
! * young adult males of officer calibre who were believed
I motivated toward good performance on the experimental test
i :
! batteries. It was anticipated that similarly motivated '
examinees might be available In the school-age populations
! as well.
Some- Further Logical Considerations
■ I
; It was indicated earlier that the abilities found
| i
in previous studies seemed to organise themselves into a
I logical if not ^natural8 ® arrangement. The Guilford model i
I of the classification of Intellectual mental function was
] also suggested as a means of formulating hypotheses i
i
! ;
| concerning easts of abilities requiring empirical verifi- j
| cation. Once such factors were verified, "new expert"
mental8 ® tests would in tarn become “marker6 ® test© in ;
[ 17
| subsequent studies seeking evidence concerning still other
i •
| vacant cells in the model.
I " ;
Although this experimental approach suggests some j
form of 53self-fulfilling prophecy” or circularity, it has j
jbeen asserted in earlier treatises (Guilford, 1959) that j
! !
| >
| spontaneous generation of "meaningful" psychological
j constructs is not one of the inevitable fruits of a factor
i analysis. The logical interpretation of a factorial
i I
: i
I configuration is dependent upon the thoughtful preparation
i
and experimental precision tfaiat enters info the formula
tion and conduct of a study. The structure of intellect j
■ \
as a theoretical model derives its status as a scientific
!
I
concept in a manner similar to other morphological systems.!
t
i An analogous example is found in the biological sciences. |
: : i
; The taxonomic system of Linacus was derived by observation
of the morphology of flora which resulted in the hierarehi-
j cal system of phylum, class, order, genus, and species, a
I ' ' ' !
j classificatory system later extended to fauna as well. |
| Another parallel may he taken from Mendeleeff (McPherson j
\ et al., 193S); he demonstrated how the existence of I
I I
i undiscovered chemical elements (and even their ores) was
i • ■ ■ !
j predictable from the classification matrix suggested by j
[ " ' ^
the Periodic Law., . His model is still a major corners tome
of theoretical chemistry.
| The analogies between Mendeleeff' s model and the
!
!strue£ur@“©f“intellee£ classification system of known and
I
still unexplored factors is an interesting set of
parallels. The credibility of inferences concerning empty
cells in either structure is based upon empirical data
|obtained tinder controlled conditions.
i
|
I Implicit in the objectives of this study was its
ipossibl^contribution toward a nomothetic explanation .
|
i (Mackinnon and Maslow, 1951)or description of traits- of
intellectual ability. In this, the writer was mindful, of
!
l one well-phrased passage in Goethe5 s (1955) Faust where
! •
i
| Mephistopholes counsels the young student about.the pit-
I falls of analytical research:
3
! To comprehend a living thing past any doubts
| You cancel first the living spirit out
| The parts lie in the hollow of your hand,
I You only lack the living link you banned ( p ; . - 82) .
;
The analogy between this caveat by Goethe and the
opening chapter of this dissertation, THE PROBhEM, is
!
further exemplified by the concept of the protasis. This
| is the first part of the ancient dram in which the
i
jcharacters are introduced. In logic, the antecedent or
19
| protasis of a conjunctive or conditional proposition is
| termed the hypothesis. This, of course, is defined in
I
| science as "a provisional supposition which accounts for
i
j known facts, and serves as a starting-point for further
i
j investigation by which it may be proved or disapproved
!
..." (Onions, 1955, p. 946). Therefore, having estab-
i
| lished a somewhat tenuous relationship between lex I-
| cography, the draica, the Devil, and science, the author
. j
turns to Kemeny (1959) for the. observation that "...
i
I
science starts with facts and ends with facts, no matter
what theoretical structures it builds in between"
i
! *
(Kemeny, 1959, p. 85).
Qrganizat ion of the Dissertation
i
Chapter 1 introduces the problem area of this
study as one of a continuing series of investigations
relative to predictions generated by the structure of
j
| intellect and its relationship to various population
groups, that is, the issue of factorial invariance.
Chapter II surveys previous investigations
associated with strueture-of-intellect theory and rele
vant factor-analytical studies or pertinent literature
20 |
i
concerning Intellectual abilities in diverse age groups. j
Chapter III discusses the hypotheses and aspects
!
of the structure of intellect in predicting the nature of
test measures of previously demonstrated factors. These !
formulations are related to experimental hypotheses con-
;
cerning cross-identification of Intellectual abilities.
Chapter X¥ describes the subjects, the administra-!
tion and scoring of the tests, and the preparation of the j
data for analysis.
Chapter ¥ discusses the statistical treatment of
the data, the intercorrelations, the extraction of factors, i
the rotation of axes, and the comparison of factor
dimensions in the two samples.
Chapter VI presents the interpretation of the
factor-analytical results.
Chapter ¥11 relates the interpretation of the I
|
factors to the hypothesised factor-content of the new !
experimental tests and to the other experimental hypothe
ses. The implications of the results are discussed in j
terms of structure-of-intellect theory and suggestions forj
future research. I
t ' \
Chapter ¥111 summarises the objectives, results
j and general conclusions of the study. I
CHAPTER II
!
I
REVIEW OF THE LITERATURE
|
i
In this chapters the experimental literature
i leading to the formulation of the strueture-of“intellect
j
| theory is introduced. This encompasses, for the most part,
!
the series of investigations by Guilford and his associ-
1 - ■
| ates of the classic categorizations of aptitude domains
!
j in populations of high-level personnel. The contributions
I
| of other factor-analytically oriented investigators are
!
j then discussed. Attempts by others to organize mental
; abilities into unified theoretical systems are related to
Guilford's theoretical model. Subsequent studies by the
Guilford laboratory are presented to indicate hoi? the
model served as a source for classifying previously found
aptitudes, for discovering new ones, and for suggesting
the type of tests required to measure them. A brief
review is then presented of studies initiated concurrent
to the present one which applied hypotheses from the
theoretical model to population samples other than the
military officer-candidates heretofore employed. Some of
21
22
these investigations are discussed in relationship to the
I present study within the contest of factorial invariance. I
t
‘ This concept of invariance is treated within the bounds I
of identifying the same factors across different popula- ;
|
i
tions and the scope and treatment of the problem by
various investigators is related to the present Investi= j
I j
I gabion. The balance of the chapter presents a review of |
I i
i I
| selected studies pertaining to growth of intelligence j
| and its effect upon factor structure. i
I " I
! ■ ;
! Aptitudes Frolect studies antedating the structure of
| intellect
In formulating the experimental questions of this ;
| ■ 1
| study the search of the literature was directed first to j
; I
the series of reports from the Psychometric Laboratory at i
j
the University of Southern California. Commencing in 1950
after the inauguration of the Aptitudes Project in 1949, j
these research reports were published periodically. They
encompassed a logical extension- of the World War II Amy
i
|
Air Force Aviation Psychology Research Program of which
Guilford was the doyen. (Guilford and Laeiay,1947)
The Aptitudes Project's initial studies, of
| reasoning and of creativity, were followed by basic
j inquiries into the intellectual domains .of flexibility,
23
evaluation, verbal fluency, and planning abilities.
Subsidiary research in problems of educational progress,
selection, or classification were also reported but were
I not considered pertinent to the present study.
i
The first investigation (Guilford, Green, and
i
! Christensen, 1951 was of four categories of reasoning
abilities (1) induction, (2) deduction, (3) classifying
| ability, and (4) ability to manipulate symbolic material.
The tests of these factors employed items encompassing
verbal, symbolic, and figural material. These factors
j
i
I were classified under rubrics of concrete and abstract
■ -
j abilities. Thorndike (1926) had earlier trisected the
i
| intellectual domain into mechanical (concrete), abstract
i
I (verbal), and social (empathy) intelligence. In design
ing the study, although the authors reviewed known tests,
they resorted finally to constructing or adapting 21 new
tests to include as part of a battery of 34 measures,
since many known tests were'inadequate.
In a concurrent study, of creative thinking,
Guilford, Wilson, Christensen* Lewis (1951) state that in
* - - '
their search of the literature:
While much has been written about the creative
process there have been few experimental studies
and no previous factor“analytic studies reported
. . , very little ... is put out in a form that
could be verified and measured in the potentially
creative individual. It- was necessary to develop
a group of hypotheses about these abilities which
could be tested. (P. 2). . .
Although Gestalt psychology had emphasised
organisation and reorganisations! processes as key factors
| . !
with such fundamental questions as the interactions of
parts and wholes , the er eative*“ thinking study set aside
such Gestalt concepts for a factor“analytic approach to
| to such concepts as synthesis, analysis, flexibility, or
I
redefinition. Tests believed to measure these abilities
used verbal as well as figural material. Productive
thinking abilities were found in tests which measured
. Brick Uses, a verbal test, which requires
that a variety of uses'be given for a common brick, was
a measure of the latter, Match Problems, which requires
a specified nmiiser of squares or triangles was a measure
of the former. Synthesis was believed to be a unique
ability to organise parts into wholes. Such an ability
thinking (Wertheimer, 1945), when dealing j
the problem. Part**whole stimulus situations were related
what are now known as adaptive flexibility and
the examinee (E) to remove a number of matches and leave
called perceptual closure had been found by Thurstone.
In the.creativity study, although a conceptual synthesis
factor was also hypothesized none was found. In the
| factor analysis of the data the authros (Guilford, Wilson,
and Christensen, 1952) found
. . . the synthesis hypothesis, that had to do with
| the production of perceived objects was substantiated
! by factor F, closure. We expected to find Thurston®"s
| closure-I factor in this area. We were also testing
whether this ame factor would be so general as to
| appear in tests involving conceptual organizing or
I whether a separate synthesizing factor would be found
| in the realm of thinking. . . We believe that our
selection of tests gave good opportunity for both
analysis and synthesis factors to emerge in the
domain of thinking. Since our findings are negative
| ... they will probably require other types of tests
to discover them (p. 23).
| *^<2 closure factor that was isolated was defined by
Penetration of Camouflage, which required that hidden
faces be defected in a background of figural material,and
by Mutilated Words which required that partially erased
words be identified. A third measure of the factor,
Street Gestalt Completion, required that objects be
identified when portions of the drawing are missing.
The initial reports on the creative-thinking and
the reasoning studies represented the general theoretical
framework and experimental approach applied in subsequent
studies by Guilford and his associates on the Aptitudes
j Project in formulating hypotheses concerning primary j
abilities and the types of tests necessary to measure j
| I
j t h e m ,
!
Spearman (1927) had earlier shorn some concern j
about the proliferation of "faculties" being reported.
S Such-abilities as keeness in noticing resemblances, . or j
the power to break up a complex, or censorships or fore- |
sight, or the ability to rearrange a bit of mental content
were cited as being novel, but that "no attempt is made
to demonstrate, or even discuss their psychological
foundation and significance" (p. 34).
i ’
i ■ " " .
Following on the results of wartime armed services 1
studies, the profusion of factors being reported by other j
i
investigators embued with the possibilities of.factor-. . |
j
analytic technique indicated, that Spearman's concern my . j
|
not have been too premature. Although the work of the :
Guilford laboratory was oriented toward a search for a i
; !
| ' i
greater number of abilities than .suggested by either j
Spearman (1927) or the Thurstone concept of primary mental |
| abilities (1938), it appears from a review of the i
Aptitude Project's reports that Occam's injunction that |
27
entities should not be multiplied beyond necessity
(Boring, 1950) was well observed. The factors were
identified in terms of uniqueness (orthogonal simple-
I . •
| structure) and in terms of making sense psychologically.
\ A study of problem-solving abilities (Merrifield,
i
i Guilford, Christensen, and Frick, 1960) represented the
| last study reported in terms of the traditional rubrics
I
outlined above. The “new look" in exploration of the
aptitude domain is reviewed in a later section of this
I chapter.
i The organisation of human abilities
!
Although not specifically directed at factor-
j analytically-based trait theories of intellectual abili-
j ties, Anastasi (1943) also became concerned about the
number of traits that were emerging as descriptive
concepts but contributing little (in her opinion) to the
understanding of human behavioral processes:
It is our thesis that this diversify of trait
concepts is the result of an underlying methodo
logical limitation which has characterized not only
trait studies but many other types of psychological
investigations as well. The trait investigator has
usually asked: "What is the organization of behavior?"
or "What are the traits into which the individual's -
behavior repetory groups itself?" rather than asking
"How do psychological traits develop?" Much of the
i consent of psychology—‘ .including trait theories--
still consists of generalised factual descriptions
rather than principles of behavior. It represents
a cataloguing of responses within a specific. . .
s@ttings without reference to the conditions which
bring about such responses (p. 128).
I . . .
| Her objection to the factuo-descrlptlve approach
is that Intellectual traits, while showing greater con
sistency and ease of identification when contrasted to
emotional aspects of behavior, can be attributed to. the
greater cultural standardisation of activities. She
believed more understanding could be obtained, relative
! to the development of traits, by comparison of factor !
j i
j i
! patterns while systematically varying age, education,
! J
culture, sen, and occupation. The writer feels. Anast&si
Is correct in part, but what is varied must be decided in
.advance. Manipulating vaguely defined variables could
s
hardly contribute to the comprehension of the develop- |
mental processes Anastasi is seeking. Furthermore, the
writer has not found in his survey of the literature any
proliferation of empirically based systems or theories j
concerning the organisation of mental abilities. j
Although Professor Boring (1950) could have
alluded to a Zeitgeist calling for a greater unification
in the concepts of'the organisation of human abilities,
29
the writer suggests that a poltergeist might have been
j more apropos. The rapping for a cessation to disorder
!
j came with the International Colloquium on Factor Analysis
in 1955 in Paris. That meeting became doubly important
;
j because of the impending expansion of high-speed computer
facilities and their availability to psychometric labora-
I
| tories and a probable increase in the outflow of factor-
| analytic results.
I
!
i French (1951) had attempted to achieve some order
i
I ■ ' '
I by cataloguing descriptions of aptitudes and achievement
j
! factors reported by various investigators. He was instru-
| mental in organizing a conference at Princeton on aptitude
! j
I and personality measures (French, 1952) and organized the j
Educational Testing Service "kit** of selected tests of
reference aptitude measures (French, 1954). Hone of
i * - .
these efforts provided any theoretical organization that
would tend to integrate or unify concepts of the intel
lectual processes. Thurstone (1938) believed that a
small number of conmon-factors or primary mental abilities
1 was sufficient to describe adequately the aptitude domain.
Second-order factoring and oblique simple structure would
provide the parsimony necessary for preserving his system.
30 |
la the proceedings of the Paris colloquium Cattell
i
(1955) again introduced his "'Universal Inde^" for account”
lag for all factors in the total personality sphere,
including interest, temperament, as well as aptitude
factors. . In a manner somewhat analogous to the Harvard
i
i
Observatory, to which all newly discovered celestial bodies
are reported, Gattell would give.all newly discovered j
I
factors a decimally coded indes for future reference.
!
A student of Spearman, El Khoussy (1955) also j
presented his views on the organisation of abilities eon- !
earned with the visual perception of space. His discus- •
sion of tests of these abilities encompassed such cafcego-
| |
j ries as fora, content, and function. The latter term
I included the traditional categories such as induction, |
! !
! |
deduction, memory, and some lesser known rubrics such as
manipulations and visualisation. El Khoussyy places
space as a content with others such as figures, symbols,
numbers, words, time, or situations.
It ms at this same meeting that Guilford (1955)
presented a discourse on classification of the dimensions
of intellect, which later received elaboration and wider
dissemination in a Psychological Bulletin paper (Guilford,
31
1956) a® "The Structure of Intellect.”
Incorporated into Guilford's system are Spearman0®
three fundamental laws of awareness, eduction^of relations,
i —
and the eduction of correlates. Subcategories of cognition
concern the different classes of relations, the different
kinds of fundaments entering into such relations and the
ways and complexities in which relations and fundament®
interact. Concepts such as span, retentivity fatigue,
conation, and primordial potencies are other aspects of
lawfulness in Spearman's complex system of abilities.
Guilford (1956) alludes to similarities between
his system and Burt's (1949). The similarities of
organised systems lend further weight to the conclusion
that theoretical organisations of abilities are not merely
artifact® of the encyclopedist, but may possibly represent
"natural” classification systems in psychology as the
Periodic Table of Mendelleeff, discussed in the previous
chapter, does for chemistry.
Although Eysenck (1951) and Moursy (1952) present
organisational theories of human intellect based upon
factor-analytic experimentation, with the exception of
Cattell*s Universal Index, the structure of intellect
appears to be. one of the few trait theories which maintain j
| the scope as well as the rigor of a scientific j
l
! psychological theory.
| |
! The evolution in the conceptual framework of |
| Guilford3 s model was reviewed in terms of two Aptitudes
, |
Project reports incorporating the " anew look3 3 of the i
i
I
theoretical organisation of factors across operations, I
I
i
contents, and products (Guilford, 1957, Guilford and j .
Merrifield, I960). Although not directed as a response
;
to Anastasi3s (1948) comments, in a presentation to the j
Hew York Academy of Sciences, Guilford (1960) emphasised
; i
knowing what aptitudes is propedeutic to subsequent
; .
! analyses of thinking involving the how3 s and why3 s of :
j
development, function, or purpose. It would appear, at j
!
first glance only, that one is again confronted with the - j
classic litchener (1948) polemic against functionalism j
as the antithesis of scientific psychology. In that i
I
celebrated discourse, Titehener insisted that the- search j
for the contents of consciousness was the basic task for j
the true experimental, scientific psychology. He likened
structuralism to isorphology in the biological sciences
while functionalism was paired with physiology; scientific.
33
psychology could not proceed to function until more was
known about what were the basic elements of consciousness.
j
Although Guilford*s theory introduced no systematic
position relative to behaviorism, functionalism, or other
!
i classic schools of psychology (Heidbreder, 1932) he.
I indicates that the informational approach of structure-
i
!
| of-intellect theory is a central rather than peripheral
!
| psychology. Guilford (1960) states that the model goes
j "well beyond the time-honored explanatory concept of
! association" (p.'11). Information is regarded in the
I
t
I theory as that which the organism discriminates. He does
I
i take a systematic position with respect to one of the
i
I dimensions of the model:
|
j The products of information . . . are not best
interpreted as varieties of association . ... but
rather in accordance with the thinking of the
psychology of Gestalt, without necessarily adopting
all of the Gestalt principles . . . (p. 12).
I
As a central psychology, the processing of
i
information lends organization to what is produced, and
in this sense is compatible witha Gestalt viewpoints
although the idea of analyzing behavior into unitary
components or traits would be rejected by proponents of
that school.
In seeking- comparisons of isones between
behaviorists, gestaltists, and other systems, no fruitful
I
!
result could obtain, since the writer would In a sense be j
2 ’ beating a dead horse.c s The survey of the literature j
i
turned rather to those experimental studies with a "new i
look" generated by strueture»of“intellect theory. !
Merrifield, Guilford, Christensen, and Frick (1960)1
state that when the problem-solving study was initiated, I
i
circa 1956, "the structure-of“intellect theory had not
been developed to the point where it-was thought capable j
of serving as the sole source of hypothetical intellectual j
i
abilities" (p. 5). They indicate that in examining the j
concepts of problem-solving, however, that they did
3
attempt to guess which of the known factors or structure- j
I
of-iatellect cells, were Implied, as the study ms j
i
i
primarily oriented toward establishing which primary j
abilities might enter into the concept of problem solving, |
per se. In reporting their general findings, however,
structure-of-intellect terminology was assigned to the
factors identified. The cross-referencing of factors was
j
phrased in terns of alternative hypotheses. These did
| not enter into any of the theoretical implications of
i the Guilford model other than the indications that the
factors defined represented unitary constructs with
' ! positions in cells in the structure-of-intellect model.
i
|
| One new factor, the convergent production of semantic
j classes was a coincidental finding of the study. The
authors indicate that this was the first indication
"that there are any distinct class-production factors”
(p. 25). One measure of this NMC factor, Word Grouping,
i
i
i required that each word of a given list must he used only
!
; once in entering into a few mutually exclusive classes.
!
i
| The emergence of the factor with such tests led the
i authors to suggest that future plans would call for a
!
i
study of classes "across the board” (p. 25), meaning in
the classes row of all operations, across all contents.
The first study based uniquely upon hypotheses
generated from the strueture-of-intellect model was
directed toward the symbolic-content category. This
category had been originally (Guilford, 1956a) termed
"structural.1 ® In the matrix including five operations
columns and six product rows are at least 30 possible
symbolic factors, but only eleven had been previously
identified. Since more was known about verbal and
I
j figural abilitiess the 19 empty symbolic cells of the
model offered a relatively fertile area for empirically j
i i
| determining the (Guilford, et al., 1960) "fruitfulness of j
the . . „ theory as a source of hypotheses to be I
r
investigated” (p. 2). It had been thought that the study !
of symbolic thinking would be of significance in con=> |
nection with language and mathematics including symbolic
;
logic. The study hypothesised fi,ve factors, for which 14 j
. new tests were developed, and included measures of seven ■
i ' .
;
! reference factors. Only abilities of symbolic content
i i
; i
and semantic content, and of cognition and convergent
j production, were investigated. Four of the five pre-
I :
| dieted factors were found. The value of including ;
! t
j |
reference factors was substantiated since nine new tests i
i
* !
loaded significantly on them. The authors concluded that j
;
the model as a source for hypothesising new factors stood i
i
i
the test well. '
!
i
A more distinct separation of symbolic and I
| semantic factors was obtained, with all but one of 18
! ■ |
cognition cells and 12 of 18 convergent“production cells j
i
being occupied. Specific hypotheses concerning empty j
! 37
| cells of the model and concerning the type of tests that
i might measure them became henceforth the primary expert**
! mental strategy and orientation for the Aptitude Project
i
I research staff. Of particular interest was the definition
j of the cognition of symbolic classes (Guilford et al.,
!
| 1960) which was one of the four new factors isolated in
I the study:
!
i
... we see that a symbolic class may be composed of
| single numbers having a common property (Number Group
I Naming and Number Classification)„ pairs of numbers
with a common relation (Number Relations), and
common letter or number systems (Letter Grouping and ■
I Number Series Correction). . . (p. 21). |
i
: The authors point out that the class feature of the j
I . . !
| Number Series Correction test is not obvious. They j
; I
! !
i state that the series of numbers in each item could in a
i
i
1 sense be regarded as a set or relations between numbers.
j
I ■ ' !
| In the test the examinee must find a number in a series
of five or six numbers that does not follow the rule for
■
the entire series. In their discussion of the same
factor (CSC) they point out that Letter Grouping also
contributed to the definition of this factor. They also
state that "The presence of one letter test in the list
for factor CSC indicates that the factor is not confined
|
to number tests." (p. 21). This finding, that both j
I
t
t
‘ ------------- — ------- M -----------------------------------------------------------f
38
letter and number tests jointly determined CSC was believed
i
to be ©f importance for test construction Ideas in the
further exploration of symbolic abilities,
!
!
The study entitled "Creative Thinking in Children
|
at the Junior High School Levels" (Guilford, Merrifield, |
:
and Cox, 1961) sought confirmation of' divergent-production j
abilities in groups younger than heretofore used as j
i
subjects for factor-analytic studies by the Aptitudes- j
!
;
Project. Measures of six semantic factors, two figural,. j
and two symbolic, and of a semantic-ev&luation factor
j (EMI), Sensitivity to problem, were used.
j ■ ;
In this "creative-adolescent study0 8 eleven factors :
were identified in two samples of about 700 and 220 boys
and girls in the ninth grade. Findings included clarifi- j
cation of three factors by the use of new test ideas
i
suggested by the theoretical model. The factors appear !
to be of potential importance for early identification of
creative talent. An additional finding was that, with
these factor-unique tests, individual differences in
abilities say be defined irrespective of sex or level of
"giftedness," in terms of IQ.
The extension of structure-of-intellect descrip
tions to younger groups was taken to provide further
{Confidence in the model as a "natural" classification
j scheme.
!
Several studies employing adaptations of the new
i
|
divergent-production tests designed to measure three
j
|contents were also reviewed by the writer. Schmadel (1960)
|used a sample of 600 sixth-grade students to relate
measures of achievement with adaptations of several new
I |
|figural and semantic divergent-production tests. Her j
| !
I attempts to relate her findings to Bloom1 s taxonomy j
! . !
|(Bloom, 1956) were inconclusive. A subsequent factor- j
| j
j analysis of the data (Merrifield, Guilford, and Gershon,
I . I
j 1963) indicated that the modification of the adult forms j
] I
I of the tests resulted in identification of several
I |
: semantic divergent-product ion abilities (DMU, BMC, DM5,
! j
i j
i . |
| DMT and m i .
|
Lauritzen (1963) in a cooperative study with the
I
jAptitudes Project staff used a number of divergent-
production tests, including Figure Production (DFI), three
DMI tests--Planning Elaboration, Alternate Signs, and
Possible Jobs, and Plot Titles (DMT) and a revision of
Consequences, (DNT). The latter two tests were also used
as measures of DMU. Her tentative findings indicate that
40
! individual differences in these basic aptitudes are
differentiated at £i£th=grade levels when sufficient
internal“consistency reliability is obtained with the
!
I test measures.
Two studies in the literature, that were not under j
j the aegis of the Aptitudes Project were reported by
Torrance (1962) and by Getaels and Jackson (1959) who
used tests from the structure-of-intellect model in their j
investigations of creative abilities in school children.
| These authors appear to have adopted strueture-of-
intellect terminology such as convergent and divergent
new factors but incorporated the concepts of Guilford
Another study employing structure-of-intellect
concepts (DeMille, 1961) was concerned with differences
in factorial patterns in institutionalised subjects. A
sixteen-variable battery of strueture-of-intellect tests
matched to 150 schisophrenic controls. BeMille found
somewhat dissimilar factor structures in each sample. The
thinking in describing creative abilities in the popula-
t ions samples. These authors did not attempt to isolate
and his associates in their investigations.
were administered to 150 lobotomised sehisophrenies group- I
41
I most striking difference being that spontaneous fleas!-
| bility (DMC) was found in the lobotomized group in which
i
they resembled the "normals.8 1 The lobotomized group,
however, showed greater impairment in other factor-
I
I defined tasks.
Although the three foregoing studies (DeMille,
| 1961; Getzels and Jackson, 1959; Torrance, 1962) did not
I contribute to the isolation of new factors for placement
| in the theoretical model, it was considered pertinent to
I the present investigation to determine in which kinds of
I populations structure-of-intellect tests could be fruit
fully employed, it was concluded that with appropriate
| modifications the factor-tests were not restricted to the
i
! more highly educated levels such as college students and
I
I military officer-candidates. This was further substan
tiated by the Lauritzen (1963), Merrifield (et al., 1963),
and Schmadel (1960) studies with children populations in
the elementary schools.
Factorial Invariance
In reviewing the methods of comparing ability
patterns, it was found that Thurstone (1947) had indicated
a number of seeming paradoxical statements. Thurstone8s
42
viewpoint is perhaps best encapsulated in the following:
i
J
fhe exploratory nature of factor analysis is
often not understood. Factor analysis has its '
principal usefulness at the border line of science.
It is naturally superseded by rational formulation
in terns of the science involved. Factor analysis
is useful, especially in those domains where basic j
and fruitful concepts are essentially lacking and I
where crucial experiments have been difficult to j
conceive. The new methods have a humble role.
They enable us to make only the crudest first map
of a new domain. But if we have scientific intuition |
and sufficient ingenuity, the rough factorial map
of a new domain will enable us to proceed beyond
the exploratory factorial stage ... (p. 56).
tilth respect to invariance, he discusses two kinds}
metric and eonfigurafcional. The latter referring to
similarity of factor patterns while the former referring
to constancy of a test loading on a factor. Again,
I
Thurstone is quoted as an indication of the bias of the
i
writer of this study in searching the appropriate litera- I
j
ture to the needs of the investigation (Thurstone, 1947): j
. . . the factor loading cannot be expected to be ;
invariant from one population to a different popu
lation. Any criterion of invariance In factor j
analysis assumes that it is applied to analyses on j
the same population or to equivalent populations. j
In psychological analysis this principle means that
factorial composition cannot be expected to be j
invariant for different age groups, for example or j
different groups of subjects, selected f e y criteria j
that are related to the factors involved. (We shall
•see later that the configuration may remain invariant
for different populations, but we are here concerned j
with the numerical invariance of the factor loadings |
(p 361). !
j The experimental problem set forth in the opening
!
!chapter of this investigation suggested that patterns of
factors might be found to be similar even if such seemingly
;different groups as military officer-candidates and junior-
I high-school boys and girls were used as subjects. It was
i also found in the studies reviewed earlier in this
[ ■ I
| chapter that factors found previously in high-level adult
populations could also be isolated in younger population
| j
| samples as well where interpretations of similarity were
I ~ I
I based upon rational and inspectional procedures. The j
| i
search for more rigorous indices of similarity led to the
writings by Cattell (1949), Tucker (1951), and Wrigley and j
' ■ ■ !
jNeuhaus (1951), all of whom have essentially the same j
I solution. Burt (1932) had previously attempted to demon-
I
| strate similarity of two sets of loadings on two axes
by computing a Pearson product-moment correlation;
Cattell"s (1944) shape correlation coefficient is
essentially the same. He later (Cattell, 1949) demon
strated how a coefficient of pattern similarity (for
comparing two profiles) could also be applied for
appraising the similarity of factors. Wrigley and
Neuhaus (1951) offered a formula similar to that for
44
Tucker5s coefficient of congruence. The essential
difference between these and Burt's indess is that values
are not derived from deviations from the means. They
represent the ratio of the sum of the cross-products of
loadings on two factors to the square root of the product
of the sum of squares of the loadings.
The term B 0 index of factorial similarity6 5 intro
duced by Urigley and Neuhaus (1955) would seem more
appropriate than the tern "coefficient of congruence"
suggested by Tusker (1951). The latter*s more complete
formulation is encompassed within considerations of
synthesising two factor matrices from separate studies
to obtain an indication of the "congruent common”factor
space,6 0 which is a further means of indicating factorial
i invariance;
i
The term congruence is used in this development
to indicate a lower level of precision of coincidence
than is associated with its use in geometry, lather
than meaning that an exact fit of one matrix to the
other has been obtained, approximate fit is to be
indicated by the tens. Two matrices will be con
sidered as congruent if they are generally similar,
with only relatively small differences (p. 18).
Pervading most discussions of metric invariance,
however, is the ubiquitous statement that a theoretical
i
distribution for determng the statistical significance
45
I of differences between factor loadings is yet to be
i
j demonstrated in any practicable fashion (Maxwell, 1959),
i although I.awley (1949) attempted to provide a method for
l
j
j eatimating standard errors of factor loadings.
;
One phase of the literature that was not reviewed
j by this writer to any significant degree pertained to
j
methods of rotation of axes. Much has been written in
recent years relative to the merits of analytic solutions
as scientifically objective procedures (Carroll, 1953;
| Harman, 1960; Raiser, 1958; and Saunders, 1953). It
! appears that the Raiser (1958) requirements for the
| varimax solutions, would necessitate inclusion of at least
| five measures of each factor in order to cassure that
! ?
I It was " over determined.” The Aptitudes Project had found
I
i
| that the scope of studies would be severely limited if
the Raiser criteria were observed. Test batteries
exploring a factor domain would be inordinately long.
The Thurstone (1947) concept of achieving a compelling
solution through the qualitative criteria of simple
structure appears to have provided the more satisfactory
solutions (Guilford et al., I960®).
The preceding discussion has indicated that the
wartime Aviation Psychology Research Program had provided
i the impetus for the Aptitude Project research on primary
mental abilities in high-level personnel. With the
promulgation of the strueture-of-intellect theory an
increased research endeavor was initiated. Growing
I
scarcity of military populations of appropriate kinds for
factor-analytic studies led to the use of school children
(Guilford at al., 1960) in the ninth grade and even
younger samples (Merrifield and Gardner, 1963; Merrifield
at al., 1963) as test subjects.
| Although tentative findings had indicated that
| such populations were adequate (Schmadel, 1960), it had
| been indicated that ability patterns varied with age. The
j work of Thurstone and Thurstone (1954) had shorn that
i
school-age children were adequate for exploratory
experimentation and many of their conclusions were based
upon such samples. Garrett (1946) has stated that general
intelligence undergoes greater differentiation as the
j child grows to adolescence. This developmental theory
was supported with results of a battery of six memory
47 S
i
i
tests and four tests to measure verbal, numerical, and j
| ■ I
| spatial abilities and speed of response. Groups of boys
I j
| and girls aged 9, 12, and 15 in New Jersey schools
| composed the samples. Garrett, Bryan, and Perl (1935)
had earlier reported:
| ... With increases in age, the abilities measured
by our tests tend to become more specific. This j
is shown by a study of the average iutercorrelations {
of groups of tests, and by multiple factor analysis
of the correlations. Four factors were calculated . j
... Of these factors, only the first was large j
enough to account for any appreciable share of the
I variance of the battery. This first factor exhibited
a consistent decrease as age increased from 9 to 15
years .... As a tentative explanation of the
drop . . , it is suggested that in young children j
ability is amorphous to a greater degree than during |
later growth periods (p. 412). I
Garrett (1946) provides additional data from
| studies with Chicago Tests of Primary Mental Abilities to
show that correlations among the tests of six factors
(V, N, S, W, M, and R) showed a regular tendency to drop
i
with age. In his Presidential Address to the American
Psychological Association he goes on to state ”I do not
think that at elementary school level we should attempt,
except very tentatively, to fractionate the IQ into say,
language ability, number ability, reasoning and the
like” (p. 377). Garrett points out several paragraphs
48 I
:
i
| later, however, that at high school and college levels,.
intelligence does break down into independent factors
! and that mental measurement should not hold to a unitary
: I
IQ assessment. I
i The studies reviewed for the most part have
I i
| tended to agree with the Garrett hypothesis. Gardner i
| (1963) found that IQ was an adequate measure of rated j
! j
creativity in comparison with strueture-of-intellect
tests applied to seventh-grade children.
i :
| Perhaps the clue to the Garrett findings may lie
I
i
j in a report on the Berkeley Growth Study (Bayley, 1955)
!
I
J which asks "Does a heavily-loaded first factor show a
I characteristic developmental process of change?" (p. 810). :
| ;
| Although Bayley does not discuss Garrett8s data, it is
: clear from the quotation presented earlier that he has ;
performed a factor-analysis but that the interpretation '
|
and conclusions about the factor structure and the change j
j
in intelligence are not based upon comparison of factor
i
patterns. The interpretation is based upon a shift in j
i |
the percentage of variance accounted for at each age level |
by the centroid equivalents of principal components. It j
would be,of interest to refactor his correlation matrices j
| 49 I
! I
i
j
and rotate the principal components to a simple structure
: and to compare the resultant factor patterns intuitively, !
! !
| as well as by some measure of congruence.
I
!
In support of the Garrett hypothesis, are the
!
results of Balinsky (1941) who inspected variations in !
I !
i
jfactor patterns on the Wechsler-Bellevue Intelligence
I Scale for groups ranging in age from nine to sixty years.
I !
I He finds that the number of factors increase slightly
i i
with increasing age at the pre-adult levels. Somewhat
; ambiguous are the data of Jones (1949) who interpreted j
; ■
! . i
factor patterns on. the Standford-Binet Scales at ages 4, 9,
! ;
11, and 13, and found little change, although support for j
i ■ |
i the developmental theory is expressed. Chen and Chow j
! . I
i !
! (1948) find that there is decrease in the number of |
; i
: ■ ;
| factors as age increases. Thurstone (193S) and Thurstone |
1 and Thurstone (1941) show similar factor patterns at j
various groups from age 5 through college. Thurstone
j
(1955) views the problem not as one whether the abilities
exist at certain age levels (5 to 19 years) but finds the
I ' .
important question to determine the differences of rates
of maturation of mental Abilities: j
• I
Instead of trying to determine which is the best
method of teaching reading we might discovers that
| 50
!
j . i
; children of different imagery types would learn to
| read best if the teaching method were adjusted to -
the child’s imagery type. Some children are aided
| by visual devices while other children are annoyed !
! by them (p. -4). '
: Using a Gomperts function to illustrate his !
‘
| findings, Thurstone (1955) reports:
I
I ... we have produced all .seven of these mental
! growth curves to the same scale where unity represents I
I the asymptotic adult performance. From this figure !
I we can make a rough comparison of the rate of matura
tion of these abilities. For this purpose we note
I the age at which the average mental growth curve
reaches four-fifths of the adult performance (p. 4).
i ■
He indicates that with this criterion the Per-
i
!
eeptual Speed factor reaches 80 per cent of the adult,
performance at the age of 12. The Space and Reasoning
i
| factors attained the same relative performance at the
age of 14, while the Humber and Memory factors reached
I i
| the four-fifths level at age 16. The.Verbal Comprehensioni
; ; !
and Word Fluency factors were the slowest to mature,
L
reaching the same relative level at ages 18 and 20,
I
respectively. Of particular importance to the present
i
investigation dealing with figural material was Thurstone'&
!
(1955) observation that ® s In other studies it has been j
found that the first Closure factor reaches adult level • !
!
at about the age of 10 or 12, so that children of that
|
j age do as well on the average as educated adults” (p.4). i
Meyers, Orpet, Attwell, and Dingman (1962) j
i administered a battery of 13 tests, hypothesising the four
! j
factors of reasoning, linguistics, perceptual speed and j
| i
hand™eye psychomotor abilities to 100 six year old school
children and to 100 institutionalized retarded subjects
i
I with average mental age of 6 years. A "divergent” or
!
i j
| expressive language factor was tentatively found isolated
| in the normal group only and five other factors were j
i
;
I found in both groups. The authors conclude
| • !
Results were such as to suggest that properly imple-
mented studies can discover a rather large array of
factors and that, at the developmental stages in i
question, differentiation of abilities is already
well advanced, (p. 2 2)
I • i
O'Neil (1962) has presented an interesting j
! j
: f
analysis of the Balinsky (1941) data and ascribes the
I changes in factor loadings to variations in the lengths
I ' I
i of test vectors. This is accomplished by inspection of
the two"dimensional plots of the first and second centroid
factors for four age levels: 1 2, 15, 25 to 29, and 35 to
44 years. He employs a graphic technique for determining
ability differentiation by inspecting the angular separa
tion of test vectors. O'Neil used Balinsky*s data on the
.
Wechsler-Bellevue subtests to demonstrate that angular
52 |
separation of test -vectors remains relatively constant
although variation in length of the vectors vary. He j
i
attributes Balinsky's conclusions relative to the Garrett j
i
hypothesis to differences in vector length, which he !
!
finds inappropriate for supporting a differentiation
theory of mental development. i
The search of the literature was directed to
three principal questions: (1) What could be derived from
previous studies that would indicate appropriate test
ideas for dlvergent^production abilities suggested by
the model? (2) How appropriate is the description of a
unitary ability found in adults for a factor defined by
the same tests with samples of children? (3) Does the
experimental literature reflect satisfactory means for
comparing factor patterns in different populations or
samples when a fixed battery of tests is used?
1. The literature reviewed, mainly the research
reports of the Guilford laboratory, indicated that
unitary abilities hypothesised by the strueture-of-
intellect model could be measured with tests suggested
by the descriptive terns used to specify cells of the
model. In addition, new test ideas appear to be usefully
derived from the format of tests for known factors. In
j
general, measures of unitary abilities are best obtained
I |
i when the new tests are constructed to the specifications
i
of the factors. Tests adapted from studies which did not
■ I
; !
i have factor“analytic orientation appear to be too complex.
| In general they are limited to operations of cognition or
i
j convergent production, and mainly of a semantic or verbal .
|
i character.
i
! i
2. The studies reviewed, those supporting and j
i I
: those refuting Garrett's developmental theory of intelli“
gence, have employed fixed test batteries at the various
i age levels sampled. The findings of these studies present
■ i
i |
j conflicting points of view. The position of adolescent
:
j groups on non-verbal factors appear on growth curves
| closer to the levels for adults than do their positions
on verbal factors. High school samples generally appear
to occupy positions on such curves close to the asymp“
I totic levels of adults on all abilities in the narrow
t I
categories of aptitudes described by Thurstone FM&. It
was concluded that investigators tend to define the same
abilities at all age levels, in school children and in
adults.
! 54
3. Alternatives to simple structure as a basis
j
| for determining factorial invariance are subsummed under
| two categories of investigation: (a) those which depend
|
i upon analytical means of rotation which do provide
invariant results (numerically) when the same factor
matrix is rotated upon different occasions, and (b) those
which reflect the degree of numerical invariance by some
index of similarity or coefficient of congruence. The
!
i studies reviewed do not indicate that the analytically
|
rotated solutions necessarily provide the psychological
; sense to the solutions they produce, although the
| solutions are rigorously replicable. It was found that
configurational invariance, determined by logical or
intuitive comparison of factor patterns served as the
i
primary criterion for determining whether factors were
similar when defined by the same tests in different
studies.
Figure 1 represents the status of cells in the
divergeat“production matrix prior to the completion of
i
the present study.
Products
Figure 1
Divergent-Production Matrix
Content
55
Figural Symbolic Semantic
Units H
R
Classes
Relations
Systems
Transformations
H H
H
R
R
HR
Implications H R
Diagram of the divergent-production matrix showing
positions of factors under investigation in this
analysis. H 13 previously unexplored factor. R ™
factors previously confirmed. The ? indicates the
cell remains to he investigated. Behavioral Content
is not indicated as no factors have been confirmed
to date.
CHAPTER III ' |
!
THE HYPOTHESES
i
i
I
The unified theoretical model of'intellectual |
I
I
abilities is described as a tri°dimensional system in j
j
which each cell is defined in terns of the intersection j
|
of “values5 8 on the operations, content, and product j
i
parameters. The formal hypotheses presented in this
chapter relate to the demonstration of those abilities
not previously isolated and to the new experimental tests
constructed to define those factors or abilities. Other,
hypotheses relative to the comparison of the obtained
factor patterns are also presented. Alternative hypoth- ;
f
j eses are discussed in terms of implications for the
theoretical premises of this investigation and the inter-
i
probation of the factor-analytical results outside the
context of structure-of-intellect theory.
Statement of the Hypotheses
Three major hypotheses were formulated for this
I
!
study;
56
...... . 57
the primary hypothesis, states that
previously unexplored divergent-production factors !
defined in terms of the strueture-of-intellect model can j
be isolated by tests that derive their operational formatj
i
and content through two approaches used jointly or j
separatelys (1) by analogy to other tests in adjacent or
; parallel cells in the model, and (2) by specifications of
i
the tri-dimensional operational definitions of structure-
! \
| of-intellect theory in terms of operation, content, and
!
| product.
i
I
! Hg, a secondary hypothesis, specifies that a
test battery measuring primary abilities in adults would
i
be applicable for measuring individual differences along
similar dimensions in a population of adolescents. This
prediction is in apparent contradiction to the Garrett
developmental theory of intelligence.
A third hypothesis, H3 , subsummed in part under
Hg, specifies that reference axes identified by the same
i
factor names in the two populations would be confirmed
as similar not only by rational or intuitive cross
comparisons, but also by more rigorous, statistical
appraisals of congruence or similarity.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .- - - - - - - ■ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -1
..................... 58
In addition to predicting the existence of
I
several previously unexplored divergent“production
factors, strueture-of“intellect operational speeifiea- j
j
tions for new experimental tests are classed as subhypoth- j
eses under major hypothesis, Each test would be
i
treated statistically as a relevant variable as well as j
one hypothetical measure of a predicted factor. For the
balance of the discussion in this study each test measure
is assigned an identifying number based upon its alpha-
betic&lly ordered position, and is discussed in terns of
the factor it is hypothesised to measure.
An initial step formulated to test the first
hypothesis was the generation of test ideas. The
i
rationale and format and content that led to the final-
battery of experimental and marker tests are discussed
under the heading "Hypothesized Test Measures.”
Since several authorities (Harman, I960; Maxwell,
1959; Michael, 1949) had pointed out the lack of an
adequate method for determining or estimating the'stand
ard error of factor loadings, the hypotheses will not be
discussed in probability terms. The secondary hypotheses
(Hg&ud H3) were ascribed two "levels of confidence” for
59
their possible acceptance: The first level* admittedly
scientifically questionable, bases the criterion of same~
j
ness of factor patterns upon the sophistication of the j
experimenter and his ability to inspect both patterns in j
order to render an opinion of similarity. j
j i
j The second level is limited to the relatively
unrefined but "objective” indices of comparability that
had been suggested by several investigators. These
indices were discussed in Chapter II.
The second hypothesis (H£) which represents a
prediction of invariance of the dimensions in the experi-
mental test battery, is couched in somewhat general terms.
It did explicitly proscribe, however, that the same
variables of individual differences are measurable in
I both populations and that a test of the similarity of
meaning of measures of those variables could be made.
It was predicted by the third hypothesis (H3)
' i
that the factor structure in the two populations obtained
from performances on a fixed battery of tests would be
essentially descriptive of the same mental abilities.
Interpretation of factors would be based upon the three
criteria normally applied by the USC Aptitudes Project in
60
the graphic orthogonal rotation of factor axess (1) posi
tive manifold, (2) simple structure, and (3) a knowledge
of the marker tests, the emerging factor pattern, and the
greater psychological meaning to be derived from further
adjustive rotations. Although logical and intuitive
considerations might lead to the conclusion that factors
with -the same names in the separate rotational solution
would represent the same hypothetical constructs, it was
i
i
predicted that application of such indices as Tucker's
(1951) coefficient of congruence would provide a more
rigorous test of similarity.
Implicit in both hypotheses (Eg and I3) is the
expectation-that evidence would be obtained concerning
the invariance of factor patterns across populations of J
t [
different ages. In.vies? of the discussion .in Chapter II,
relative to the findings of Garrett (1948), and Gardner
(1963), of Guilford and his associates (Guilford et al.,
1961), of Sehmsdel (1960), and of Lauritsen (1963), it
would appear that administration of the same test battery
to adults and to adolescents would provide more defini
tive inf ©mat ion concerning the conflicting theoretical
positions over factorial invariance. It would also extend
such a study to include new factors.
i
Current Status of the Theoretical Model
At the time the present study was initiated, 1958,
approximately 45 factors were placed in cells of the
structure-of"intellect model. The symbolic study and the
creative-adolescent study (Guilford, et al., 1960a; 1961)
j contributed six additional factors, not previously identi-
jfied, for placement in the model.
j Where the symbolic study had shown a clear dig-
I crimination between factors of symbolic and semantic
!
content and the creative-adolescent study had shown clear
separation in the divergent-production matrix of a figural
and a symbolic factor from corresponding semantic factors,
it was similarly anticipated that this study would differ
entiate clearly certain additional factors of figural and
symbolic content. The primary objective of this study was
the investigation of factors within the structure of
intellect that had not been previously explored. It was
assumed that the constructs which were represented by
cells of the model consisted of at least one factor or
intellectual aptitude per cell.
62
Evidence about the measures of the divergent pro-
duetion of symbolic units, and the divergent production of
symbolic systems had.been obtained; a number of old and
tion of figural transformations and the divergent produc°
exception of the cells of behavioral content, four cells
of figural content and four cells of symbolic content
required exploration to complete the definition of the
divergent^production matrix of the model.
The Tri-dimensional System
The divergent“production operation category was
defined in Chapter 1 as that group or class of abilities
in which a given amount of information is used as the
basis for .generating a variety of new information; this is
contrasted with the convergent“production abilities which
are concerned with the generation of an accepted, or anti
cipated, .or best solution from given information.
The format of tests believed to be best suited to
the measurement of divergent“production factors are of a
completion or B B op@n“end®3 variety in which the examinee is
required to write or draw Ms responses in contrast to the
! new&tests had successfully defined the divergent produc
tion of . 1 implications. Therefore, with the
63
coBBHon multiple-choice £onaat in which the examinee
selects responses from a display of a limited set of
possible responses. It was believed that certain varia
tions of the multiple-choice format might be applied and
be of practical value provided all probable answers were
included among the choices. If the factor could be
adequately measured by tests in such a format, consider
able energies could be conserved in the scoring process in
addition to simplifying the mode of response for the
examinee.
Figural content in the theoretical model is
concerned with the varieties of perceived information in
a concrete form such as lines, figures, patterns, or
images. The information in symbolic content takes the
form of signs such as letters of the alphabet, nusobers, or
musical notations Which have no meaning or significance
in or of themselves. Such signs were to be distinguished
from pantomimic gestures in the nonverbal, behavioral-
content column of the structure-of-intellect model, which
might be a substantive for a thought, desire, or command.
The product as well as the operation and the
content are specified for each ability in the three-way
” 64 ' "]
i
description of & factor. A product is defined as the form j
i
of the information that results from the organism's i
i
processing of information (Guilford and> Merrifield, 1960).
The development of a test battery hypothesised to measure
the factors selected for investigation in this study
required that all sis product categories be included:
units, . classes* relations * systems, t ransf omat ion, and
implications. A review was therefore made of the status
of products which apply to 18 cells of the divergent"
production matris:
Units: The divergent production of,figural units
was the only undesaonstrated factor in the units row of the
divergent"production matrix. In Figure 1, it can be seen
that the symbolic“content and semantic-content factors in
parallel cells had been previously isolated.
.Classes and Relations: The cells of the figural
content column', the divergent production of f j
classes and the divergent production of symbolic relations
L'-.'i u i . i a a i M M ^ i i i i i s q * • ,t* -1 i*i!hiiii 'i wi"— «mi nw tg a ^ o d B S S B n o s g n s B n a iw m ii■ im w j t t t W i
also required investigation. The failure to develop
appropriate test ideas for the DFR factor, however,
required that the search for further evidence for this-
factor's marker tests be postponed for a future
/
"65
investigation.
Systems In the creative-adolescent study
(Guilford et al., 1961) clarification was sought for the
presumed marker tests of the divergent production of
symbolic systems. The study resulted in shifting some
marker tests to the adjacent semantic-systems cell.
Therefore, in the systems row, the divergent production of
^ ■ » ini m w i 1 1 * B B B D
figural systems was the only cell which had no previous
exploration, although the status of the symbolic^systems
cell requires future clarification.
Transformations: In the creative-adolescent
study, clarification was sought for the divergent produc
tion of figural trans format ions by using variations in its
known marker tests. It was thought that further experi
mentation in format, instructions, and scoring might
result In more efficient measures of this factor.
Although the adjacent cell in the symbolic-content
column, the divergent production of symbolic transforma
tions required verification, the lack of appropriate test
ideas required that the study of this factor be postponed.
The parallel semantic-content cell, the divergent produc-
tion of semantic transformations had been identified in a
66 |
number o£-studies by Guilford and his associates (Wilson j
et al., 1954; Guilford and Christensen, 1956). It was
■ |
decided to develop more efficient marker tests of the DFT j
factor. She known abilities and those to be found in each j
!
cell of the transformation product across all operations
was considered important for measurement of creative
thinking (Guilford, 1959).
Implications; In the sixth row of the divergent-
‘ ' ' ■ 1
production matrix only the divergent production of
symbolic implications required investigation. The
creative-adolescent study had clarified the distinction
between the figural and the semantic factors in the row
by analysing new experimental tests along with the
previously known marker tests. That analysis resulted in
the clear delineation of the two factors and their
respective tests leaving only DSI to be defined.
From the review of the status of the model, if
I
appeared that eight previously unexplored divergent-
production factors still required verifying test data to
establish their identities. The investigation of two
factors, BFR and BFT, was suspended from consideration,
since known tests did not appear to be likely candidates
as measures of the factors. To develop promising new
test ideas to measure these factors did not appear feasi-
!
ble either within the time schedule for the study. In
addition to the six factors for which tests were forth
coming, one previously explored factor was also desig-
| mated for further clarification.
!
!
! Hypothesized Test Measures
i
I
|
| The DFU cell. "Units*1 are defined as "relatively
! segregated or circumscribed items of information having
thing character** (Guilford et al., 1960^>). in the
| semantic column, the factor of divergent production of
semantic units is measurable by a test in which the
I
| examinee is called upon to produce a list of objects that
| are "round and edible." The factor has been called
i _ -
ideational fluency by Thurstone (1948). The parallel
symbolic factor in the units row has been defined by tests
which require the examineer to produce words beginning
with some specific letter, or to produce a variety of
words with the same suffix. This factor, isolated by
... ... . . .
Thurstone (1938) is called word fluency. Both these
factors were found to fit in the appropriate cells of the
' 68 1
structure of intellect. Therefore, in using the system j
of analogies suggested by. the theoretical model, it would
appear that a test to measure the divergent production of
figural units would require the examinee to produce a
variety of graphic responses or drawings under conditions
which are as relatively free from restrictions as in the
parallel semantic- and symbolic- fluency tests. The
emphasis in these figural tests would be upon the
quantity of responses generated, with minimal considera
tion to the quality of what is produced. Esthetic con
siderations such as goodness of form, originality, or i
artistic ability should have little bearing on the
scoring criteria.
It was the foregoing type of theoretical orienta
tion and general considerations that guided the develop
ment of three tests that were hypothesised to measure the
. divergent production of figural units. The tests are
' i
Make a Mark, Make a Figure Test, and Sketches.
Make a Mark was considered to be the units-test
freest from either restriction or semantic context. The
examinee is told;
e 8 la this test you will- see. a number of blank
squares. You are to put a different mark in each
69
square. You will be told in general what kind of
mark will be accepted. Do not use letters or
numbers. Each mark should be different from the
others.88
I
The examinee is then given an example: "Make
different marks using only dotted lines." This is fol«
I
| lowed by several graphic examples. In the first part of
! . . .
I - - ■
| the test the examinee is told to "Make a different open
| mark in each square. Use only straight lines." In the
i ■
! second part, the examinee is told to "Make a different
i - -
closed mark in each square. Use only curved lines.18
Knowing fehat was an "open” or "closed" figure or
the difference between "straight" and "curved88 lines was
not considered a measure of comprehension or semantic
ability.
In the Make A Figure Test, similar to Make A Mark,
the responses are drawn in a series of squares. The
examinee is instructed that:
"In this test you will be given simple lines,
some straight, some curved. You are to make as many
different figures as you can using only the given
lines. Use all the given lines in each figure."
The examinee is then given some graphic examples
of how the given lines could be arranged to make different
figural arrangements. Here again, minimal language
70
comprehension is necessary to understand the printed test
instructions. !
in the Sketches test, the examinee is told “In
this test you are to make many different sketches using
I
the same given figure.5 5 The sample figure is a circle j
j and examples are shown how details can be added to dif- j
i
!
ferent circles to make a “face,” or a “hat," or a
"baseball.” The examinee is told that artistic ability j
I
| is unimportant and that he does not have to label his pro-j
I duction. The major restriction is that he "Use just
! enough detail in each sketch to make it recognisable,"
I
In each of these three tests, no requirement is j
i
imposed upon the examinee to interrelate the responses or
to place them in various categories. The tests are aimed
1
at eliciting the production of. relatively segregated or
circumscribed items of information having "thing"
character; it was unnecessary for the examinee to label
Ms production in any of the three tests.
In the manner outlined in the foregoing para- j
graphs, the taxonomic system of Guilford8 a theoretical j
i
model specified the three dimensions for the types of
responses to be elicited by the three new experimental
71
figural tests: (1) The "divergent-production operation"
required that a variety of responses be produced from a
i
given source or stimulus item. (2) The "figural-content"
category emphasized the tangible, concrete, or perceptual
i
information in the structure. (3) The “unit product*® j
specified that the responses are the result of dealing
with information in terms of distinct, segregated elements
or fundaments.
The DFC cell. "Classes" is defined as "aggre
gates of items of information grouped because of their
| consson properties." In the classes row, the divergent
i
| Production of semantic classes had been previously con-
i
t
firmed. A dependable measure of this semantic factor has
been Brick Uses (shifts score). This test calls upon the
examinee to list all the uses he can think of for a common J
brick.. Previous studies have linked the ability with the
concept of spontaneous flexibility, and defined it as a
disposition to seek a variety of answers, or generate
information, with freedom from perseveration, or inertia.
In typical tests of spontaneous flexibility, the examinee
receives no instruction to change his set, category, or
class of response. The extent to which he does so
72
without specific instructions, however, represents the
degree to which he possesses the ability. The scoring of
5
the Brick Uses test is based upon the number of times the
examinee changes or shifts from one category to another.
An analogous factor in the figural column of the struc-
ture of intellect, therefor®, should emphasise the abil
ity to produce a variety of classes by reason of common
shape, or other common properties. The number of classes
that can be produced should be limited only by the test |
duration, the information given, and the ability pos
sessed by the examinee.
Guilford and Merrifield (I960), have designated
the previously identified figural spontaneous flexibility
factor as the divergent production of figural classes.
i.m_. M.'ux^a d r a s s a a n a n m a a a v ■ » » — M Jw im .h L in rfw w t a w i . ll, . J . . i . i l.1iini.iiLMii«
They indicate that this factor was formerly interpreted
as rate of fluctuation of ambiguous figures in Thurstone8s
(1944) factorial study of perception. The three
Thurstone tests (Guilford and Merrified, 1960) as markers
for this factor were:
€ub® Fluctuations - Indicate the number of
changes in perspective of ambiguous cube....
Windmill Alternations - Indicate the number of
alternations from one illusion to another while
observing shadow of rotation rectangular blade.
...RetInal-rivalry-reversals - Indicate the number
73 ”|
j of reversals when a blue field is presented j
j sfer&oscopically to one eye and yellow field to
| the other eye (p. 23).
I • ■ ' '
To the writer, these tests did not appear, on an
a priori basis, to meet the theoretical description of the
factor. The tests seem too dependent upon the perceptual
!
j phenomena associated with optical illusions. No clarifi
cation could be obtained from the analogous semantic
| measures of spontaneous flexibility. Since the Utility
j Test or Alternate Uses did not appear to depend upon a
■
| context of ambiguity. It was determined, therefore,
to construct new tests to measure the factor. Three teste
were specifically designed as hypothesized measures of the
divergent production of figural classes. These were
Alternate Letter Groups, Figural Similarities, and Varied
Figural Glasses.
The Alternate Letter Groups test idea, when first
conceived, appeared to be of symbolic content, but it was
consonant with the definition of figural content required
concentration upon the shape of a letter would minimize
its symbolic information. Although a number ”1” may have
a qualify of "oneness” about it, a ”5” does not connote
"fiveness" by its form or shape. Using such a rationale,
74
the Alternate Letter Groups test was constructed to
contain the following instructions:.
HMost letters in the alphabet have different form
or shape. Some letters are very similar and some
have only similar parts. In this test, you are to
find letters that belong to a group because some
parts of the letters are similar in shape or form."
i
These test instructions were illustrated by an
example in which the given letters A H V T 0 are simple
line drawings 12 mm high. The examinee is told that AH¥T
is a possible group because all its letters are made up
of straight lines, and he is told that the group ACT is
not acceptable because it is a word. The examinee does
not need to explain why a .group of letters belongs in a
| certain category, but in order to indicate the category
| clearly, he is to write all given letters that can be
| classed in the group.
i
Figural Similarities, a hypothesised test of the
same factor, does not use familiar graphic foms as in the
Alternate Letter Groups test. Six designs are shown to
the examinee and he is told:
"Figures drawn on this page have many character"
isties, such as the kinds of lines, the shading, the
number of parts in the figure, and many others,. In
this-test you will see six figures. You are to look
for properties that 3 of the figures have in common."
The examinee is then shown how the use of fcriangu~
lar elements in three of the given designs is one basis
for producing a group from the three givenffigures. In a
A
|similar manner, shading, is a property in three of the
given designs. There is a mathematical possibility of
j ‘
producing 20 triads from the given material [n(n-l)
|(n-2)/6|. In order to avoid the necessity of the
|examinee's stating why a triad forms a class, all 20
triads are listed. The examinee circles either c s yes
"no.,” or w?” to indicate that some common property of the
given designs was used to produce a class. Although it
is possible that classes greater than three could be
produced, the practicalities of scoring dictated a more
restrictive approach. Appropriate corrections for guess-
ing are also necessitated in this multiple-choice format.
Varied Figural Classes was developed as an
analogous divergent-product ion version to the Figure
Classification test. The latter is a known test for the
cognition of figural classes. This factor is described
as the ability to classify perceived objects (Guilford,
1957a). In the Figure Classification test, the examinee
is given a graphic design and told to "discover8 * the class
76
to which the given figure belongs by identifying it with
a series of figures. One of the series has a property
comzaon to the given figure, such as-shading, solidity, or
curved lines.
In the Varied Figural Glasses test, the examinee
is told that a triad of figures my have some property in
common with more than one other single figure. This
sB2ltiple=elass msmbership is based upon several qualities
found in the Figure Classification test. In the latter
test, however, each given figure was restricted to a
single class. In the Varied Figural Glasses test, the
examinee Is required to "create" classes b^sed on princi
ples that formerly did not necessarily exist in his
repetoire. The examinee's ability to produce "new3 5
i ‘
classes represents his characteristic position >on that
factorial dimension. In this test, as well as in the
othersnew figural -and symbolic tests, the examinee does
not have to verbalise his responses. Rather than requir
ing open-end responses, a multiple-choice format is used.
The scoring task Is simplified since all probable
responses are listed.
A fourth hypothesised measure of this factor was
obtained by applying a secondary scoring criterion to the
Make A Figure Test. As a test designed specifically to
measure the divergent production of figural units. its
|
score is based upon the total number of different figures j
produced. When the same test was used as a measure of the
divergent production of figural classes, the score was
based upon the number of times the examinee changed or
shifted his style or approach producing the various
figure©.
The divergent production of figural classes, was
thus hypothesized as defined by four different measures
which emphasize class properties based upon common prin~
ciples. The ”shift" score as suggested by the parallel
semantic ability, was applied only to the Make A Figure
Test (shifts).
The DSC cell. Three tests were hypothesised to
measure the divergent production of symbolic classes:
Number Grouping, Name Grouping, and Varied Symbols.
In Number Grouping the examinee is instructed to
generate from a given set of small numbers a variety of
number groups; each new group produced is to be based upon
a different common principle. In the sample item, the
78 I
!
given numbers are 2, 3} 4, 6, 17, 23, 26.
Two possible solutions ares 2, 4, 6, 36, which
would indicate to a scorer that Keven numbers” is the
eoEson property used, and 3, 17, 23, would show that the
common property of. "all odd numbers" is used. The
©s&miaee is told in the test instructions that combining
the numbers in an equation such as 2 4 - 4 1 5 3 6 would be
disallowed, as it does not indicate a comiEon unifying
principle or class. The production of an equation or a
relationship between the given, numbers might be a measure
of another factor, but it is not considered an appropriate
response to the instructions of this test.
A parallel test devised to measure the same
symbolic classifications ability is Name Grouping. In
this test, a given list of names is formed into various
groups due to some common principle. In the sample item,
i ■ ■ ■
the names Bill* Carrie, and Belle are shown to form one
subgroup since each name has a configuration of double- .
consonants (11, rr, 11). Some of these same names such as
Carrie and Belle could be joined with other names to form
a class of names "which begin with a consonant and end
79
with a vowel . ® * Neither meaning nor aesthetic qualities
in names per se are deemed to have any bearing upon the
1
capacity of examinees to perform on the test. To simplify
the task of responding and scoring, each name is assigned
| a code number so that class can be indicated by quickly
i •
i ;
writing down a set of numbers.
In Varied Symbols, instructions to the examinees
are somewhat more lengthy than in the other hypothesised
measures of the DSC factor. In this test, three sets of
letters (almost like nonsense syllables) can produce a
class because of some principle in common with a fourth
set of letters. One sample item illustrates how three
sets of letters PBQ. TMD, EZF form class with EOS because
in each triad the first and last letters are in direct
alphabetical sequence: P-Q, T-U, E-F, and R-S. A variety
of productions is obtained in this test when the first
set of three is grouped with other triads because of
different principles of classification.
The three new experimental tests were constructed
so that neither meaning is ascribed to the letters nor
does tangible form compose the basic information to be
processed. In all three hypothesised measures of
80
divergent production - of symbolic classes- a multiplicity
of classes lias to be produced with the same given sets of
letters or numbers.
The classes factor in the adjacent semantic cell
is represented by tests that require uses be found for a
common brisk in the Utility test or that a variety of
different ©r peculiar uses be found for eomsson objects in
the Alternate Uses test. The tests of this semantic
*
spontaneous flexibility factor have imposed relatively
allt- ‘' - ' L ' ,LVI ■■»■«»*. I ' - I I I I ■ ' i ■ ■ I «l '■ T-JH— -‘ a 1 1 - L I ill. JJmiMLlMPllllM J i l . H 1J HIM.. « •
few restrictions upon the examinee. In, developing
analogous tests of symbolic spontaneous flexibility, the
instructions of the tests require that a variety of
classes be formed. The format of the test does not reveal
as readily the ^shift8 ® from one class to another. The
score in each of the three new tests represents a fluency
i
of production of different classes, rather than the
frequency of shift from one class to another. In follow
ing this approach, the new figural- and symbolic- classes
tests are developed upon principles derived from the
operational definitions of their- respective cells, rather
than by analogy to tests'in the semantic classes cell.
The Make A Figure Tests (shifts) is the one exception.
81
The DSR cell; The divergent production of symbolic
relations was the only relations factor Included for
exploratory study. Relations in the divergent“production
matrix are defined as "connections between units of infor
mation based upon variables that apply to them" (Guilford
and Herrifield, 1960).
In the semantic column of the matrix, the diver
gent production of semantic relations is com&only measured
by the Associational Fluency test which requires producing
a variety of correlates by writing several synonyms for a
given word. The test involves producing words meaning
"about the same as" the given word in the same sense as a
thesaurus relates a variety of concepts to a given word or
|predicate. The hypothesized tests for the parallel
i .
symbolic factor would require using alphabetical, numeri
cal , or notational information for producing a variety of
relationships. Three tests, 8 Letter Group Relations, 19
Number Rules, and 1 Alternate Additions, were constructed
as hypothesized measures of the DSR factor.
In the sample item of the instructions for the
Letter Group Relations test, the letters A B C are given.
The example shows how this triad is analogous to 6 HI
82
because of similar alphabetical order, to T T E because
each letter-triad contained two consonants and a vowel,
and to S A U because both A » C and S - u are in
"alphabetical order with one letter skipped."
In this test format the examinee does not have to
call upon his abilities of verbal expression to explain
what principles guide the relationships that he produces
from the givens. For each set of letters, he has only to
circle "yes” to show that a "symbolic simile" is establ
ished . In this test, as in several others new experi
mental tests where letters are used as stimulus objects,
the full alphabet is printed out at the top of the page.
This is done in order to minimize variance due to memory
for letters or perceptual factors that might be
confounded with measurement of the factor of interest.
Another hypothesized measure of the DSR factor x^as
the Number Rules test which requires the examinee to re
late two small numbers in a variety of ways. In the sam
ple item, he is shox-jn how one could start x-jdth 2 and get 6_
by several different simple arithmetical operations. Re
sponses such as 2 - i - 4 = 6 or 2 x 3 = 6 are acceptable, but
the examinee is told that 2 -r 5 - 1 = 6 is not sufficiently
different from 2 + 4 = 6 . Credit is not based upon mathe
matical sophistication such as the use of fractions, deci
mals, or mixed numbers; the examinee is limited to
addition, subtraction, multiplication, and division. As in
most of the other new tests in this study, the examinee
does not have to express reasons for his responses. In
general the scoring guides designed for the test are com
prehensive enough to account for most of the probable
responses that are acceptable.
A somewhat more restrictive variation of Number
Rules was Alternate Additions. In the example of the test
instructions, the examinee is given the numbers 1 2 3 4
and told to obtain 7 in a variety of ways. He must use
only addition, use only the four given numbers, and not use
them any more often than given. In this example he is told
that 4 + 3 = 7 and 3+4 = 7 are too similar. Responses
such as 1 3+ 3 = 7 and 2+5 = 7 are unacceptable since
3^ is given only once, and _5 is not given at all.
As experimental controls, Seeing Trends II and Word
Relations were included in the test battery to determine
whether the new experimental tests were related to the
reference factor of cognition of symbolic relations. In
84
the Seeing Trends II test the examinee is given a set of
words, such as "anger bacterial camel dead excite," and he
is required to discover a trend, the principle here being
that the words are in alphabetical order. In this cogni
tion test, once the relationship is discovered, no further
processing of the given or discovered information is
required.
Discovery is also exemplified in the Word Rela
tions test. In the instructions, the words "on no" and
"top pot" are given as examples of one kind of symbolic
relationship to be found. The same relationship is then
to be found between "part" and one word in the set "art pat
rapt tar trap." Since no and pot are the reverse of on
and top. respectively, the obvious symbolic correlate to
"part" would be "trap." These ttjo tests would help to
indicate whether the new measures were primarily of dis
covery or of production of symbolic relationships.
The DFS cell: This was the only cell of the sys
tems row in the divergent-production matrix that had not
been previously explored. Since systems are more than a-
pattern or complex set of relationships among elements,
ability in this factor calls for the organising of
i
85
aggregates of items of information to form structures, in a
variety of ways.
The only one other known parallel, figural-systems
factor in the model from which to derive inferences is the
cognition of figural system, otherwise designated as the
spatial orientation factor. This ability involves struc
turing arrangements perceived objects in space or main
taining orientation with respect to such objects (Guilford,
1959a)# analogous divergent-production factor should
require a variety of integrated or organised space forms
to be produced from the same given figural elements.
It did not appear that guidance was to be derived
by analogy from the divergent production of semantic
systems tests such as: Expressional Fluency or Simile
Interpretations. The former requires the examinee to make
up four-word sentences where the first letter of each word
is supplied. In the second, a simile-building test, given
words have to be organized into phrases in a variety of
ways. In these tests, the concept of a semantic system
was a sentence or a phrase.
The results of a parallel investigation into the
divergent production of symbolic systems were not available
86
at the time this study was planned (Guilford et al, 1961).
In constructing tests hypothesised to measure the diver
gent production of figural systems,therefore, less
emphasis could be drawn from analogies to parallel factors.
More reliance was placed upon the operational specifica
tions of content and product as defined by the theoretical
model. The DFS factor would be the ability to produce a
variety of figural constructs composed of organised or
structured aggregates of items of information. . Two tests
that were constructed to measure the factor by these
specifications were Designs and Monograms; in addition,
2
Dot Systems x - j a s adapted from a test idea of G. T. Myers.
The Designs test instructs the examinee to com
bine or rearrange any of a given set of simple straight
and curved lines and angular forms in a variety of figures
that are different from each other. Restrictions in the
test instructions are minimal. The examinee Is told that
the shapes of the “given5 1 elements has to be kept con
stant, but their size and orientation can be varied. The
same given element may be used repeatedly in the same
^The xjriter wishes to acknowledge the kind per
mission of Dr. G. T. Myers which led to an adaptation of
the Dot Systems test idea.
87
design system, but no requirement is made that all the
given elements must be used.
The Monograms test requires the examinee to use
the same three initials in a number of different combina
tions that are considered "monograms." In this test
neither size nor shape of the initials has to remain con
stant, but the letter must remain essentially in printed
style rather than assume the form of cursive letters. In
the Monograms and in the Designs tests, artistic ability
or beauty of the figural system produced is not a basis
for acceptability of a response. Credit is given to those
systems that employ a variety of different principles in
producing the graphic representations.
In the Dot Systems test, the examinee is asked to
draw a certain letter in two positions in a regular
matrix of dots. The letters are to be inscribed in a
multiple of ways under restrictions that they must not
touch or overlap and each letter must span exactly four
dots. Although the test was not hypothesized by
strueture-of-intellect theory, it seemed logical that the
production of multiple arrangements involved in this test
might be an alternative approach to measurement of the
88
DFS factor. Although the spatial“orientation factor (CFS)
may account for the variance in some of the new figural
tests, limitations of testing time did not permit the
inclusion of a measure of that factor as a control.
The DFT cell: This figural adaptive flexibility
factor's marker tests involve el©nents that must be
manipulated by alternative approaches or strategies in
order to solve relatively difficult problems. Various
forms of match°problem tests are believed to require the
examinee to revise his conceptions of figures in order to
give additional acceptable solutions. It is presumed that
the examinee effects a number of changes in perceptual
organization. It was suggested in the flexibility studies
(Frick, et al., 1959) that this factor might be parallel
to the semantic factor of originality. Although this
might imply the production of clever, remote, or unusual
responses, the tests that have been commonly associated
with figural adaptive flexibility do not call for ! ! cleverl t
answers per se, as is true of some tests of originality.
With the exception of Planning Air Maneuvers, in
which the examinee must seek the most efficient paths
with "skywriting" diagrams, the measures of DFT have
89
generally tests with match-stick problems in which
patterns of squares or triangles are presented in diagram
matic form. In Match Problems II, for example, the
examinee is told to remove a specified number of matches
from a given pattern and leave a specified number of
squares or triangles. The matches to be "removed" are
indicated by crossing them out with a heavy stroke mark.
In Match Problems V the examinee is told to remove a
specified number of matches from a given pattern of
squares to make a new pattern. The new experimental test
constructed to verify DFT were Making Objects, Match
Problems III, and Match Problems IV.
In Match Problems III, the new experimental varia
tion on these tests is where the examinee is asked to
obtain the "same number of squares arranged in different
patterns by removing a specified number of matches." The
variation in Match Problem IV is specify a number of
squares in different patterns to be obtained by removing
of the same principles as other forms of the match-
problems tests.
In Making Objects, simple lines or shapes are
given and the examinee must combine them in order to draw
certain named objects. Some, or all, of these simple
"building blocks" may be used once or several times to
form a specified object. The givens may be used repeat
edly, reoriented, or altered in sise. Their shapes must
remain constant, however, A set of givens may include a
straight line, a circle, rectangle, trapesoid, and
triangle. Use of these figures in more than one manner
in any specific response augments an examinee’s score.
There is no requirement, however, that all the givens be
used to produce the object named. Using one given in a
variety of ways may be as highly scored as using several
givens in only one manner. It was anticipated that
Making Objects would contribute to the determination of
the DFT factor in the event that the match-problems tests
were only "alternate forms" of the same test and not
i
independent measures accounting for comm-factor variance.
In the planning study (Guilford, Berger and Christensen,
1955) and in the flexibility study (Frick, et al. , 1959)
the factor defined as adaptative flexibility included
match-problem tests as well as other tests of different
contexts.
91
The PSI cell: It was originally anticipated by
the writer that he would include measures of the three
content areas across the implications row. Clarification
of factors in the figural and semantic cells and verifica
tion of the previously unexplored symbolic cell could thus
be simultaneously accomplished. The fortuitous availa
bility of testing time in the creative-adolescent study
permitted deleting the figural and semantic cells from
consideration in the present study. Results from the
creative-adolescent study did not become available in time
to help guide test construction for factor DSI. Informa
tion was available, however, from previous studies of the
“ divergent production of semantic implications concerning
six implication factors in other operations. It was from
these sources that analogies were drawn for test ideas to
define the divergent production of symbolic implications.
The implications product deals with extrapolation
of information in the form of expectancies, predictions,
antecedents and consequences. Although variety is to be
emphasized in the DSI measures, fluency of production must
be modified by restrictions. These restrictions require
that information should be generated by extrapolation from
92
the given information and not by simple analogies, as in
’ ’ relational thinking.” In addition, such inferences or
extrapolations are not dependent upon discovering or con-
verging on one or more unique solutions. It is through
elaborations based upon the antecedent or consequent
condition that acceptable responses are produced.
®ne cognition of symbolic implications measure,
IJord Patterns, requires that the examinee arrange a list
of words efficiently in a kind of cross-word-pussle pat
tern, Another test. Symbol Grouping, requires that the
examinee rearrange scrambled symbols in a specified order
as efficiently as possible (Guilford et. al., 1960a). The
concept of ”foresight” associated with the cognition-of-
implications factors was not extended to the divergent-
production matrix. It was presumed that seeing one step
ahead in an infinite series of relations is different from
the ’ ’ elaboration5 1 concept. Elaboration is the key
implications concept in the adjacent figural and semantic
columns of the divergent-production matrix.
The memory for symbolic implications, or numerical
facility factor, is best represented by the Numerical
Operations test. It was found, however, that in
93
constructing tests to measure the DSI factor, no parallels
could be taken from this marker test. The MSI factor is
defined as the ability to recall rapidly well-practiced
implications. There appeared to be only a minimal paral
lel with the divergent-production of a variety of symbolic
implications. It was not evident how a simple arithmetic
test could be taken as an analogy. It was important,
nevertheless, that the Numerical Operations test should be
included in the test battery to account for the numerical
facility variance in the new experimental symbolic tests.
Several of these new tests used numbers and required simple
arithmetical operations.
The divergent production of semantic implications,
the elaboration factor, has been defined by the Planning
Elaboration test. The task in this test requires filling
in as many details as necessary for carrying out an activ
ity. The parallel figural factor defined by Decorations
requires that a duplicate set of objects be embellished
by adding a variety of graphic designs. It was hypothe
sised, therefore, that analogous symbolic tests xrould use
a set of givens such as letters, numbers, or signs from an
established notational system. Extrapolations drawn from
94
this set would provide the required symbolic inferences.
Symbol Elaborations and Limited Words were the
two tests constructed as hypothetical measures of the DSI
factor. Symbol Elaboration appears to be similar to a
measure of elementary algebra. Performance on the test,
however, is not predicated upon a knowledge of algebra per
se. The examinee is presented with two or three simple
linear equations and told to “x-jrite new equations” using
the given letters. In one example, he is given the two
equations B - G = D and Z = A - f B, and is shox-m how five
or more different equations can be generated from this
given information. The test is obviously symbolic, it
calls for producing a variety of responses from the same
given source of information, and it appears to require
multiple extrapolations from antecedent data. All these
considerations seem to meet the specifications of the DSI
description.
The other new experimental test, Limited Words,
requires that the given information provide the inferen=
tial basis for suggesting new information. In this test,
the letters of two given words are to be juxtaposed into
a variety of two-word anagrams. In the example, the
95
examinee is shown how the given pair of words 11 shirt bean”
could result in such word-pairs as "hairs bent" or "bears
thing." It was intended to construct this test suffi
ciently different from the simple anagram-type task, which
would be more related to cognition factors, and also
minimise the variance due to word fluency. A variety of
words is produced in the Word Fluency test using the given
information. In Limited Words, however, diligent regard
for antecedent conditions and their consequents under
relatively greater degrees of restrictions is required.
Emphasis is upon such symbolic inferential processes as
Elaboration by combining letters in the given words in
many ways.
Table 1 lists the 21 new experimental measures and
the eight marker tests that composed the full test
battery. Numbers preceding the test names correspond to
the alphabetical ordering of the tests. The alphanumeric
designation following each test name is the USC Aptitudes
Project code identification for test forms. Appendix B
presents similar information organized according to the
hypothesised factor structure of the test battery.
Appendix C presents short descriptions of the task in each
TABLE 1
96
THE TEST BATTERY
Variable3
Number Test Name Code* 5
1. Alternate Additions DSRO'LA
2. Alternate Letter Groups DFC03A
3. Designs DFS01A
4. Dot Systems DFS02A
5. Figural Similarities DFC01A
6. Figure Classification EF01A
7. Four-Letter Words (GSU01A)
O
o . Letter Group Relations DSR03A
9. Limited Words DSI02A
10. Make A Figure Test (fluency) DFU02A
11. Make A Figure Test (shifts) DFC02A
12. Make A Mark DFU03A
13. Making Obj ects DFT06B
14. Match Problems III DFT03B
15. Match Problems IV DFT04A
16. Monograms DFS03A
17. Name Grouping DSC02A
18. Number Grouping DSC01A
19. Number Rules DSR02A
20. Numerical Operations (MSI) Form Ad
21. Perceptual Speed (EFU) Form Ad
22. Picture Classification (CFG) EF03A
23. Seeing Trends II (CSR)
24. Sketches DFU01A
25. Symbol Elaboration DSI01A
26. Varied Figural Classes DFC02A
27. Varied Symbols DSC03A
28. Verbal Comprehension (CMU) Form A
29. Word Relations CSR02A
aBased upon the alphabetical ordering of the tests.
bCode indicates the USC Aptitudes Project alpha
numeric designation of hypothesised factor content of the
21 new experimental tests; the known factor content of
each of the 9 marker tests is enclosed in parentheses.
Appendix A provides listing of the strueture-of-intellect
code designations.
cBased upon test of same name by C. T. Myers.
dTests published by Sheridan Supply Company,
Beverly Hills, California.
97
test and of the scoring criteria, the number of separately
timed parts, the number of items in each part, and the
working time on the test exclusive of instruction time.
Alternative Hypotheses
ICemeny (1959) has stated the scientific truism
that
A scientist holds his theories tentatively,
always prepared to abandon them if the facts do
not bear out his predictions. If a series of
observations, designed to verify certain predic-
tions, force us to abandon our theory, then we
look for a new or improved theory (p. 86).
The existence of a number of divergent-production
abilities has been suggested by structure-of-intellect
theory. The empty cells in the model are focal points
for hypotheses concerning nature abilities represented
by the empty cells. The tests to measure unverified
factors were in turn suggested by analogies to tests of
known factors in parallel cells. The descriptions of
these previously unexplored factors x^ere believed to be
defined in the theoretical terms of the operation, con
tents, and products. The existence of new divergent-
production factors and the experimental figural and sym
bolic tests to measure them represent the principal set of
98
hypotheses (H-^) that have been presented in this chapter
for verification.
It is incumbent upon this investigator, neverthe
less, to suggest that the empirical evidence obtainable
by these new tests may lead to a number of alternative
explanations. Although not set forth as specific experi
mental questions, they are, in substance, alternative
hypotheses. The following paragraphs will discuss these
questions and will also undertake to review some alterna
tive considerations concerning factorial invariance (B2)
and the comparability of factors in different samples(H3).
A basic premise in the evolution of the structure-
of-intellect theory has been that the factors have
generated their own categories; these categories, in turn,
suggest the type of tests that define the factors. It
would be a tenable hypothesis,then that some cells in the
model are not as strictly organised in parallels as
present conceptions of the theory might suggest.
The broad specifications of the type of tests
predicted from the model should contribute to the validity
of the model as a source of hypotheses concerning new
tests. Should the data obtained in this study lead to
99
factors other than those predicted, then, excluding
methodological error, revisions in the theoretical model
wotild be indicated. Tests predicted by the model which do
not load as predicted, would be supplanted if they do not
contribute to the interpretation of other meaningful
common factors. Should the common factors obtained with
new tests define a factor pattern at wide variance to the
theoretical factor structure, then the appropriateness of
the model as currently conceived would be questionable.
A scientist abandons his theoretical models with at least
the reluctance of the master of a foundering vessel;
fortunately, however, the salvage value of an abandoned
scientific theory is usually quite high, since its basic
postulates and supportive data, phoenix-like, provide the
basis for revised or new theoretical formulations.
With respect to the six investigated cells of the
structure of intellect as currently defined, no revision
is anticipated in the descriptive term, divergent produc
tion. The battery of new experimental tests should clearly
distinguish the hypothesized factors of divergent produc
tion from factors in other operations.
Measures of six reference factors were included in
100
the test battery. Since ample evidence existed (Guilford,
1956^) concerning the univocality of the tests of CMU,
MSI, and EFI, only one measure per factor x * ? a s selected for
inclusion in the test battery. Limitations of testing
time also required that CSU be represented by only one
measure, Four-Letter Words. Although this test had not
been demonstrated to be univocal (Guilford et al. , I9603),
it was a tenable hypothesis that this factor would not be
a dimension in the factor analysis. The CFG and CSR
factors were each represented by two marker tests. These
factors would probably be identified in the study. Since
the levels of difficulty and scoring criteria had been
established for most of the tests of the six investigated
factors, it was probable that test performance in the .
Adult sample would parallel previous results with adults.
The undetermined difficulty for these tests with the
Adolescent sample, on the other hand (Thomson, 1948) might
result in an Adolescent factor structure different from
that of the Adult sample.
The inclusion of these marker tests for reference
factors in the study was primarily for control purposes.
It was to obtain evidence that the new experimental tests
101
were measures of factors distinct from those previously
identified. Several alternative hypotheses were implied
by the inclusion of these tests:
1. That the hypothesized measures of DFG would
exhibit their highest loadings (share variances in common)
with the measures of CFC. That is, they would be
alternative measures of the ability to classify perceived
obj ects.
2. That a number of figural tests would require
a significant degree of the ability to identify a given
figure among similar figures as represented by the EFU
factor.
3. That the symbolic tests requiring number
manipulations were alternate measures of the numerical"
facility factor (MSI).
4. That the symbolic tests hypothesised to
measure DSC, DSR, and DSI were basically alternate
measures of the ability to discover relations involving
letter patterns (CSR), or simply the ability of being
aware of the structure of symbolic units (CSU).
5. The Verbal Comprehension test was included to
determine whether the knowledge of the meaning of words
102
(CMU) would be involved in the new tests , due to variance
in understanding the tests’ instructions. Inclusion of
this measure served as a test of the alternative hypothe
sis that word knowledge is a determining element in
performance on non-verbal tests and that most intellectual
factors are correlated with it.
Based upon findings in previous studies, it was
not anticipated that confounding would occur between
factors of symbolic and of figural content. It was
thought to be more probable that a lack of definition
might occur between products within content-columns.
It appeared likely that a figural fluency factor
(DFU) would be defined for placement in the units row
of the matrix. It was anticipated, however, that some
confounding between the units and the systems products
would occur. In order to differentiate the synedochical
characteristics of units and systems, it would be
necessary that some clear perceptual distinctions should
occur. T h e ; tests require that the rules for ordering or
patterning elements in visual space should be quite
distinct from the production of simple perceptual parts,
units, or fundaments. If the parts are taken for the
103
whole, or the whole for the parts, then alternative
formulations concerning tests of these two divergent-
production factors would be required.
In the classes row of the matrix, no confounding
was anticipated between DFG and DSC. Figural Similarities
and Varied Figural Classes have multiple-choice response
formats. Letter Group Relations and Varied Symbols also
have fixed sets of the most probable responses in their
response formats. The examinee is then constrained to
maintain his repetoire of potential responses within
preordained sets. Even within these limitations, hoitfever,
it was anticipated that sufficient possibility for
variation of responses existed to permit individual
differences on the factor to occur. Because of the
restrictions in the tests in these cells, an alternative
conclusion might be that differences between examinees
would rest upon their ability to see or discover a figural
or symbolic class, in contrast to the task of producing
classes.
The classes row in the divergent-production matrix
is hypothesized to represent aspects of spontaneous
flexibility. It has been suggested that there may be some
104
distinction between factors involving spontaneous shift
of classes and those having to do with producing a
diversity of classes (Guilford, 1959a). Since only the
Make A Figure Test had a shift score, it was not anti
cipated that the "shift" hypotheses concerning the classes
row could be verified from the data in this study.
Although the DFT cell has received previous
verification, two alternative conclusions concerning the
new tests for this factor were possible. The figural
adaptive flexibility factor is associated with the
restructuring or redefinition of perceptual information.
It is hypothesised that this is appropriately descriptive
of the restrictive type of tasks in the new match-problem
tests. It does not appear to be descriptive, however, of
a factor of figural originality in which cleverness,
uniqueness, and uncommonness are emphasised. In the
instructions to Making Objects, originality is not
emphasised. The test seems more similar to the semantic-
transformations (DMT) measures which explicitly require
originality than to the problems of match-problem solutions.
Test measures of cognition of symbolic relations
and the memory for symbolic implications were included
105
in the battery in order to differentiate the factor
pattern among the new symbolic tests in this study. There
appeared to be strong evidence for alternative hypotheses
that seeing or discovering a symbolic class or relation
ship would contribute more to the variance in some of the
new tests than the production of relationships. It was
anticipated that such cognition variance in the new
symbolic tests would be indicated by loadings on the
reference factors. Numerical-facility, for example,
would indicate to which degree well-practiced arithmetic
habits are involved in Alternate Additions, Number
Grouping, and Number Rules, and perhaps in the Symbol
Elaboration test.
In order to differentiate the three symbolic
products of DSC, DSR, and DSI it would have been desirable
to have included measures of the corresponding reference
factors from the cognition operation and possibly the
convergent operation. The limitations of testing time
imposed the necessity of restricting such controls to the
CSU and the CSR factors. Since no measure of the CSC
factor was included, it may be hypothesized that the
f
three tests designed to measure DSC may in fact be
alternative measures of CSC. One test of this hypothesis
106
rested upon the degree to which the hypothesised DSC
tests correlate with other divergent tests as compared
to their correlations with cognition tests.
Since all the new tests in the symbolic column
use letters or numbers as the form of information to be
processed, it may be hypothesized that the new divergent,
symbolic tests are really measuring the same general
factor. In view of previous findings in the symbolic
i
study (Guilford et al., 1960a), it was anticipated that
orthogonal divergent, symbolic abilities may be
differentiated.
One final alternative hypothesis was relative to
the loadings of the new experimental tests. In the
absence of other known divergent reference factors in
this study, it was anticipated that the new tests would
measure some form of divergent“production ability, if not
the content or product originally specified. Loadings of
the new tests should be higher on factor axes defined as
divergent production than on axes presumed to be reference
factors. Should the new test load higher on these
reference factors, it would be that they are but
alternative measures of those abilities.
107
The secondary hypotheses, H2 and concerning
factorial comparability and factorial invariance also led
to a number of alternative hypotheses. If it were con
cluded that the factor structures were the same in the
two populations, an alternative hypothesis would be that
the finding of similarity was due to the subjective bias
of the investigator. Such an hypothesis would hold
greater likelihood if the method of rotation were a
graphic procedure. Bias, however, might occur even in
inferences derived from an analytical, rotational
solution, since it is the investigator who interprets the
axes. In the absence of an adequate test for the signi
ficance of a factor loading, accepting or rejecting any
given solution still is based upon arbitrary standards.
Within the specifications of the third hypothesis
(H3), that the two factor structures can be shown to be
statistically similar, no firm level of credibility exists.
In the absence of a probability distribution for coeffi
cients of similarity or congruence only extreme indices
or proportions are at levels of confidence.
It would appear then, in the light of the present
state of the art, alternative hypotheses to basic
experimental questions posed by this study would enjoy
the same degree of acceptance as their counterparts,
since conclusions cannot be based upon rigid statements
of probability. Acceptance or rejection of the hypotheses
rests largely upon rational inferences derived from the
empirical results.
CHAPTER IV
PROCEDURES
The Samples
The adult sample consisted of 238 young-adult,
male, pilot trainees at the U. S. Naval Air Station at
Pensacola, Florida. This superior group of young men from
the Navy and Marine Corps were designated as Aviation
Officer Candidates or Navy or Marine Air Cadets assigned
for pilot training. They did not arrive at the Naval Air
Station at one time but were assigned during the course of
the spring and summer of 1960 and were tested in groups of
approximately 40 each. These men were representative of
the population of pilot trainees tested at Pensacola in
previous factor analytical studies of the U.S.C. Aptitudes
Project. (Guilford, et al., I960; Merrifield, et al., I960)
These pilot trainees were neither volunteers for
the testing situation, nor were they informed that the
test was part of the orientation and indoctrination
procedures of the Navy pilot training program. The
109
110
experimental battery was administered within the context
of the Navy training command test program for pilot
trainees. These men were believed to be well motivated to
succeed in all required procedures which would lead to
"Navy wings," (Ambler, 1962). No biographical data were
requested of the men personally other than a designation
of class number, rank, and the date.
The adolescent sample consisted of the entire
ninth-grade student population of the Claremont Junior
High School of Claremont, California. Although 220 boys
and girls participated in the testing on January 6th and
7th., I960 during two 3-hour sessions, the sample was later
reduced. Complete test data ware available on all of the
29 measures in the battery for 205 of the original group.
Thi s same group of 205 had been tested one month
previously in the creative-adolescent study, (Guilford et
al., 1961) and the students were familiar with the general
objectives of the research group, and the routine of the
test“administration procedures. Appendix includes the
orientation statement that was read to the group at the
start of the test series. This statement was designed to
enlist the cooperation and full attention of all the
Ill
students who had been assigned by the school administra
tion to participate in the test program. It was empha
sized that the research staff was interested in "how
ninth-graders think."
The school is part of a suburban, largely
Caucasian, community. The homes in the area are primarily
one-family houses in the $15,000 to $35,000 price range.
The area is developing as a residential community for
professionals, sub-professionals, and merchants, and
Claremont is considered a "college town" with an
enlightened citizenry . This, was reflected in the coopera
tion of the school administration who assisted in the
promulgation of the testing program. Industry in the area
serves the nearby military bases, defense plants and an
extensive agricultural complex.
Students remained anonymous, having been assigned
code numbers to identify-their test booklets. Although
IQ information was available, students were not deleted
from the sample because of low indices of general intelli
gence since an ability to understand the test instructions
was the basic criterion for inclusion in the sample. None
were dropped because of failure to attain that level, nor
112
did the test data later indicate that any should have been
dropped. None demonstrated consistently poor performance
on all measures.
It may be seen from the foregoing, that the two
populations were quite dissimilar. The adult sample was
all male, of superior IQ. They were a selected group with
respect to discipline and leadership qualities. All were
motivated to perform well on the tests and to become
pilots. The ninth-grade student sample might be described
as average, middle-class American "kids.” Some were well
disciplined, others not; some were spoiled, and some
appeared to be bright, while others seemed dull. It was
anticipated that the orientation statement, which empha
sized their school’s contribution to science would be one
major reason x-jhy the students would be motivated to
perform well on the tests.
Administration of the Test Batteries
The adolescent sample was tested on two successive
mornings. The tests were arranged into booklets of four
or five tests each. Each booklet required approximately
52 minutes for administration, and short recesses were
113
given between booklets. Each day's procedure for testing
began when the students reported to their usual home rooms
for an attendance check. After a short announcement was
made concerning the testing procedures the Aptitudes
Project staff began administering the test battery while
teachers acted as proctors.
The total adolescent sample, in six separate groups
of approximately 35 each, were tested simultaneously. A
test administration manual was used by each staff member
who first read the introductory orientation statement and
then introduced each test by reading the printed test
instructions aloud while the examinees maintained pace by
reading the test instructions to themselves.
The same manuals, without the orientation state
ment were furnished to experienced professional personnel
at the Department of Psychology, Navy School of Aviation
Medicine to administer the battery to the pilot trainees
at the Pensacola Naval Air Station Training Command.
Although exactly parallel conditions to the ninth-
grade sample testing procedure were not feasible, the
test booklets, the order of tests, the working time on the
tests, and the reading of instructions were similar to the
114
ninth-grade test administration. The composition of the
i
administration manual was in the format of a play manu
script with words to be spoken and directions for
administration.
Scoring
Scoring criteria for the tests, x?ere developed
upon preliminary results obtained with university students
in undergraduate psychology courses. The 21 new experi
mental tests had never been administered to an adolescent
population before nor had the pretest results been factor
analyzed. Although the tests had been originally designed
for investigations using adults samples (i.e., university
students and military officer candidates) test instructions
and to a lesser degree, item difficulties, were modified
so that the ninth-grade students would readily understand
the instructions and the examples given in each test.
Since one goal of the study was to determine if these
tests could meassre individual differences in the same
factors in both a young-adult and a ninth-grade student
population, the scoring criteria adapted for the tests was
the same for adults as for the children.
115
No change was made in the scoring guide that was
not applied to both samples. Since the scoring criteria
for the marker tests were based upon previous studies with
the adult populations, they were applied without revision
in this study. The scoring criteria for the experimental
tests were developed during the period that the tests were
constructed, some were modified, however, during the
scoring phase of this study when revisions commensurate
with the hypothesized factor content seemed x-jarranted. In
such cases, all responses in the tests were rescored by
the revised criteria.
Scoring of the 29 test measures in the two samples
was conducted by the staff of the U.S.C. Aptitudes
Project. Assignment of such staff was based upon the
level of difficulty and the scoring criteria of the tests.
The scoring was classified into three levels of difficulty:
(1) routine, (2) scoring requiring some subjective
judgment, and (3) scoring requiring well-trained and
experienced personnel.
Eleven tests were scored by relatively routine
procedures such as IBM window keys for tests using
answer-sheets or keyed responses for multiple-choice test
116
formats. Seven of these tests were marker tests: Numbers
6, 7, 20, 21, 22, 28, and 39. The remaining four Were new
experimental tests: Numbers 5, 8, 26, and 27.
There were seven experimental tests, Numbers 1, 2,
9, 14, 15, 18, and 19 in the medium difficulty level.
These were scored only by personnel with the acumen and
training necessary to recognize acceptable responses not
anticipated by the scoring guides. In addition, test No.
23, a marker test, was considered of sufficient complexity
to be placed in this category.
The remaining ten tests in the battery were in the
most difficult scoring category. These experimental tests
were in an '"open-end” format, and could not be completely
scored by a predetermined scoring key. They required
scoring by personnel who were familiar with the test
hypotheses. In addition, personnel were required to
possess sufficient sagacity and experience to be consistent
in scoring all 443 sets of responses in the test. All
scores were checked by a second staff member who was
trained to similar scoring standards. The writer super
vised all stages of scoring for test numbers 3, 4, 10, 11,
12, 13, 16, 17, 24, and 25.
117
Only two of the 21 new experimental tests were
scored routinely, nine required some subjective evaluation;
ten were considered relatively difficult to score because
of the high degree of subjective evaluation required.
Twelve of these 19 tests were designed to be of figural-
content and seven were designed to be of symbolic-content„
In general, the figural tests were more difficult to score
than the symbolic tests, since there was less precedence
for scoring the type of responses elicited. In designing
these tests the Aptitudes Project staff were aware that
scoring "open-end" type tests for large groups would foe
time consuming and a burden on research funds. It soon
became evident, however, that identification of some of
the hypothesised factors was probably dependent upon the
"open-end" type of test item. This necessitated devising
relatively comprehensive and somewhat complex scoring
instructions for some of the figural tests. The rationale
involved in both test construction and the consequent
scoring of some of these new experimental symbolic and
figural tests may be exemplified by some of the following
considerations:
The "letters" AN could be construed to be of
118
semantic, symbolic, as well as figural content. AN, as
semantic information, is obviously a word implying oneness
or singularity. As symbolic information, it might be a
word beginning with the letter A, or a vowel followed by a
consonant, or two letters widely separated in the alphabet.
It could be described as an adjective or an article,, as
part of the class or set: a, an, and the. As a figural
element it could be a unit or class design composed of
straight lines and angles, or a horizontal display
inscribing, in part, a trapezoidal area. In the sense of
the Monograms test, it might be a system.
The latter uncertainty highlighted a major problem
in developing the scoring criteria for the figural tests:
the difficulty of differentiating between a figural unit
and a figural system. In general, the figural-units tests
were of an open-end variety and were scored upon a basis of
fluency, provided the specific requirements of the test
instructions were followed. The figural-classes tests were
for the most part in a multiple-choice format. , They were
i
scored by keys xdiich accounted for most of the probable re
sponses. In one exception, the Make A Figure Test (shifts)
the scorer had to decide whether a genuine "spontaneous"
119
change had been made in the orientation and relationship
of the given figures. In Varied Figural Classes, although
most of the probable responses were accounted for in the
scoring key, a list was kept of all non-keyed responses.
A determination was made later whether such responses
were due to guessing or whether they were acceptable,
although not anticipated in the test development process.
In the experimental figural-systems tests, such as
Designs, close evaluation of each response was required.
Properties such as contiguity, overlapping, orientation,
repetition, and alternation were used in order to produce
a variety of acceptable figural-systems responses. The
scoring guide was based upon the combinations of these
qualities in the responses.
In the Monograms test all of the givens were to be
used repeatedly, so that different figures were produced
under somewhat greater restrictions than in the Designs
test. Care was exerted in the scoring to be sure that
monograms were not mere variations using the same set of
properties. The Dot Systems test was the figural-systems
test most likely to elicit variations on a single
principle because of the limited area in which the
120
examinee could manipulate the given figures. In scoring
this test3 however, less effort was required than in the
Designs and Monograms tests. Since the examinee encoun
tered to relatively fexjer spatial restraints, the scorer
was required to evaluate a greater variety of responses
in the latter two tests.
In scoring the figural-transformation tests most
of the probable match-problem solutions were anticipated
by the scoring key. In the Making Objects test, however,
a relatively greater degree of precision was required to
ensure that "transformation" variance was measured rather
than "unit" variance: In the Sketches test, for example,
the examinee had only to produce "recognisable" objects
that were not duplications of previous responses. In the
Making Objects test, however, the drawings produced had
to be recognizable, and in addition, the scorer had to
determine whether same givens were used in different ways
within each production.
Although the experimental symbolic tests were less
vulnerable to effects of such subjective evaluations, it
was not possible to develop fixed or "objective" scoring
keys for all of these new tests. In the test-construction
phase of the study it had been determined to minimise the
necessity for the examinee to lable the responses produced
None of the new symbolic tests require the examinee to
explain how, or why, or the principle, or the reason sup
porting his response. In a sense, this facilitated the
mode of response, and to some degree resulted in simpler
scoring criteria. In this simplification process, however
some curtailment may have been imposed upon possible
responses outside the structured-response format. Another
disadvantage was that, padding, exhausting all possible
combinations, or other manifestations of guessing or
chance responding, was facilitated. In those instances
in which an examinee appeared to exhaust the list of all
possible letter or number combinations, appropriate cor
rective scoring formulas were applied. Although there
were some instances of this among responses of the
adolescent sample, it was not evident in the adult sample.
In those instances where padding seemed obvious, an
inspection was made of an examinee's response patterns on
other tests in the battery. In no case was any examinee
found to be a consistent odds player or padder to the
degree that it was necessary to eliminate him from the
122
study sample.
Appendix C lists each test, a brief description of
the task imposed, and the type of scoring criteria applied.
Statistical Treatment of the Score Data
Subsequent to scoring, a preliminary inspection of
the obtained raw scores was followed by computation of the
descriptive parameters of the test measures. Scores x^ere
punched into hollerith cards and processed by electronic
digital computer which provided means, standard deviations,
frequency distributions, and inter-part correlations for
the data on each test variable.
In those instances in which score distributions
appeared symmetrical and approached normality, no change
was made in the scoring criteria. If reliability esti
mates were below .60, another review of the scoring was
made to determine whether all procedures were properly
applied. If no major errors were discovered, then possible
modifications in the scoring criteria were tried, in order
to determine whether the revised approach would achieve a
higher degree of alternate-form reliability.
Where reliability estimates appeared satisfactory,
123
but score distributions appeared mildly skewed, no change
was made in either the obtained score distributions or the
scoring criteria. Where distributions of scores were
moderately skewed, or were truncated, a normalising trans
formation was applied. Dot systems did not appear to be
as difficult a test for the Adults as it did for the
Adolescents. In the younger group the distribution was
negatively skewed. Make A Figure Tests (shifts) and Match
Problems III and Varied Symbols were positively skewed and
truncated in the two samples. In addition, for the Adoles
cent sample Symbol Elaboration appeared quite difficult
and resulted in a positively skewed and truncated distribu
tion. A number of zero scores resulted in a truncated dis
tribution of the Seeing Trends II scores in the Adoles
cents. Normalized score distributions were obtained by
applying a C-scale transformation (Guilford, 1956a) to the
four tests in the Adult sample (4, 11, 14, and 27) and to
five tests (11, 14, 23, 25, and 27) in the Adolescent
sample. This resulted in means of approximately 5.0 and
standard deviations of approximately 2.0. Limited Words,
test 9, was positively skewed, truncated, and extremely
leptokurtic in the two samples, therefore, it was
necessary to dichotomize the distributions .
124
Prior to the scale transformation it was necessary
to develop a weighted scoring key for Varied Symbols in
an attempt to obtain a higher interpart correlations.
Although weighted scoring keys were also attempted with
other tests, no increases in estimates of reliability were
obtained.
Table 2 lists the means and standard deviations
for each of the 29 test measures in the two samples. As
might be anticipated, for most of the tests, the mean per
formance of Adults were found to be at higher levels. It
could be assumed that parallel abilities, if they do exist
in the two populations, would be more highly developed in
adults through training and experience. Since a wider
range of IQ was represented in the Adolescent sample
(Guilford et al., 1961), equivalent or greater variances
might be anticipated in the ninth-grade student sample.
Table 2 presents two-tailed tests of significance for F-
and t- ratios computed to compare variances and means in
the two groups. Since the samples were large, 238 and 205
standard deviations of the test scores were used as the
bases for estimating population variances.
TABLE 2
COMPARISON OF MEANS AND VARIABILITIES SD OF THE ADULT AND ADOLESCENT SAMPLES
238
205
Adults
Adolescents
Ratios
Tests
Mean SD
Mean SD
a b
F t
1. Alternate Additions
2. Alternate Letter Groups
3. Designs
4. Dot Systems
5. Figural Similarities
6. Figure Classification
7. Four-Letter Words
8. Letter Group Relations
9. Limited Words
10. Make A Figure Test (fluency)
11. Make A Figure Test (shifts)
12. Make A Mark
13. Making Objects
14. Match Problems III
15. Match Problems IV
16. Monograms
17. Name Grouping
18. Number Grouping
19. Number Rules
20. Numerical Operations
25.03
21.38
13.68
28.52°
36.20
8.66
26.03
38.03d
3.99
59.36c
7.03
21.18
40 -57c
5.46 °
28.93
13.97
9.03
10.95
27.41
52.04
5.00
5.34
4.04
8.84°
6.43
2.18
8.23
5.98d
2.49
15.68c
4.99
8.20
7 .78
3 .21°
6.71
4.31
2.46
3.69
6.02
19.08
20.11
15.91
12.20
23.18°
31.49
8.04
21.04
37•62d
1.87
43.44,
6.42
18.44
36.130
4.70°
24.39
13.14
7.30
8.77
21.01
35.43
5.05
1.02 10.25**
5.60 1.10 10.52**
4.08 1.02
9.66
1.19 6' . 0 7 * *
6.54
1.03
7-59**
2.23 1.05 3.10**
8.04
1.05 6.48**
6.70-} 1.26*
.67
1. 82d
1.87** 1.06
16.23
1.07 8.75**
3.98
1.57 1.41
7.23 1.29*
3.75**
9.52
1.50**
5.35**
2.80
1.31 2.69**
6.46 1.08
7.32**
4.55
1.11
1.98*
2.69 1.20
6.92**
3.56
1.07 6.41**
7.64 1.6l**
9.69**
15.24
1.57**
12.98**
to
U i
TABLE 2-Gontinued
Tests
238
Adults
205
Adolescents Ratios
Mean SD Mean SD fa t3
21. Perceptual Speed 46.18 9.90 36.63 9.51
1.08 10.38**
22. Picture Classification
20.13 3.66 17.63c
4.41 1.28* 6.92**
23.
Seeing Trends II 9.89 3.31 6.21 3.62 1.20 11.15*W
24. Sketches 22.04 6.46 16.12
4.95g
1.70 10.96**
25.
Symbol Elaboration 25.84
12.45
8.84°
9.71 1.64** 16.03**
26. Varied Figural Classes
28.25g
7.64 31.52 8.04 1.11 4.36**
27.
Varied Symbols
11.99 6.29° 10.03° 5.83
1,16 3,44**
28. Verbal Comprehension 25.28
5.03 17.26
5.09
1.02 16.71**
29.
Word Relations 18.06
^.37
13.72 6.01 1.89**' 8.68**
aF-ratio
bt-ratio
c
Parameter prior to C-scale transformation of scores (Mean - 5.0, SD - 2.0)
^Dichotomized near the median (Adults p -.53* q -.47; Adolescents p - .55, q - .4f)
127
Reliabilities
Three estimates of the reliability of the test
measures are listed in Table 3. Alternate-form estimates
(r^) , based upon interpart correlations were extended by
the Spearman-Brown formula (Guilford, 1956). Communal!-
ties (h^), obtained as a result of the factor analyses of
the score data, were taken as lower-bound estimates of the
proportion true variance in each set of measures
(Guilford, 1956). The third set of reliability estimates
was based upon the squared multiple-correlation coeffi
cient between each variable taken in turn and a linear
combination of the 28 other variates in the battery (Harmsr\,
1960). Examination of Table 3 indicates that in only one
instance was the alternate-form reliability estimate less
than either of the other two reliability estimates.
Since five of the eight marker tests were single
part tests no alternate-form estimates of reliability are
available for these measures. This deficiency is indi
cated by blanks in Table 3. Where distributions were
dichotomized or C-scaled, the alternate-form reliability
was based upon the distributions prior to scale trans
formation. One possible effect regarding the factor
TABLE 3
RELIABILITIES3 OF THE TEST SCORES
Adults Adolescents
Tests
2
R h2 r
11
2
R h2 r
l:
1 . Alternative Additions
47 55 59 57 65 68
2. Alternate Letter Groups
27 34
45 54 60
59
3.
Designs
37 43
64
57 65 64
4. Dot Systems 26
33 37 44
51 65
5.
Figural Similarities 20
29
21
30 36
23
6. Figure Classification 18
25
—
36 42
7.
Four-Letter Words 28
37
—
34 42
8. Letter-Group Relations
17 24 11
20 27 44
9.
Limited Words 26 32 41
33 38 36
10. Make A Figure Test (fluency) 38
45
66
57 65 79
11.
Make A Figure Test (shifts)
19 25
42
17 22
27
12. Make A Mark 32 41 56
37 43 53
13-
Making Objects 44
51 65 44
53 63
14. Match Problems III 50 58
53 52 60
43
15. Match Problems IV
37 45 57 44
51 65
16. Monograms 44
53
62 46
53 78
17. Name Grouping 29
37
34
30 36
47
18. Number Grouping 26
33
60
52
59 55
19. Number Rules 41
51 59 65 70 80
20 . Numerical Operations 39 48 --
45 51
‘--
(Continued)
TABLE 3-Continued
Adults Adolescents
2 P - 2 2
H h2 ru fi2 h2 , ru
21.
Perceptual Speed
39 47 36 43
22. Picture Classification
31
40 21 40
47 39
23.
Seeing Trends II
36
43 55 54
60
71
. -'24.' .Sketches 38 47
58
39
48
57
25.
Symbol Elaboration 34
43 57
48 56 70
, -. 26 . Varied Figural Classes 20
27 35
18
25
38
; 27. Varied Symbols
39
46 ' ‘26
33
28. Verbal Comprehension
■ ' 31 ‘
.4 1
- -
43 51
«. —
29.
Word Relations"
43 49 56
53
60 72
£
Three estimates of reliability were obtained for each test except those with
single parts which are Indicated by a dash in columns headed r^:
2
R is a squared multiple-correlation;
2
h is the communality of the test taken as a low-bound estimate;
rll is based uP°n an alternate-form correlation corrected by Spearman-Brown formula.
130
analyses can be seen from inspection of Table 3 which
indicates that in only eight of the test measures were
estimates of reliability in the Adult sample greater than
in the Adolescent sample. The length of test vectors and
their loadings on factor axes could be expected to be
similarly represented.
The reliability estimates obtained for the marker
tests with the Adult population were of similar levels
to the previous findings of the USC Aptitude Project with
these same tests. Although only fourteen of the variables
in both samples had reliability estimates of .55 or
greater, it was decided to include all tests in the
battery, even those with low reliabilities. Since it is
experimentally desirable to overdetermine the factor
structure, few variables could be dropped from the
correlation matrices without seriously restricting the
possible interpretation of the resultant factor structures.
CHAPTER V
THE FACTOR ANALYSES
Intercorrelations
The score matrix of 29 raw, scaled, and dichoto
mised variates x^ere punched as non-negative integers into
Hollerith cards and processed by IBM 7090 computer at the
Western Data Processing Center of the University of
California, Los Angeles. All intercorrelations computed
by the BIMD 17 program (Hayward, 1961) x^ere Pearson r fs
with the exception of the point-biserial correlations
obtained with the dichotomized variable 9, Limited Words.
The correlation matrices for the Adult and the Adolescent
samples are listed in Tables 4 and 5, respectively. The
point-biserial coefficients if converted to biserial rfs,
as estimates of Pearson r's, would result in coefficients
that x*ere approximately 25 per cent greater (Guilford,
1959a) . The biserial x _ assumes a continuous, normally
distributed variable underlying the dichotomized scores.
Had a better scoring distribution been devised for the
131
TABLE 4
CORRELATION MATRIX sa ADULTS
132
1
2 3 4 5 6
1 . Alternate Additions 19 15 16 24 13
2. Alternate Letter Groups 19 11 27 18 16
3. Designs 15 11 26 07 -00
4. Dot Systems 16 27 26 15 09
5. Figural Similarities 34 18 07 15 05
6. Figure Classification 13 16 -00 09 05
7. Four“Letter Words 33 10 18 05 12 01
8 . Letter-Group Relations 11 -01 -00 -02 08 -07
9. Limited Words 31 23 10 15 12 20
10. Make A Figure Test (fl) 21 20 34 28 09 05
11. Make A Figure Test (£x) 09 -09 12 05 -09 01
12. Make A Mark 01 06 25 18 12 -03
13. Making Objects 13 15 44 18 10 -05
14. Match Problems III 36 24 19 29 . 20 19
15. Match Problems IV 33 24 29 30 13 14
16. Monograms 16 12 40 10 -01 -03
17. Name Grouping 31 22 12 17 15 06
18. Number Grouping 27 17 14 09 09 05
19. Number Rules 40 30 22 20 10 15
20. Numerical Operations 47 19 18 09 20 11
21. Perceptual Speed 34 24 26 16 17 21
22. Picture Classification 12 20 11 10 23 25
23. Seeing Trends II 30 27 17 12 25 12
24. Sketches 02 =02 33 12 -07 -05
25. Symbol Elaboration 15 22 20 20 11 13
26. Varied Figural Classes 07 -08 -03 -09 -08 14
27. Varied Symbols 40 17 13 05 23 18
28. Verbal Comprehension 12 09 08 14 10 17
29. Word Relations 40 25 07 17 26 18
(Continued)
aBecimal points have been omitted.
TABLE 4--Continued
133
7 8
9b
10 11 12 13 14 15 16 17 18
1. 33 11 31 21 -09 01 13 36 33 16 31 27
2. 10 -01 23 20 -09 06 15 24 24 12 22 17
3. 18 -00 10 34 12 25 44 19 29 40 12 14
4. 05 -02 15 28 05 18 18 29 30 10 17 09
5. 12 08 12 09 -09 12 10 20 13 -01 15 09
6. 01 -07 20 05 01 -03 05 19 14 -03 06 05
7. 15 19 03 -01 04 10 17 15 17 24 11
8. 15 09 05 04 03 04 08 09 01 22 17
9.b 19 09 09 -02 03 06 27 13 05 20 08
10. 03 05 09 06 37 36 24 19 40 13 08
11. -01 04 -02 06 13 22 02 05 22 -08 -05
12. 04 03 03 37 13 30 -01 13 39 05 03
13. 10 04 06 36 22 30 25 16 37 16 15
14. 17 08 27 24 02 -01 25 39 03 11 12
15. 15 09 13 19 05 13 16 39 20 20 24
16. 17 01 05 40 22 40 37 03 20 13 10
17. 24 22 20 13 -08 05 16 11 20 13 23
18. 11 17 08 08 -05 03 16 11 24 10 23
19. 18 20 22 30 00 11 13 30 27 19 27 36
20. 18 04 31 14 04 06 15 17 25 16 27 18
21. 28 05 18 23 16 06 26 39 36 21 17 12
22. 07 04 25 06 00 14 9 23 09 -00 11 07
23. 29 11 27 11 -05 -02 15 34 18 OS 23 16
24. 10 14 -04 31 21 30 41 -04 10 45 09 “00
25. -02 11 15 20 -01 -01 16 39 30 04 11 30
26. -02 12 01 03 -08 02 11 -14 06 -00 01 10
27 . 32 12 29 16 -07 -02 08 32 29 06 28 23
28. 21 08 24 04 -06 09 02 17 08 -07 29 13
29. 26 12 31 09 -11 -04 05 42 16 -01 20 24
(Continued)
TABLE 4=~Continued
134
19 20 21 22 23 24 25 26 27 28 29
1. 40 47 34 12 30 02 15 07 40 12 40
2. 30 19 24 20 27 -02 22 -08 17 09 25
3. 22 18 26 11 17 33 20 -03 13 08 07
4. 20 09 16 10 12 12 20 -09 05 14 17
5. 10 20 17 23 25 -07 11 -08 23 10 26
6 . 15 11 21 25 12 -05 13 -14 18 17 18
7. 18 18 28 07 29 10 2 -02 32 21 26
3. 20 04 05 04 11 14 11 12 12 08 12
9.b 22 31 18 25 27 -04 15 01 29 24 31
10. 30 14 23 06 11 31 20 03 16 04 09
11. 00 04 16 00 -05 21 1 -08 -07 -06 -11
12. 11 06 06 14 -02 30 1 02 -02 09 -04
13. 13 15 26 07 15 41 16 11 08 02 05
14. 30 17 39 23 34 -04 39 -14 32 17 42
15. 27 25 36 09 18 10 30 06 29 08 16
16. 19 16 21 -00 08 45 04 -00 06 -07 -01
17. 27 27 17 11 23 09 11 01 28 29 20
18. 36 18 12 07 16 -00 30 10 23 13 24
19. 28 23 07 32 07 32 06 29 22 40
20. 28 30 04 31 09 28 01 38 12 27
21. 23 30 26 24 08 21 01 37 19 30
22. 07 04 26 28 -09 12 02 14 33 28
23. 32 31 24 28 -02 22 00 31 33 41
24. 07 09 08 -09 -02 -03 10 07 -09 -09
25. 32 28 21 12 22 -03 5 19 04 23
26. 06 01 01 02 00 10 5 08 01 10
27 . 29 38 37 14 31 07 19 08 12 37
28. 22 12 19 33 33 -09 4 01 12 26
29. 40 27 30 28 41 -09 23 10 37 26
TABLE 5
CORRELATION MATRIXfa ADOISECENTS
1 2
3
4
5
6
1.
Alternate Additions
47 31
28 34 33
2. Alternate Letter Groups
47
40
39 39 37
3.
Designs
31
40 41
13
20
4. Dot Systems 28
39
41 28 18
5.
Figural Similarities
3^ 39 13
28
23
6. Figure Classification
33 37
20 18
23
7-
Four-Letter Words 20
15 15 15
16
17
8. Letter-Group Relations
17
20
13 17
10
09
9.
Limited Words 22
31
28 22
23
21
10. Make A Figure Test (fl) 28
35 54 45
04 01
11. Make A Figure Test (fx)
09 17
26
23
11
07
12. Make A Mark
07 23 35
36
13
06
13.
Making Objects 28
25 47 35
16 -02
14. Match Problems III 48 48
31
41
37
36
15.
Match Problems IV
31 39 29 34
23
22
16. Monograms
15 25
40
29
02
05
17.
Name Grouping 21
37
26
25
20 22
18. Number Grouping 54
47 37 23
32 29
19.
Number Rules
59
56 38
31
34 34
20. Numerical Operations
49 37
28
05
18 24
21. Perceptual Speed
33 31
41 18 17
28
22. Picture Classification 26 41 22 16 26 32
23.
Seeing Trends II
45 51 33 29 35
44
24 . Sketches 20 20 42
33 03
-01
25.
Symbol Elaboration 41 42 32 21
27
30
26. Varied Figural Classes 04 10 04 18 06
-05
27.
Varied Symbols 22 24 16 08 06 12
. 28. Verbal Comprehension
27 23
22 12 16 32
29.
Word Relations
(Continued)
48
47 32 24 22 36
Decimal points have been omitted.
Table 5-Continued
136
7
8
9
10 11 12
13
14
15
16
17
18
1. 20
17
22 28
09 07
28 48
31 15
21 54
2.
15 20
31 35 17 23 25
48
39 25 37 47
3-
15
13
28
54 26
35 47 31 29
40 26
37
4 ,
15 17 22
45 23 36
35
41 34 29 25 23
5- 16 10
23
04 11
13
16
37 23
02 20 32
6.
17 09
21 01
07
06 -02 36 22
05
22
29
7. -01 28
07 07 07 24
15 19 07 25 32
8. -01 10 20 11
15
21
09 13 07
16 12
9- 28 10
13
Ob 02
17 l?
20
03
28 32
10.
07
20
13
22 44 40
19
21 52 24 21
ii.
17
11 06 22 16 28
17 25 13
11
09
12.
07 15
02 44 16 32 19
22 34 12
13
13. 24 21
17
40 28 32 44 21 28
35
18 22
14.
15 09 17 19 17 19
21 52
53
08 32 34
15.
19 13
20 21
25
22 28
53
18
27 34
16.
07 07 03
52
13
34
35
08 18 10
15
17.
25
16 28 24 11 12 18 32
27
10
23
18.
32 12 32 21
09 13
22 34 34
15 23
19. 32
15 ^3
21 11
07
22 42 32
13 36 60
20.
28
17 34 11 01
03 17
21 22
13 25
36
21.
23
22 20 14
17 09 25
30 32
07 30 33
22. 12
15 31
10 06
13
24
35
34 08 22
25
23. 32
07
30 16 20 05 17
47
36 02 30 47
24.
18
05
14
39
11
31 33
21
23 49
12
15
25. 20 10 36 18 11
-07 18
33
21
03 35
40
26. -10 20 -01 24
09 10 08
05
12 08
07
06
27. 14
13
18 22 04 11 -01
17 19
20 26 21
28.
39
-10 24 02 02 02 10
25 07
-06 16 38
29. 29 15
40 18 12
-03 17 39 38 05 37 51
(Continued)
Table ^-Continued
137
19
20 21 22
23
24
25
26
27
28
29
1 .
59 49 33
26
45
20 41 04 22
27
48
a. 56
37 31
41
51
20 42 10 24
23 47
3.
38 28 41 22
33
42 32 04 16 22 32
4. 31
05
18 16
29 33
21 18 08 12 24
5. 34 18
17
26
5 03 27
06 06 16 22
6. 34 24 28 32 44 -01 30
-05
12 32 36
7.
32 28
23
12 32 18 20 -10 14
39 29
8.
15 17
22
15 07 05
10 20
13
-10
15
9. 43
34 20 21 30 14 36 -01 18 24 40
10. 21 11 14 10 16
39
18 24 22 02 18
11. 11 01
17
06 20 11 11
09
04 02 12
12.
07 03 09
12
05 31
-07 10 11 02
-03
13.
22
17 25
24
17 33
18 08 -01 10 17
14. 42 21 30 35 47 21
33 05 17 25 39
15. 32 22 32 34 36 23
21 12 19
07
38
16.
13 13 07
08 02
49 03
08 20 -06
05
17- 36
25
30 22 30 12
35 07
26 16
37
18. 60 36
33 25 47 15
40 06 21 36
51
19. 52 34 40
57
18
37
04 24 44
55
20.
52
33 31
42
17 35 -03
21 28 44
21.
34
33
28
33
11
25 05
21 16 38
22. 40
31
28
39
10 36
05 13 33 39
23. 57
42
33 39 13 39
04 21 38 52
24. 18 17 11 10
13
08
09
26
05
10
25. 57 35 -25
36
39
08
-09 25
38
51
26. 04
-03 05 05
04
09 -09
-02 -15 -03
27. 24 21 21
13
21 26
25
-02
13
24
28. 44 28 16
33 38
05
38 -15
13 35
29. 55
44 38
39 52 10
51 -03 24
35
138
Limited Words test it would have probably yielded distri
bution approaching normality. As a consequence of not
correcting the obtained point-biserial r's, the lengths
of test vector 9 will be proportionately underestimated
in the test configurations in the factor structures.
Extraction of Factors
Squared multiple-correlation coefficients, as
lower-bound estimates of communality, were inserted into
the principal-diagonal cells of each correlation matrix by
the computer program (D¥?yer, 1939). The reduced matrices
(Harman, 1960a were factored by the program that applies
Jacobi's algorithm (Goldstine, Murry, and von Netiman, 1959)
for obtaining a principal-factor solution. It was assumed
that the factor space would be adequately determined
(Harman, 1960^) by two criteria: (1) that the eigenvalues
should be positive, and (2) greater than zero. Seventeen
principal factors were extracted from each correlation
matrix. The principal-factor axes in the Adult sample,
Table 6, are designated by capital letters. The axes in
the Adolescent sample, 'are designated by Roman numerals
in Table 7.
TABLE 6
139
UNROTATED FACTOR MATRIX, ADULTS
A B C D E F G H
1 .
-61
15 -25 -09 -15
14 -10 -02
2. -43 07
18 -04 11 20 01 -01
3.
-42
-43
08 02 -02
-05 07 -09
4.
-37
-12
29 -05
14
13
04
-17
5 • -33
14
07
11 01 10 -24 -11
6 . -24 20 24
05
-10
07
14 22
7. -39
06
-27
21
-17 -03 09
-22
8. -19
02 -26 01 18 -19 04 -06
9.
-43
20 01
15 -05
08 01
13
10. -42 -41 11 -04 12 12 -14
05
11. -03 -31
08 04 -19 -16
17
10
12. -21
-47
08 22 16 11 -10 06
13-
-39 -51
04 06 01 -18 -11 -04
14. -58 12 32 -16 -12 -18 -08
-15
15.
-51
-08 08
-25
-06 -04
09
-08
16.
-32 -60 -10 06
-07
11
05 07
17.
-43 05 -23
11
15
12
15
-12
18. -37 05
-18 -21
25
-08 10 06
19.
-58 04 -11 -16 24
03
10
09
20. -52 07 -20
-09 -18 18 00 16
21.
-56
-03 09
04
-29 -14
05 04
22. -34
17 27 36
07
-12 -06 14
23.
-54 22 -02
17 03
-06 -02
-05
24. -17
-61
-17 06 -04 -04 01 02
25.
-42 06
19 -37 13
-11
03
08
26. -03 -05 -31
00
15
-22 -18 14
27.
-55 17
-21 -04
-19 -01 -08 04
28.
-34 24
05
38 18 -06 19 -01
29.
-56 34 -04
05 05 -09 -14
03
TABLE 6-Continued
140
1 J K L M N 0 h2
1.
-04 -08 00 -02 -11
-07
-04
55
2. 01 04
09
00 20 -10 06
3^
3. 03
08
15
-06
-07
11 02
43
4. -08 -04
-05
-12 -04 -06
03
34
5.
-04 16
-09
16 -01 -00 -00 29
6. -06
-09
-02 01
07 05 -03
26
7.
04 -08
07
06 00
03
04
37
8. -01
-03 -23 09
04 -01 04 24
9. 05
-01 -10 -15 -02 -01
09
32
10. 02
-15 -05
-02 02 06
-09 45
11, 07
02 -10 06 -06 -12 01
25
12. -09
-01 -06 11 -12 01 02 41
13.
08 14 02
-09 05 -07
-08 52
14. 07
-12
-09 -03 -03
01 -02 58
15.
-28 02 02 -01 -04 01
09
45
16.
06 -06
09
10 02 -02
05 53
17.
-07
10 -08 -05 09 -03
-08
37
18. -05
08 11 11 -01 -01
-03 3^
19.
12
-17
04
05
-04 -02 -01
51
20. 07
22
-05
-06
-09
-01 -01 48
21.
-13
-01
07 05 05
-06
-07 47
22. -10 06 01 06 02 00
03
41
23.
20 08
07
-01 02 04 06
43
24. 02
-05
-10
-07
10
05
04 48
25.
09
14
-05 02 -01
07
01
43
26. -17
-02
07
-14 -00 -04
03
28
27. -09 -01 -05 02
09 13
-01 46
28. -03
-00
03 -07 -09
04
-07
41
29.
10 -13 04 01 -01
-05
02 50
141-
TABLE 7
UNROTATED FACTOR MATRIX, ADOLESCENTS
I II III IV V VI VII VIII
1. 67 11 -01 15 -21 -22 -20 -03
2. 72 -02 -17 08 -15 01 12 -04
3. 61 -37 18 -07 11 -03 03 -24
4. 50 -36 -18 -18 -06 -04 15 11
5. 43 11 -26 -10 -09 -12 06 13
6 . 46 26 -14 -09 -10 15 01 -21
7 . 39 13 27 -25 14 03 -12 24
8 . 24 -15 -15 32 18 -07 03 01
9 . 47 15 15 02 15 02 19 14
10. 44 -61 11 11 -09 -04 16 -03
11. 25 -22 -14 -09 18 -04 -01 -03
12 . 27 -51 -06 -15 -02 02 01 -02
13. 44 -40 07 -13 27 -22 -05 -00
14. 62 03 -36 -16 -12 11 -11 -01
15. 54 -11 -29 -05 10 15 -20 09
16. 30 -56 22 04 -18 09 -06 -05
17. 48 01 -03 10 14 20 15 14
18. 65 15 09 02 -11 -20 -11 07
19. 77 24 10 07 -09 -15 07 06
20. 55 21 22 21 05 -05 -15 -02
21. 51 04 -03 12 27 08 -19 -12
22. 52 14 -12 -04 12 08 09 -14
23. 68 24 -10 -10 -04 03 -05 -02
24. 35 -46 23 -06 -12 15 -12 09
25. 59 26 11 06 -01 01 24 -05
26. 08 -24 -25 20 01 -10 04 12
27 . 34 -03 16 20 -12 32 -03 09
28. 44 34 25 -32 -03 -03 07 -07
29. 68 27 04 12 09 05 01 -01
(Continued)
142
TABLE 7--Continued
IX X
VT
A.1 XXI XXII XIV XV h2
1. -06 -06 -12 02 06 01 04 65
2. 07 02 02 -06 -07 -08 -01 ' 61
3. -12 01 04 -08 -05 11 -04 65
4. -08 02 -01 -05 05 08 08 51
5. 11 00 -11 -10 -08 -02 -06 36
6. 05 17 -02 -07 02 -02
t
08 42
7. 01 12 -04 -00 03 -06 04 42
8. 09 10 -11 04 03 01 02 27
9. 09 -05 08 -10 -06 08 03 38
10. -10 07 03 08 06 -04 03 65
11. -15
-01 05 -04 03 -12 -09 22
12. 15 16 -08 06 -07 02 -02 43
13. 06 -13 -08 03 02 -06 01 53
14. -07 -12 -08 03 05 07 00 61
15. -02 -13 11 06 -07 -01 02 51
16. 09 -04 04 -05 -04 -10 04 53
17. -07 06 -10 -02 02 -02 02 36
18. -06 11 08 09 -18 01 -01 59
19. 02 -02 05 -01 02 04 -06 70
20. 17 -01 - 00 -09 08 -00 01 51
21. -07 11 -06 -02 -04 07 -03 43
22. 30 -11 06 12 02 -00 -01 47
23. -03 09 14 -07 12 -06 -06 60
24. 06 -11 04 -04 06 08 -03 48
25. -12 -18 -09 04 -01 -03 -04 56
26. 04 10 16 07 10 05 -03 25
27. -04 04 -OS 06 -01 -01 -10 33
28. 02 09 -02 15 06 02 -02 51
29. -12 -05 09 05 -03 -03 12 60
143
Rotation of Axes
The objective in rotating axes was to obtain an
orthogonal simple structure in which the reference vectors
would be interpreted to represent a set of statistically
independent traits (Tb.urstone, 1947). In Thurstone5 s
concept of parsimony, the scientific problem is primarily
one of seeking a set of descriptive categories or traits
that would explain the correlation matrix in simple but
meaningful terms. He believed that this goal was accom
plished in a rotational solution by substituting for the
arbitrary reference frame another orthogonal frame which
would provide both a logical and a scientific interprets-
tion of the correlation matrix.
Within the context of a discussion of oblique
rotational solutions, Thurstone (1947) had outlined the
criteria by which to evaluate a simple structure. Harman
(1960^) has indicated that these criteria apply equally
well when the factor pattern and the factor structure
coincide, as an orthogonal solution. He has restated
Thurstone*s five basic terms in such a context:
1. Each row of the factor matrix should have at
least one zero.
144
2. If there are m common factors, each column
of the factor matrix should have at least
m zeros.
3. For every pair of columns of the factor
matrix there should be several variables
whose entries vanish in one column but not
in the other.
4. For every pair of columns of the factor
matrix, a large proportion of the variables
should have vanishing entries in both
columns when there are four or more factors.
5. For every pair of columns of the factor matrix
there should be only a small number of
variables with non-vanishing entries in both
columns (p. 113).
Guided, in part, by these criteria for simple
structure, the axes in each matrix were .rotated by the
Zimmerman (1946) orthogonal graphic rotational procedure.
In using this somewhat subjective method, the writer was
persuaded by successful results and experience of the
Aptitudes Project (Guilford, et al.. 1961). In dealing
with aptitude variables they had found that maintaining
positive manifold and rotating to a simple structure were
major initial steps to the interpretation of a factor
structure. In order to derive the fullest meaning from
the factor analysis, however, further rotations beyond
these two initial criteria were usually necessitated.
These additional rotations would be guided, in part, by
145
the known factor content in the configuration. Super
imposed upon these relatively unbiased criteria, however,
would be a somewhat subjective one of "psychological
meaningfulness." Although such considerations of logic
were joined with Thurstone's qualitative criteria for
simple structure, they were believed to provide more
satisfactory solutions than the "analytical" methods.
Kaiser (1951) had indicated that "the" ultimate criterion
"of a rotational procedure is factorial invariance, not
simple structure--although the two notions appear to be
very highly related" (p. 1). It was the writer's persua
sion that mathematical approximations to simple structure
and factorial invariance are laudible objectives,but the
adequacy of such solutions to basic psychological research
have yet to be satisfactorily demonstrated. Guilford
(1962) has aptly stated the case for the provisional con
tinuation of rational criteria for rotating:
The rotation problem has bothered many
psychologists and others. Those with a strong
mathematical conscience insist upon a completely
objective analytical rotation or none. If such
kind of rotation were successful from the
psychological point of view it would be fine.
Unfortunately it rarely is. The reason is that we
can never know enough in advance of the analysis
to include just the right variables to represent
146
each common factor. We should have to know as much
as we do after the analysis, perhaps more. The
sampling of experimental variables is all-important
for achieving rotation mechanically to satisfy some
rigorous mathematical criterion. If we knew enough
for this purpose in advance we should hardly have to
do the analysis at all.(p. 124).
Analytically rotated, orthogonal solutions, based
upon the Kaiser (1958) varimax criteria, were obtained,
nevertheless. Since they did not provide sufficiently
clear or meaningful solutions in either sample, it was
determined that extensive discussion of the analytical
rotational results was not warranted in this study. The
two varimax solutions are listed in Appendix E. These
will be discussed within the context of "congruence" later
in this Chapter.
Fifteen principal-factor axes x^ere graphically
rotated 138 times in the Adult sample and 121 times in
the Adolescent sample. In each solution, approximations
to a simple structure were obtained before other rotations
were made to the criteria of psychological meaning. The
factor structure and positive manifold were improved by
ten further adjustive rotations in each solution.
Each principal-factor axis in the separate
samples, was rotated at least once against every other
147
axis in the factor matrix. The plot was then examined to
determine (1) if there were a large concentration of
points in two radial streaks, and (2) that there were a
large number of points near the origin in the hyperplanes
of the two axes, and (3) that there were a small number of
points that were "off the two radial streaks" (Harman,
I960, p. 113). These three methodological criteria were
Thurstone’s bases for assurance the simple structure was
unique and that the structure was "compelling."
In the subsequent interpretation of the graphi
cally rotated solutions, loadings of .30 or greater were
taken as "significant." Loadings of an absolute value of
.15 were considered as "zero." Harman (I960) had desig
nated loadings of .40 or greater as significant, and he
interpreted loadings of .20 or less as being in the hyper-
p
plane of a factor. Studies conducted by the Aptitudes
Project, have taken absolute value of .10 as the bounds of
the hyperplane. Since the levels of significance are
arbitrary, the value of .15 ttfas believed appropriate as
the reliability estimates for most of the tests in this
battery were only moderate (between .11 and .89) with
higher reliabilities, stricter criteria could be imposed
with greater confidence.
The orthogonal graphically rotated factor matrices
for each sample are presented in Tables 8 and 9, for the
Adults and Adolescents, respectively. Although 17 factors
were extracted, the last two axes represented six per cent
of the total variance in each matrix. Therefore, in the
rotated solutions, the sixteenth and seventeenth axes were
relegated to the residual-factor space. The two axes are
not listed in Tables 8 or 9, nor were they rotated
against any of the other fifteen axes in their respective
matrices. The interpretation of the factor-analytical
results in this study are based upon these two graphic
rotational solutions.and are discussed in Chapter VI under
the heading "Interpretation of the Factors."
Computational Checks on Rotations
j
The matrix of fifteen unrotated axes, in each
sample, was pre-multiplied by its transpose in order to
reproduce an approximation to the original correlation
matrix. The coefficients in that matrix were compared to
a similar matrix generated by the pre-multiplication of
the rotated factor matrix by its transpose. Comparison
TABLE 8
ROTATED FACTOR MATRIX, ADULTS
149
DFU DFS ; DFT DSC DSR DSI CFG CM!
A C D E F G H I
1. 00 05 27 26 23 -05 16 18
2. 05 29 . 07 v03 12 14 17 10
3. 36 36 22 -01 -04 20 06 08
4. 19 27 31 04 05 09 01 18
5 . -09 13 09 21 01 06 40 09
6. 06 -11 11 02 00 11 13 11
7. -03 15 10 23 02 -03 03 13
8. 04 07 08 34 12 04 -04 02
9 . 05 03 .19 11 03 00 14 29
10. 41 36 20 10
a
14 -05 19 05
11. 30 -01 19 ' -17 10 04 03 -11
12 . 44 25 09 - 09 01 -06 25 01
13. 39 40 17 -04 10 12 16 08
14. -10 24 51 12 01 18 18 16
15 . 14 16 39 24 02 27 00 03
16. 52 32 11 -02 09 -06 09 -13
17 . 15 16 -01 31 15 10 04 26
18. 08 11 06- 23 31 33 -02 06
19. 14 22 24 21 45 17 02 16
20. 15 -02 18 06 19 11 20 17
21. 16 10 ' 30 13 -09 19 21 10
22. 04 09 08 . 13 -15 19 35 27
23. -07 24 14 13 08 19 21 29
24 53 27 07 07 -07 -12 -05 -11
25. 04 13 31 05 20 42 10 03
26. 08 00 -04 19 -02 -04 -12 07
27 . 03 02 18 36 04 08 14 08
28. 02 07 02 19 03 16 10 48
29. 16 16 24 23 20 09 19 27
(Continued)
TABLE 8"-Continued
150
csu
J
CSR
K
EFU
L
MSI
M
S1
B
Rl
N
R2
0
h2
1. 16 17 20 38 05 19 03 54
2. "15 16 20 16 -13 10 14 33
3. 17 =03 02 09 02 15 -13 44
4. =15 -07 09 03 -18 12 07 34
5. =01 07 = 01 14 =06 05 02 28
6. -11 26 26 -09 -13 09 10 26
7. 40 15 18 19 -07 -02 =08 37
8. 13 04 =08 05 06 -22 12 24
9. 00 36 09 14 -06 02 06 32
10. =03 =02 03 =02 09 20 04 46
11. 18 -04 05 -04 -02 = 14 04 24
12. =06 =10 -04 -03 01 -05 -20 40
13. 21 -12 •-02 12 20 02 09 52
14. 08 11 17 =05 01 18 21 56
15. =05 =03 19 23 -05 16 01 45
16. 22 01 09 13 02 06 -15 52
17. 12 08 05 26 = 16 =01 10 37
18. 02 03 09 19 09 =03 04 34
19. 05 21 16 10 05 03 07 52
20 16 28 -02 42 02 15 07 49
21. 21 11 38 16 01 11 08 49
22. =09 22 22 =09 00 = 12 -02 42
23. 18 35 09 12 00 -01 04 45
24. 19 =05 =08 08 10 01 00 46
25. =08 11 =03 06 07 13 00 43
26. =04 -03 03 16 39 -13 -04 27
27. 20 29 17 26 08 19 11 47
28. 07 21 16 =07 -13 -14 =07 43
29. 07 33 24 10 14 01 09 53
151
TABLE 9
ROTATED FACTOR MATRIX, ADOLESCENTS
DFU
I
DFC
II
DFS
III
DFT
IV
DSC
V
DSR
VI
DSI
VII
CFG
VII
1 . 26 17 06 21 09 21 22 -04
2 . 27 38 12 18 21 20 21 27
3. 49 04 35 14 01 08 29 17
4. 40 26 20 31 13 -01 17 04
5. 06 44 04 18 06 06 04 12
6. 15 20 -10 13 08 09 -06 36
7 . 01 01 08 -03 11 16 06 00
8 . 08 09 18 -03 22 -07 -01 02
9. 02 16 04 -08 11 15 29 24
10. 51 05 37 08 23 07 28 -08
11. 11 10 22 19 -06 -03 03 04
12 . 39 13 36 13 22 -01 -06 05
13. 24 00 54 13 01 -05 19 02
14. 21 22 -04 54 13 07 08 22
15. 12 09 14 45 20 19 01 21
16. 48 -04 34 00 27 11 20 -01
17. 04 17 02 09 32 -01 20 14
18. 14 24 14 14 06 45 16 01
19. 17 27 01 05 06 32 36 16
20. 14 01 04 -15 14 21 18 17
21. 12 01 12 14 13 06 -02 19
22 . 04 09 11 11 10 14 12 51
23. 19 24 -08 16 00 27 08 27
24. 46 -10 16 08 25 11 24 -00
25- -03 19 -01 10 06 10 49 23
26. 16 08 06 04 09 08 -08 -08
27. 11 02 -11 01 41 15 20 05
28. 02 05 -03 01 -09 22 17 22
29. 00 08 02 16 13 27 27 24
(Continued)
TABLE 9=- “Continued
152
CMU
IX
CSU
X
GSR
XI
EFU
XII
MSI
XIII
Si
XIV
Ri
XV
h2
1. 15 01 28 21 49 01 12 65
2. 04 01 28 11 19 07 07 60
3. 10 09 IS 28 =06 =08 = 11 65
4. 01 19 14 03 = 12 13 11 51
5. 06 16 07 07 21 07 13 36
6. 19 01 31 06 16 -13 10 42
7. 23 49 21 10 06 = 13 04 42
O
O . =04 = 11 12 28 07 24 06 27
9. =01 27 16 22 03 =03 16 38
10. 04 =07 15 03 -18 16 =06 65
11. =02 10 20 09 -09 13 =16 22
12. 11 08 = 10 =01 =14 10 =05 43
13. 06 26 07 15 07 16 =03 53
14. 10 16 20 09 21 08 04 61
15. =10 21 18 16 11 14 =06 51
16. =06 02 -02 = 12 00 =02 =19 53
17. 06 14 29 21 -04 04 02 36
18. 18 11 24 25 22 09 14 59
19. 18 17 29 26 29 04 18 70
20. 09 15 25 28 41 =02 06 51
21. 09 08 29 45 13 -02 -08 43
22. 13 10 11 11 19 17 13 47
23. 16 22 43 14 20 04 04 60
24. =02 24 =06 -02 01 01 =13 48
25. 20 04 28 18 16 -05 09 56
26. = 15 -09 03 09 -09 36 07 25
27 . 11 01 12 12 05 =04 =18 33
28. 47 25 19 03 09 -15 16 51
29. 07 10 45 27 19 -06 14 60
153
of the correlations in the Adult sample revealed no dis
crepancies in excess of .05 between corresponding elements.
A check of the Adolescent sample indicated that errors had
occurred in the rotational procedure that required cor
rection. In order to preclude a tedious search for the
sources of error, a computer program was devised to
reproduce the graphic rotational solution. The sequence
of rotations, the angles of rotation, and the loadings on
principal-factors were the basic input data. The result
ant solution was to be almost identical with the original
solution with only minor variations. In the graphic
solution of the Adolescent sample a number of loadings
were .28 or .29, just barely significant. After machine
reproduction of the solution some of these loadings were
slightly higher, some lower. It was determined, however,
that the factor pattern was sufficiently "compelling",
to permit meaningful interpretation without additional
adjustive rotations.
A computer program was used to obtain computations
of the communalities of each test variable. This was con
sidered as an additional check upon the accuracy of the
graphic rotations. No discrepancies greater than an
154
absolute value of .05 were found between beginning and
final rotations in either sample after the errors of
rotation in the Adolescent rotational solution were
corrected.
Comparison of Factor Patterns
The fifteen axes of the Adult rotated factor
matrix were compared to each of the fifteen axes in the
corresponding Adolescent matrix. A computer program based
on Tucker's (1951) statistical model provided coefficients
of congruence for all pairs of factor axes in the two
matrices.
Table 10 lists corresponding pairs of factor axes,
one from each matrix, which are identified in Chapter VI,
The Interpretation of Factors, by the same factor names.
Column 1 lists these "parallel" factors by structure~of“
intellect code letters. Column 2 lists the factors from
the Adult matrix in capital letters; column 3 lists those
from the Adolescent matrix in Roman numerals.
The coefficients of congruence, 0 , computed for
corresponding factors are listed in column 4. It was
implicit in Hypothesis 3 that those factors identified by
TABLE 10
COEFFICIENTS OF CONGRUENCE (0r) COMPUTED FOR THE TWO GRAPHIC ORTHOGONAL ROTATED
SOLUTIONS: ADULT MATRIX, lg, AND ADOLESCENT MATRIX, 2g
Factor
Matched
Rotated Axes
Coefficient
of
Congruence3
0r
Other Axis-
Pairs With
Higher 0r
Proportions of
Variance
lg 2g lg 2g
DFU A I .84 DFU/DFS .86 .13 .12
DFC B Hi -. 16 .03 .06
DFS C III .79 .10 .08
DFT D IV .81 .10 .07
DSC E V .73 .08 .06
DSR F VI .67 DSR/DSI .68 .05 .06
DSI G VII .59 DSl/CSR .75 .06 .08
CFC H VIII .73 .06 .07
CMU I IX .74 .07 .04
CSU J X .56 .05 .06
CSR K XI .78 .08 .10
EFU L XII .64 EFU/CSC .77 .05 .07
MSI M XIII .63 MSI/EFU .71 .07 .07
Singlet B XIV .47 .03 .03
Residual N XV .10 .02 .03
aHighest 0r was obtained with matched-axes, except as otherwise indicated.
^Proportion of variance is ratio of sum of squares of each factor's
loadings to the sum of communalities within each matrix.
155
156
the same factor names in the two solutions would be
similarly identified by a high index of similarity. In-
spec-tion of Table 10 will indicate that in five instances
the matched pairs were not the highest 0r obtained.
Where axes were found to be matched by a higher value,
those axes and the 0r were listed in the fifth column.
The obtained "between-matrix" coefficients are otherwise
listed in column 4.
The proportion of variance accounted for by each
factor in the graphic rotated solutions is listed in
column 6 or 7. These proportions were obtained by summing
the squares of the 29 tests' loadings on a factor and
dividing by the sum of connmmalities. Some indication of
the composition of the two factor matrices can be obtained
by noting that the matched pairs of factors also tend to
have similar proportions of variance account for rela
tively similar proportions of variance in their respective
matrices. With reference to 0r, Tucker (1951) has stated
that a high coefficient of congruence is a necessary
condition for identifying the invariance of factor
measurements of the same mental function in two popula
tions. The sufficient condition for factorial invariance
157
can be achieved, in part, by a high degree of overlap of
tests administered to the two groups. In the present
study, the overlap x^as complete.
Although Tucker (1951) accepts values between
.93 and unity as evidence of significant congruence, and
rejects values of .43, he states:
For practical purposes it may be desirable to set
up some value . . . less than unity which will be
regarded as acceptable for indicating the identity
of the factors in the two studies. However, no
guiding values have yet been developed, and it
seems proper to delay specifying any minimally
acceptable value . . . until adequate experience in
the application of the method has been gained (p. 43).
Kline (1956) attempts to relate levels of relia
bility of good tests as one basis for accepting values of
congruence. He indicates coefficients above .90 would
evidence high congruence. Those between .80 and .90 would
be generally acceptable, and those between .70 and .80
xrould be regarded as liminal: "accepted by some workers
and rejected by others" (p. 44).
None of the coefficients of congruence in Table 10,
hox^ever, were of sufficient magnitude, by Tucker's
standards, to support the second hypothesis (H2) that the
1
factor axes identified with similar names represented the
same mental functions in the two populations, at least
158
when the two graphic orthogonal rotated solutions were
compared.
Factorial Invariance in Analytical
Orthogonal Rotations
The survey of the literature had indicated that
a number of investigators had taken issue with Thurston's
concept that a simple structure should provide invariant
factor loadings for a fixed battery of tests provided
neither the selection of groups of subjects, nor the
difficulty level of the tests, nor the testing conditions
were altered.
In view of the low degrees of congruence obtained
with axes in the graphically rotated matrices, it was
decided to examine the degree of congruence of factors
rotated by analytical procedures. The same correlation
matrices that were factored by the BIMD 17 program also
provided the analytical solutions shown in Appendix E.
The loadings on fifteen axes of the varimax
orthogonal rotated solution for Adults was compared to
each of the fifteen axes for Adolescents. In the Table 11
notation, _ 1 and 2 represent Adults and Adolescents,
respectively, and the subscript a indicates that the
TABLE 11
159
COEFFICIENTS OF CONGRUENCE (0 ) COMPUTED FOR THE
TWO VARIMAX ORTHOGONAL ROTATED SOLUTIONS:
ADULT MATRIX, lv; ADOLESCENT MATRIX, 2v
Rotated
lv
Axes
2v
0r
Proportions
Matrix lv
of Variance3
Matrix 2v
a i .85 .18 .34
b ii .93 .20 .20
c iii .70 .07 .07
d ix .78 .12 .04
e vi .48 .04 .04
f vii . 19b .02 . 04
g
xi .66 .04 .03
h vi .55 .03 .05
i iii .81 .06 .03
3
viii .67 .05 . 04
k i v .50 . 04 .04
1 i .85 .10 .02
m i .61 .02 .01
n xiv
A
C M
.03 .04
o V .34 .01 .01
aProportion of variance is ratio of sum of squares
of each factor’s loadings to sum of communalities within
each matrix.
^Within matrix 0r is greater: f/n = .37;
iii/xiv = .61
160
matrices were rotated by analytical procedures. Table 11
designates axes by lower-case letters in column 1 for
factors in the Adult matrix, and by Arabic numerals in
column 2 for factors in Adolescent matrix.
Coefficients of congruence, obtained by procedures
similar to those reported for comparing the graphic solu
tions, are indicated in Table 11. The factors in the
graphic solutions were matched pairs in Table 10 on a
basis of similar factor names. In Table 11, however, the
factors are paired by the magnitude of congruence coeffi
cients. These coefficients appear in columns 1 and 2.
Inspection of the 435 congruence coefficients for
paired-comparison of 30 axes indicated that between-
matrices coefficients were generally greater than the
within-matrix coefficients. Column 3 lists the obtained
coefficients of congruence in descending order' of
magnitude. Each axis from the Adult matrix (la) was
paired with an axis from the Adolescent matrix (2a). No
axis in matrix la showed any "significant" relationship
( .93) with more than one axis in matrix 2a, if at all.
In Chapter V it was indicated that no psychologic
ally meaningful inferences could be obtained from the
161
analytical orthogonal rotated solutions. No further
interpretations or elucidations concerning the efficacy
of analytical rotational technique were forthcoming as a
result of the computation of congruence coefficients of
analytically rotated axes.
With respect to the similarity of factor structure
as indicated by the congruence indices, it appears that
if similar factors were measured in the samples from the
adult and from the ninth-grade student populations by
this common battery of tests, such similarity was not
indicated by evidence of congruence.
The varimax rotational solution for each matrix
maintained positive manifold but provided results that
departed markedly from a simple structure. In each
matrix, two large factors were obtained that they were
loaded in divergent-figural and in divergent-symbolic
tests, respectively. Of fifteen factors rotated in each
sample, two factors in each matrix accounted for 38 per
cent and 54 per cent of the variance of its respective
matrix. The balance of the factor-space was composed of
"doublet" and "singlet" factors. Although modification
of Kaiser*s original varimax procedure entailed a
normalizing technique, the obtained factor structures
produced "U-shaped" distributions of factor loadings and
tended to provide solutions that x-7ere not as illuminating
as a sargacious perusal of the correlation matrix.
CHAPTER VI
INTERPRETATION OF FACTORS
The interpretation of the fifteen orthogonal,
graphically rotated axes in each solution was accomplished
in terms of (1) the hypothesized factor content of the
new experimental variables, (2) the known factor content
of marker tests in previous studies, (3) and the rational
psychological meaning found in the factor structure. The
final rotated positions preserved positive manifold, but
the solutions represented only approximations to simple
structure when the bounds of the hyperplanes were taken
as .10. One could say that a simple structure was
obtained in each solution when "zero" loadings are inter
preted as being absolute values of .15 or less. Factor
axes normal to these hyperplanes were interpreted by
inspecting variables with loadings of .30 or greater.
The folloitfing discussion reflects the basis for
identifying the abilities represented by the factor
structures in the two samples.
163
164
Each factor is identified by its putative designa-
tion followed by its placement in the structure-of-
intellect model as indicated by the three-letter code name.
The significant loadings on each axis are listed
separately for the two samples. Where axes have been
matched to represent the same ability they are discussed
under the same factor designation. Only if a test
variable loads significantly on a factor is it included
in the listing preceding the discussion of each factor.
Where such a variable was correctly hypothesised as a
measure of that factor, it is preceded by an asterisk.
The loadings for each variable are based upon the
graphic orthogonal rotated solutions presented in Tables 8
and 9. The loadings for Limited Words, variable 9, have
been adjusted since Tables 8 and 9 underestimate the
probable projection of this test vector in the common-
factor space.
Figural Fluency DFU
Axis A--Adult Sample
* 24. Sketches .54
16. Monograms .52 (DFS .32)
* 12. Make A Mark .44
10. Make A Figure (fluency) .41 (DFS .36)
13. Mak ing Obj ec t s .39 (DFS .40)
3. Designs . 36 (DFS . 36)
11. Make A Figure (shifts) .30
--Adolescent Sample
10. Make A Figure (fluency) .51 (DFS .37)
3. Designs .49 (DFS .35)
16. Monograms .48 (DFS .34)
24. Sketches . 46
4. Dot Systems .40 (DFT .31)
12 . Make A Mark .49 (DFS .36)
Sketches provided the primary evidence for
identifying DFU as distinct from the other figural factors
in the study. It was the only factorially unique DFU test
in both matrices. In defining the factor in the Adult
solution, Sketches and Make A Mark had no secondary
loadings. Sketches had no side loadings in defining
figural fluency in the Adolescent sample. Of thirteen new
experimental measures constructed or adapted to measure
four divergent-production figural factors (DFU, DFS, and
DFT), seven of them were loaded significantly on the DFU
factor in the Adult solution; six in the Adolescent
166
solution. Neither of the match-problems tests appeared
significantly loaded on the DFU axis. Making Objects,
although originally designed as a measure of DFT was
loaded on the DFU and DFS axes for the Adults.
A property common to each of the tests loading on
DFU was that the production of some type of drawing was
involved. The figural multiple-choice tests designed for
DFC and Match Problems III and IV, for DFT, all involved
greater degrees of restriction than the open-end format
of the tests of figural fluency. From the results
obtained it appears that the DFU factor clearly requires
the rapid production of a variety of figural elements
subscribing to specified perceptual properties. The
placement of figural fluency in the figural units cell
of the divergent-production matrix completes the analogous
triad of parallel factors along with word fluency (DSU)
and ideational fluency (DMU). Whether the rapid produc
tion is of figural elements, or of symbolic units, or of
ideas, the emphasis in each is upon variety of production,
where the quantity of what is produced takes precedence
over quality. In the relatively unrestricted situation
presented by these tests, it was demonstrated that
differential abilities to produce the required units
could be found at the two age levels investigated.
Figural Spontaneous Flexibility DFC
Adult Sample--Evidence for the existence of the factor
in this sample is equivocal.
Axis II--Adolescent Sample
* Figural Similarities .44
* Alternate Letter Groups .38
Tito of the four tests hypothesized as measures
of DFC, Figural Similarities and Alternate Letter Groups,
formed a doublet factor in the Adolescent solution.
This provided an indication that the ability was
distinguishable by tests that emphasized the production
of classes rather than those requiring a shift score.
The Make A Figure Test (shifts) had only one significant
loading; this was on DFU in the Adult solution. The
fourth hypothesized measure, Varied Figural Classes, did
not load significantly on DFC but resulted in a singlet
factor in each solution, Axis B and Axis XIV in Tables 8
and 9, respectively. The investigator was unable to
determine if this unique loading on Axis B in the Adult
solution was related to DFC in the Adolescents or was a
168
more comparable to Axis XIV. Except for the minimal load
ing of the Make A Figure Test (shifs) on DFU (.30) none
of the hypothesized measures of DFC were confounded with
other divergent-production variables in either solution.
Figural Similarities, however, provided somewhat equivo
cal evidence in the two matrices. It appears to represent
a divergent-production ability for the Adolescents but the
test's only significant loading in the Adult solution was
on the CFG factor. It would seem the test represented a
task calling for the recognition of classes of figural
properties for the Adults.
Although the DFC factor was hypothesized to be
determinable by tests of a multiple-choice format, it
appears from these results that figural spontaneous
flexibility could possibly be more clearly identified by
tests employing an open-end format in which the classes
were positively stated. Alternate Letter Groups, although
appearing significantly only in the Adolescent solution,
presented the best evidence for the factor; Figural
Similarities shows a differential relationship as a
function of age in this study. The clear relationship of
Alternate Letter Groups to DFC may be attributable, in
169
• 6
part, to its communalit^ of .59 where the other three
measures had consistently lower values. It is suggested,
also, that this test employed less ambiguous figures than
the complex Figural Similarities tests. It also had
greater chance for item variance than the restricted
number of properties 'found in the Varied Figural Classes
test. Alternate Letter Groups required that the classes
be composed,where the others required that responses be
selected from a set of the most probable responses.
Therefore, it could not be properly grouped with the usual
form of multiple-choice tests. This interpretation,
however, must be restricted to the Adolescent sample since
it did not show a significant relationship in the Adult
population . *
Divergent Figural Systems DFS
Axis C-“Adult Sample
13. Making Objects .40 (DFU .39)
10. Make A Figure (fluency) .36 (DFU .41)
3. Designs . 36 (DFU .36)
16. Monograms .32 (DFU .52)
170
Axis H i ““Adolescent Sample
13. Making Objects .54
10. Make A Figure Test (fluency).37 (DFU .51)
12. Make A Mark .36 (DFU .39)
3. Designs .35 (DFU .49)
16. Monograms
.34 (DFU .48)
The least ambiguous evidence, for the DFS factor
is obtained from the linking Objects test. It was ini
tially hypothesised as a measure of figural transforma
tion (DFT). It appears, however, that combining the given
elements into recognizable objects involves less transform
ation ability and more the ability to produce a variety
of interrelated space forms or figural systems with the
same given objects. Such synedochical confounding, taking
the part for the whole and vice versa, was suggested as
likely to occur between measures of figural systems. This
tendency Is less evident in the productions required by
the Making Objects test. It loaded uniquely on DFS in the
Adolescent solution (.54); Its loadings are about the
same on DFU (.40) and DFS (.39) in the Adult solution.
Although originality or redefinition may be required to
combine the given elements to the specifications of the
171
named object, the restrictions necessary for measuring
figural adaptive flexibility xinto Making Objects. The cues for using the given
elements x^ere probably more immediately obvious than in
match-problems tests. In combining the given elements,
xtfhich resulted in a figural system, the examinee was not
required to use all the givens, nor was the design to be
produced restricted by shape or pattern; no penalty x-jas
imposed for using extraneous figures although they did not
increase the information content in the drax^ing produced.
Since Making Objects is univocal in the Adolescent
solution, there was justification for not "collapsing"
DFS with DFU to produce a complex figural“production
factor. Designs and Monograms x^ere constructed to the
operational specifications suggested by the structure-of~
intellect model. Dot Systems was adapted to similar
criteria for producing figural systems; it was believed
to require structuring or patterning of figural elements
in a variety of ways in visual space. The factor analytic
results, hox*7ever, indicate that these three tests were
more closely associated with the ability to produce a
variety of figural units (DFU). Dot Systems loaded
172
minimally (.31) on DFT in the two samples, but it had a
substantial (.40) loading on DFU in the younger group.
Two other tests loading significantly on DFS were
designed specifically as measures of figural fluency,
Make A Figure Tests (fluency) and Make A Mark. The
former required organising some very simple elements into
a variety of patterns. The more different patterns
produced, resulted in a higher fluency score, the quality
of what is produced being a secondary consideration. It
is conceivable that such patterning is related to the
ability to produce systems, but it is not consistent, to
extend this rationalisation to the Make A Mark test in
which the simplest of unitary figures were required. Make
A Mark did not load on DFS in the Adult solution, but
its loading of .36 in the Adolescent solution was almost
as great as its loading on the DFU axis, .39. Future
study will probably delineate this factor more clearly.
The differentiation of systems products continues to be
one of the more difficult aspects of research with the
Guilford model. It appears from the results of recent
studies attempting to isolate DSS and NSS that some
revisions in the concept may be necessitated. Whether
systems should be regarded as a complex of relations or
simply an interaction of fundaments must await develop
ment of appropriate test ideas for the DFR cell and
experimentation with DFS tests in which the unit variance
can be partialled out. Such determination should define
the divergent-production of systems as primarily oriented
toward the synthesizing of given elements, figures,
symbols, or words into more complex patterns or interrela
tionships. This is quite different from the spatio-
temporal aspects of ordering found as in other systems
factors in the symbolic study, for example (Guilford ejt al
1960).
Axis D--Adult Sample
* 14. Match Problems III .51
15. Match Problems IV .39
4. Dot Systems .31
25. Symbol Elaboration .31 (DSR .42)
21. Perceptual Speed .30 (EFU .38)
Axis IV--Adolescent Sample
14. Match Problems III .54
15. Match Problems IV .45
174
4. Dot Systems .31 (DFU .40)
A relatively clear verification of the figural
flexibility factor appears in the Adult solution.
Although BFT has been previously defined, it m s considered
important to establish the existence of both figural
sponataneous flexibility and figural adaptive flexibility
In the same factor structures at the two age levels.
Although DFC did not emerge clearly in the two solutions
none of the hypothesized measures for that factor loaded
on DFT in either solution. In the Adolescent sample also
no confounding was observed between the two types of
flexibility measures.
In designing new tests to clarify the nature of
DFT, Making Objects was thought perhaps to represent the
same type of ability as that required to solve match
problems. This thesis did not hold, as was outlined in
the earlier discussion of DFS. It was believed that a
reinterpretation of thought may occur In applying dif
ferent strategies to the varied use of the given figural
elements. It is suggested by the results, however, that
i
the task in Making Objects does not present the same level
of restriction or the same degree of complexity that is
encountered in Match Problems III and IV. It was the
. . _ 175
latter two tests which provided the primary evidence for
DFT in the two matrices.
Although Dot Systems was hypothesized as a measure
of systems, it appeared to be unrelated to the DFS factor.
Although its loadings on DFT are minimal, it emerges on
the factor in two solutions which would tend to refute
attributing its loading as a chance occurrence. In Dot
Systems as well as in the match-problems type tests the
examinee must revise his conceptions relative to the kinds
of figures that will be acceptable solutions. In Making
Objects no penalty was imposed for applying redundant
information; in the three DFT measures, however, superflu
ous information would most likely lead to marking an
erroneous response.
Although the definition of DFT in the Adolescent
sample is clear, loadings of Symbol Elaboration (.31) and
of Perceptual Speed (.31) in the Adult solution requires
some explanation. The latter test's appearance on the
factor is perhaps attributable to same sharing of common
figural variance. Although this explanation is somewhat
tenuous, it is conceivable that the task of determining
acceptable figural solutions to the problem encompasses
176
some minor degree of figural identification (EFU) as
represented by the Perceptual Speed test. It is not
suggested that the abilities are correlated; in this
population sample, however, the Perceptual Speed test
may not be univocal. The loading of Symbol Elaboration,
however, on DFT defies logical explanation.
Symbolic Spontaneous Flexibility DSC
Axis E--Adult Sample
* 27. Varied Symbols .36
8. Letter Group Relations .34
* • 17. Name Grouping .31
Axis V— Adolescent Sample
* 27. Varied Symbols .41
* 17. Name Grouping .32
In the Adult matrix, the three tests loading on
DSC are all concerned with similar symbolic information,
groups of letters. Letter Group Relations was not
originally designed as a measure of this factor. In
that test the emphasis is upon such symbolic structure
as a triad of letters containing "two consonants and a
vowel.'1 Its items are not too dissimilar from Name
Grouping in which "Bill" and other names have "double
177
consonants." In Varied Symbols the triad of letters is
associated with other groups of letters which are in
"alphabetical sequence." Since it was designed as a
relations test, Letter Group Relations should have
loaded on DSR; however, it has only one significant
loading in the Adult solution, that on DSC.
Although Number Grouping was designed as a
parallel measure to Name Grouping, its loading on DSC
was .23 in the Adult matrix and .06 in the Adolescent
matrix. Number Grouping will be discussed in connection
with the definition of DSR on which it loads only with
tests of numerical symbolic-content. Had Number Group
ing's saturations been in DSC, it would have provided
greater confidence in the commonality of symbolic content,
whether letters, numbers, or some other notational system
is used. In the present set of tests, such evidence is
not indicated. In defining the convergent production of
symbolic systems (NSS) Guilford (et al., 1958) found
that a numerical test, Operations Sequence, and a word
test, Word Changes, measured the systems factor as hypoth
esized. This provided evidence for the coherence of
letter and number tests under the same rubric of symbolic.
In this factor that coherence is not evident. The
let ter "tests appear to form a narrow group factor i^hich is
tentatively identified in each of the two samples as
DSC. It is relatively clear, however, that the tests
involve tasks of classification which parallel the figural
and semantic tests of spontaneous-flexibility. Canisia
(1962) relates this plasticity of thought as ". . . more
'Gestalt"free" an individual . . . the better his per
formance.” She invokes Duncker's (1945) "many sided
nature of thought material” as the ability to see more
than one aspect at a'time. No attempt was made in the
investigation of this factor to define it by symbolic
tests in which a shift-score was applied, which was
perhaps an experimental oversight. Two of three
hypothesised tests for the factor do emerge, as predicted,
in each solution; the evidence for defining the axes
as the divergent production of symbolic classes (DSC),
therefore, seems convincing. One limitation of the
evidence is that the factor, as now verified, may involve
letter-classes only. It was thought previously this
factor might be part of the complex process of mathe
matical analysis and synthesis wherein most alphanumeric
notation would apply.
179
Multiple Symbolic Correlates DSR
Axis F-“Adult Sample
* 19. Number Rules .45
* 18. Number Grouping .31 (DSI .33)
Axis VI-“Adolescent Sample
18. Number Grouping .45
19. Number Rules .32 (DSI .36)
Spearman's definition of a correlate involved
the completion of a relationship by providing the missing
unit of information. In the hypothesized measures of
the divergent production of symbolic relationships both
Alternate Additions and Number Rules required that several
numerical connections be produced to complete the
analogies. These numerical links were to be established
between the given numbers and the stated end-relationship
which followed the equality sign.
metical operations be performed in a variety of ways,
Alternate Additions requires only permutations of the
given numbers in simple additive sequence in order to
complete the prescribed relationship. The distinct
loadings of Alternate Additions on MSI indicated that the
While Number Rules requires that several arith-
180
test is primarily an alternate measure of numerical
facility (MSI).
The earlier discussion of Letter Group Relations
and its loadings on the same axis with Name Grouping and
Varied Symbols suggested that the DSC factor in the two
samples may be defined as a narrow group factor composed
of letter-symbol tests. The doublet formed by Number
Grouping and Number Rules for the two samples suggests
that the hypothesized DSR factor may also be defined as
a narrow group-factor involving number-symbols. It was
suggested by Guilford (et al., I960) in the symbolic
study that the Number Relations test was involved with
CSC by the possible existence of "classes. . . of
relations" (p. 19). In the present study finding Number
Grouping saturated in DSR and also having a secondary
loading on DSR would tend to describe the test as one
concerned with generating relationships between
symbolic elements.
Implicit in the distinction between the measures
of DSC and DSR in this study is the logical consistency
in the common number system. Numbers would tend to
elicit relational thinking, whereas the relations bett-jeen
181
letters of the alphabet is not as readily evident. Pro
ducing letter-symbol analogies in the divergent-production
matrix may evoke classificatory behavior. Applying the
rules of grammar to synthesise alphabetical information
in a diversity of ways may result in classes of infor
mation. The relationships may only emerge when the
letter-symfools are demonstrated to be less discrete or
arbitrarily contiguous. It was found in the symbolic
study (Guilford et al., 1960) that the CSR factor was
identified only by those tests that used "real" words
as test items. Items composed of simple letters or
meaningless symbols did not load on the factor.
The instructions in Number Grouping as a symbolic-
classification test required that common numerical
principles be used to form symbolic groups. Forming an
equation was believed to be production of a relationship
and was not acceptable as a response on this test.
This "equation-relation” concept did not appear to be the
determining idea in all instances. Alternate Additions
required simple equations and Symbol Elaboration required
relatively complex ones. Yet neither test loaded on
the DSR factor.
182
It was suggested that, in the systematic inter
relationship common to numbers, classes of relationships
may be produced which might account for the loading
on DSR by Number Rules and Number Grouping. Based upon
the evidence taken from each sample separately it would
appear that a clear separation exists between DSC and
what is tentatively defined as DSR. This clear separa
tion is not as evident in the distinction between the
DSR and DSI. Number Rules has only one significant
loading in the Adult Matrix, that of .45 on DSR. In the
Adolescent sample Number Rules has a complexity of two,
one loading on DSI (.36), and one on DSR (.32). Number
Grouping is the leading test for defining the factor in
the younger sample. Since inconclusive information
concerning DSS was obtained in the creative-adolescent
study (Guilford et al., 1961) using the same Adolescent
sample, perhaps a future study synthesizing DSC, DSR,
DSI from the present study and DSS and DSU data from
the creative-adolescent study x^ould lend greater
clarification to the nature of the factors in Adolescent
population common to the two batteries of tests.
183
Symbolic Elaboration DSI
19. Symbol Elaboration .49
9. Limited Words .36 (CSU .34;
CFG .30)
Tests of elaboration measuring factors in the
figural and semantic cells of the implications row of
the divergent-production matrix called for using given
information as a basis for inferring or extrapolating
responses consistent with the antecedent conditions
presented.
The symbol Elaboration and Limited Words tests
were designed as measures of the symbolic factor believed
parallel to these previously verified abilities of DFI
and DMI. Symbol Elaboration provided the primary
evidence for identifying the new factor and for its
placement, as hypothesized,in the DSI cell. As a test
of algebraic manipulation it generally subscribes to
the hypothesized specifications of the factor and is
based upon principals analogous to the marker tests of
the parallel factors.
In the Limited Words test a given pair of words
is used to derive additional relationships implicit in
the given set of xrords. The test items use simple
analogies, largely in the form of anagrams, as the basis
for extrapolating or producing other symbolic analogies.
In the Adult solution, Limited Words was found to be an
alternate measure of CSR, on which it was the variable
with the greatest saturation. It was also found to
have a significant loading on the verbal comprehension
factor (CMU). In the Adolescent solution it appeared
to be less closely associated with words per se and was
found to have significant loadings on DSI and CSU and a
barely significant loading on CFG. It was indicated
earlier that the attenuated correlations for Limited Words
presented in Tables 4 and 5 could be extended in the
common-factor space since the point-biserial correlations
were not comparable to Pearson correlations in the test
configuration. Since the loading of Limited Words on
DSI in the Adult solution was zero, extending the test
vector would not result in a significant loading on the
DSI factor. The communality of this test prior to
correction is .32; it was assumed that its loading of
.36 on CSR and of .29 on CMU would account for most of
the variance in the measure. Correcting the vector led
to loadings of .45 on CSR and .36 on CMU, tjhich would
185
indicate the test is primarily a measure of seeing or
discovering symbolic relations and of word knowledge,
for the Adult group.
A somewhat different interpretation must be
applied to the test in the younger sample. Without
correction for dichotomization, Limited Words loaded
.29 on DSI and .27 on CSU. Correcting the test vector
resulted in its loading .36 on DSI, and .34 on CSU and
.30 on CFC. It would appear then, that in the Adolescent
sample, the test does contribute to the identification
of DSI as hypothesized. In this sample its communality
is .38; in view of the limited range of the original
scores, however, and their truncated and leptokurtic
distribution, the obtained correlational pattern must
be accepted with caution. Therefore, without the con
tribution of Limited Words, the principal basis for
placing the factor in the DSI cell of the model is
derived from the Symbol Elaboration test as predicted,
and in part, from the contribution of the tests otherwise
identified as measures of DSR. Collapsing the axes now-
defined as DSI and DSR would not result in a clearer
interpretation of the factor pattern in either solution.
186
The resultant axes would describe a divergent production
of symbolic relations (DSR) ability. In addition a
"singlet" factor would possibly account for the algebraic
manipulation variance represented by the Symbol Elabora
tion test. In such an alternative explanation, the
relationship between Symbol Elaboration and the DSR tests
would be ascribed to items representing numerical variance
or some generalized mathematical ability. It was sug
gested earlier in the discussion of DSR that the test
represented a narrow group factor for producing a variety
of number relations. It is consonant with structure-of-
intellect theory, however, that abilities to educe or to
produce correlates is not limited to the relations row
since the implications product is also concerned with
relational thinking.
The description- of DSI as a symbolic-elaboration
ability appears sustained by the pattern of tests loading
on it in the two solutions. Although Number Grouping,
in the Adults, and Name Grouping, in the Adolescents,
each have a complexity of two, their principal loadings
are on the axes tentatively defined as DSI. Acceptance
of this interpretation completes the placement of
elaboration factors in the three cells of the
187
implications row of the divergent-production matrix.
Figural Classification CFC
Axis H--Adult Sample
5. Figural Similarities
* 22. Picture Classification
Axis VIII--Adolescent Sample
* 22. Picture Classification
* 6. Figure Classification
9. Limited Words
The Picture Classification test, although con
sistently providing secondary loadings on semantic
factors in other investigations; emerges in the present
investigation as univocal and the clearest indicator
for this reference factor in either solution. Its
loading, however, in the Adult matrix is secondary to
its companion measure, Figural Similarities, which serves
i
to identify CFC in the Adult solution.
Although Figure Classification, the best known
marker test for CFC, contributes to its identification in
the Adolescent sample, it does not appear significantly
on the factor in the Adult solution.
.40
.35
.51
.36 (CSR .31)
.30 (DSI .36;
CSU .34)
188
By contrast, a hypothesized measure of DFC,
Figural Similarities has only one significant loading
(.40) in the Adult matrix where it is saturated in the
cognition of figural classes (CFC). Apparently the new
experimental test did not represent as much a task of
production or ''creation" for the Adults as it seemed to
be for the younger group. Individual differences are
possibly shoxm in the Adults by their ability to perceive
the figural classes; for the Adolescents, the task was
primarily one of creating such classes.
The inclusion of Picture Classification and
Figure Classification in the test battery was for the
purpose of distinguishing variance attributable to the
hypothesized DFC ability from the CFC. Three of four
experimental tests of DFC (Alternate Letter Groups,
Figural Similarities, and Varied Figural Classes) x-?ere
believed to be distinct from the measures of CFC, in
which the given figures were assigned to a number of
different classes because of the multiple figural
properties contained in each.
Uifch the exception of Figural Similarities, the
two other measures maintained identities relatively
189
distinct from CFC or of any factors outside of the figural
content column of the divergent-production matrix. The
Make A Figure Test (shifts) also demonstrated its
independence of the CFC factor which was anticipated.
Figural Similarities, in the Adult sample,
strayed from its hypothesized domain by presenting
conflicting results in the two samples. The distinction
between being able to discern figural classes (CFC) and
being able to produce a variety of such classes (DFC)
was well substantiated in the Adolescent sample. The
evidence for DFC and CFC in the Adult sample could
possibly be improved by completion tests even at the
risk of confounding with verbalization abilities. The
experimental rationale for including reference measures,
however, continues to be substantiated by the results
such as presented here. The interpretation of the struc
ture has been materially facilitated by the inclusion of
the two marker tests of CFC. It is necessary to explain,
however, the minimal loading (.30) of Limited Words on
this factor in the Adolescent solution as attributable to
chance occurrence.
190
Verbal Cotnprehension CMU
Axis I-“Adult Sample
* 28. Verbal Comprehension .48
9. Limited Words .36 (CSR .45)
Axis IX““Adolescent Sample
* 28. Verbal Comprehension .47
From these results, it appears that vocabulary
was sufficiently controlled in the new experimental tests,
so that differential ability in word knowledge was not a
contributing factor to performance on most of the other
tests in the battery. The one exception was Limited
Words in the Adult sample. Although there was a
significant difference in the mean scores of Adolescents
and Adults on Verbal Comprehension, the ratio of variance
for the two samples (1.02) was not significant (Table 2).
It is noteworthy that the relative "purity" of this
factor provides additional support for what Messick (1960)
describes as "Guilford1s predilection for orthogonal
factors . . ." (p. 5). Although words were the basic
means of defining the task on each test to the pilot
trainees and the ninth-grade students, it is evident that
knowledge of the meaning of those words is an important,
191
but not all-pervasive element in the structure of human
intellectual abilities. It is possible that efforts to
reduce verbalization in the new experimental tests were
partially unwarranted. Had the examinees been permitted
to express their reasons for classes and relations and
implications, perhaps finer discriminations might have
been achieved. In any event, the one experimental ques
tion relative to verbal ability being confounded with
the experimental tests has been clarified. This problem
was initially considered of major importance in the
exploratory study with ninth-grade students.
The loading of Limited T^ords on CMU in the Adult
solution is interpreted as an indication that the test
also contains items that measure differential ability in
word knowledge for that group.
Symbolic Recognition CSU
Axis J--Adult Sample
7. Four-Letter Words .40
Axis X--Adolescent Sample
7. Four-Letter Words .49
9. Limited Words .34 (DSI .36;
CFC .30)
192
The cognition of symbolic units (CSU) was
represented in the present study by only one test variable,
Four-Letter Words. It appears from its substantial and
univocal loadings, that the one measure was sufficient
to clarify the factor pattern with respect to this ability.
Since the eight new experimental tests of symbolic
divergent-production abilities showed no significant
loading on this CSU factor in the Adult sample, it is
evident that the ability is differentiable in the two
samples, with only the questionable Limited Words test
having some relationship to it.
It may be conjectured that the configurational
pattern might be otherwise determined had DSU been
included and represented by the Word Fluency test in the
study. Such information is suggested, in part, for the
Adolescent sample only. Subsidiary information has been
obtained (Hoepfner, 1963) to indicate that in the
Adolescent sample, the correlation between Word Fluency
and Four-Letter Words was .28. In the symbolic study
(Guilford et al. , I960) the tiro measures correlated .24
in a navy pilot-trainee sample. In that study the two
tests loaded separately on their respective factors. It
193
is reasonable to expect that the similarity of correla
tions and of factor patterns would hold for the two
samples in the present investigation. It is therefore
possible to surmise that the DSC, DSR, and DSI measures
would not be confounded with either the ability to
recognize symbolic units (CSU), or with the ability to
produce a variety of such units rapidly (DSU).
Canisia (1962) found that Number Fluency loaded
.43 on the same axis with Word Fluency (.32) in what she
describes as a number fluency factor. The xjxiter believes
she errs, however, in ascribing it as a reaction-time
factor in which fluency is ambiguously described as a
"personality characteristic" (p. 21).
Education of Symbolic Relations CSR
Axis K--Adult Sample
9 . Limited Words
23. Seeing Trends II
29. Word Relations
Axis XI--Adolescent Sample
29. Word Relations
23. Seeing Trends II
6. Figure Classification
.45
.35
.33
.45
.43
.31 (CFG .36)
194
With the exception of Limited Words, none of the
new experimental test was loaded in CSR. The factor
emerged as a distinct cognition construct in the two
samples. Limited Words had its maximum saturation in CSR
in the Adult sample. For this older group, apparently the
production of a variety of anagrams required by this test
represents an ability for discovering or seeing symbolic
relationships. Perhaps the items in the test did not
provide sufficient latitude for these examinees to go
beyond the discovery-stage in order to derive further
inferences required in DSI. The test was either extremely
difficult for this superior-Adult group or possibly quite
i
confusing. An indication of this conjecture is seen in
the restricted range of scores which were from zero to
eleven with a modal response of three. Presumably most
of the working time in the test was devoted to finding the
rule involved, leaving minimal time for producing other
symbolic correlates based upon the discovered principle.
In the Adolescent sample the modal response was zero
thereby minimizing its ability to differentiate among the
ninth-grade students.
The border-line loading of Figure Classification
195
(.31) in the younger group defies reasonable explanation.
In the creative-adolescent study (Guilford et al. t 1961)
when Number Combinations was found to load on the verbal
comprehension factor it was suggested that perhaps the
examinee used ” ... the strategy of verbalizing the
number material" (p. 25). It would be too broad an
analogy to suggest that Adolescents discover relationships
between figural classes by first organizing them into
symbolic relationships. In an otherwise clear definition
of CSR in Adults and Adolescents, this loading should be
regarded rather as a chance occurrence.
Although CSR was characterized as a factor to be
defined by tests using only "real” words (Guilford et al.,
I960) it is of note that Name Grouping (DSC) showed no
significant relationship with CSR although "real” names
compose its test items. Limited Words, however, the other
"real-word” symbolic test had the highest loading on the
factor in the Adult solution. Adjusting the under
estimated vector length of Limited Words (.16) in the
test configuration would not result in a significant
loading for the factor in the Adolescent sample, however.
CSR is clearly established in the two samples, although
196
it appears to have gained a new, but somewhat erratic
marker test, Limited Words.
Perceptual Speed EFU
Axis L“-Adult Sample
* 21. Perceptual Speed .38 (DFT .30)
9
Axis XII“-Adolescent Sample
* 21. Perceptual Speed .45
The clear distinction between the new figural
tests and the ability to evaluate or identify the
similarity of figural entities (EFU) is pointedly
established by the emergence of this factor in its marker
test only. In only one instance does there appear to
exist any overlap of measures of this standard reference
factor and those in the divergent“production matrix.
The small secondary loading of Perceptual Speed on DFT
is attributable perhaps to the particular orientation
of this keen-eyed group of pilot trainees. It is
suggestive that they may further differentiate themselves
by visualising the Perceptual Speed task as a challenge
to alter their set when interpreting a figural display.
This example of figural adaptive flexibility (DFT) is
likened to the observations of Piaget and Lambercier(1958)
197
who find that young children are more concerned with the
whole of a Rorschach figure, older children perseverate
on the minutiae, while adults tend to respond to both
whole and parts. To this point, the tnriter has eschewed
the clinical or aesthetic aspects possible when scoring
figural tests. He will not elaborate upon the tenuous
evidence presented in the present findings. Except as it
may further relate to Piaget's parables. Except for this
minimal side loading of Perceptual Speed, which may be
attributable to a chance occurrence, the EFU factor is
well differentiated in the two samples.
Numerical Facility MSI
Axis M--Adult Sample
* 20. Numerical Operations .42
1. Alternate Additions .38
Axis XIII--Adolescent Sample
1. Alternate Additions .49
20. Numerical Operations .41
Numerical Operations is commonly a univocal
measure of the number facility factor. It has been
consistently verified in adults and among literate
children. Within the structure of intellect it has been
198
placed in the MSI cell and defined as th& retention of
well-practiced symbolic implications. Evidently,
Alternate Additions, as scored in the present study,
merely provides another exercise in simple addition. In
designing the test it was anticipated that deriving
relationships between the given set of simple numbers and
producing the same sum would contribute to defining of
the DSR factor. In Alternate Additions the examinee is
enjoined from employing other than the associative law to
complete the equations. Although Number Grouping and
Number Rules are obviously '’number'1 tests, the symbolic
information is processed by relating or applying different
arithmetical rules to indicate it as a production task.
This ability is distinct from retention (MSR) or the
discovery of symbolic relationships as in CSR. The
absence of any side loading of Alternate Additions on DSR
in the Adolescent sample supports the interpretation of
the two axes as representing MSI in the two factor
solutions.
Although this study has not attempted to define
MSI as a mathematical ability, it is quite possible that
DSCj DSR, and DSI do represent orthogonal aspects of
199
mathematical thinking. It appears that measures of this
computational ability (MSI) are pointed indications that
the relational and inferential facets of methematics also
require that "reasoning" become a possible fourth jr in
elementary school curricula (along xtfith reading,
'rithmetic, et cetera). The automatic nature of this
ability as a function of training may fade from future
'rithmetic classes in which each child would have a small
computer console adjacent to his class desk.
Singlet Factor
Axis B -** Adult Sample
26. Varied Figural Classes .39
Axis XIV -- Adolescent Sample
26. Varied Figural Classes .36
Although Varied Figural Classes was designed to
define the figural adaptive flexibility factor, it was
the only significant loading on either Axis B or XIV in
the two solutions. In view of its low communality, .27
in Adults and .25 in Adolescents, rotation of the
reference axes in each matrix to maximize the saturation
of this relatively short vector resulted in its
"significant" projection in the common-factor space. This
200
subjective resolution to the other alternatives such as
creating additional residual factors was supported,
independently, by the analytical solutions (Appendix )
which also created such a singlet in the two samples.
This test was based upon the type of items found
in the Figure Classification tests, but its divergent-
production format failed to evoke any commonality with
the antecedent test or with any of the tests that were
included in the study. Varied Figural Classes, like
Figural Similarities, was believed to involve an ability
to cope simultaneously with a number of conflicting per
ceptual properties while in the process of composing
classes of figures with similar properties. It seems
that the plasticity required by such an ability was not
evinced by this measure in either group. In view of the
low estimates of reliability for the measures, it is
conceivable that the factorial identity of the test could
be established if the degree of error variance induced by
guessing on the response format could be reduced by a
completion type answer. Open ended responses would have
imposed an extremely arduous scoring schedule and may
have been confounded with verbalisation variance.
201
Avoiding these latter risks probably contributed to
undefinable aspect of this singlet factor. It is sug
gested that the salvage value of this test may be in a
different response format.
Residual Factors
In the Adult sample, axes N and 0 had no loadings
greater than an absolute value of .22 and .18, respec-
tively. In the Adolescent sample, Axis XV and 22 loadings
less than .16, of which 15 were less than .11. In the
Adult sample, Axis N had 23 loadings less than .16 of
which 14 were less than .11. Since these axes were not
interpretable they were relegated to the residual factor
space.
CHAPTER VII
DISCUSSION
The experimental findings will be treated in this
chapter primarily in terms of their relationships to
strueture-of-intellect theory. The fruitfulness of the
theoretical model will be reviex^ed as to its precision
in predicting the existence of primary abilities and
their placement in empty cells of the divergent-production
matrix. The new experimental tests will be evaluated
by their obtained versus their predicted factorial
relationships. The efficacy of the procedures by
which the test ideas were developed from operational
specifications of the model will also be reviewed.
The identification of primary intellectual
abilities at the two age levels investigated will be
discussed in terms of the hypotheses against a background
of conflicting theories concerning intellectual develop
ment and factorial invariance. The mathematico-
statistical congruence of pairs of factors will be
202
203
compared to the logical or intuitive rationale for assign-*
ing parallel factorial interpretations to axes. The
abilities will be reviewed in terms of their compati
bility with concurrent concepts of mental organization.
Relation of the results to the hypothesized operation
Little doubt was anticipated that the term of
divergent production would be appropriately applied to
the factors obtained with the new experimental tests. For
each of the 21 new tests the task requires that varieties
of new information be generated from the given figural or
symbolic information. Eighteen of these tests had
saturations in the seven divergent-production factors
hypothesized from the theoretical model.
Although exceptions were encountered, in general,
the results supported the hypotheses. Only Limited
Words and Figural Similarities strayed from their
predicted positions to load significantly on reference
factors which represented other operations. Although
Alternate Letter Groups was a prime indicator for DFC
in the younger sample, it failed to contribute to any
factor description in the older group. In the Adolescent
204
solution Make A Figure Tests (shifts) and Letter Group
E.elations failed to make any significant contribution
to defining the factor pattern. Limited Words was
found to have relationships with several factors.
The validity of the model for predicting the
operation category for tasks involving divergent
production activities appears to be well established.
The results indicate that a high degree of precision
can be obtained for constructing tests to fit specific
operations of the theoretical model.
Relation of the results to the hypothesized contents
The separation of symbolic and semantic abilities
with reference to content was well supported in the
earlier investigation of symbolic factors (Guilford et al.,
1960a). The present results provide further verification
for the separation of symbolic and figural abilities.
Thirteen figural tests were designed to describe four
figural factors and eight symbolic tests were designed
to describe three symbolic factors. This separation of
contents was rather well accomplished with a few ep-
tions. Symbol Elaboration (DSI) had a secondary, small,
significant loading on DFT in the Adult matrix. Limited
205
Words in the same matrix had its only two significant
loadings on CSR and on CMU. This same test in the
Adolescent matrix loaded on tx?o different types of content
and in three operations: DSI, CSU, and CFC. The range of
scores on this test was extremely restricted in the two
samples, their distributions were truncated and extremely
leptokurtic. After dichotomization the test measures
still continued to provide erratic results that were not
encountered with other variables in either sample.
The only other indication of possible confounding
of contents was with Figure Classification (CFC) which
had a barely significant secondary loading on CSR. The
distinction between factors of figural and symbolic
content in the divergent production matrix appears well
established. What confounding did occur appeared to be
due to chance occurrence, the erratic behavior of Limited
Words notwithstanding. Since no measures of semantic
divergent production abilities were involved in the
analyses the separation of semantic and the new symbolic
abilities can only be assumed.
Relation of the results to the hypothesised products
The satisfactory confirming results obtained in
predicting the operation and content of the experimental
variables in the study were extended to a lesser degree
to the product dimension. The four hypothesised figural
factors (DFU, DFCS DFS, and DFT) emerged in the
Adolescents as predicted, where relatively clear
delineations were obtained between measures of units,
classes and transformations. Some degree of obliquity
was suspected in the results obtained with units and
systems. The univocal description by Sketches (DFU)
and by Making Objects (DFS) of their respective factors
was taken as evidence for the orthogonality of these
constructs, although the complexity of other tests
measuring DFU and DFS was somextfhat similar in the two
samples. DFC emerged only in the Adolescent solution.
Equivocal findings were obtained with the presumed
measures of DFC such as Varied Figural Classes, which
loaded on a singlet factor in the two solutions, and with
Figural Similarities which was found to be a measure of
CFC in the Adult solution.
Table 12 indicates that eleven of the-21
experimental tests had significant saturations in the
factors they were hypothesised to measure in the Adult
207
TABLE 12
COMPARISON OF FACTOR PATTERNS IN THE TWO GRAPHIC
ORTHOGONAL ROTATED SOLUTIONSa
Hypothesized Test Adult Adolescent
Factor*3 Number Matrix Matrix
DFU 10 1 1
12 1 1
24 1 1
DFC 2 0 1
5 0 1
11 0 0
26 0 0
DFS 3 1 1
4 0 0
16 1 1
DFT 13 0 0
14 1 1
15 1 1
DSC 17 1
1
18 0 0
26 1 1
DSR 1 0 0
8 0 0
19 1 1
DSI 9 0 1
25 1 1
aUnity (1) indicates a significant loading for the
test vector on the factor it was hypothesized to measure;
zero (0) indicates that the loading was insignificant.
Significant loadings are .30 or greater; insignificant
loadings are less than .30.
^Reference factors are not included although their
pattern emerged as hypothesized in the two samples.
208
matrix, and in the Adolescent matrix 14 out of 21
hypothesised loadings were obtained. In this younger
sample all factors were defined by at least two of their
hypothesised measures with the exception of DSR which was
defined by only one of its two hypothesized measures. The
results in the Adult solution were less precise. Three
tests loaded as predicted on DFU, two on each of the
factors DFS, DFT, and DSC. Only one test loaded as
predicted on DSR and on DSI. These results tend to
confirm the efficacy of the theoretical model for the
generation of specific hypotheses about the types of
tests to measure unverified factors.
Relation of the results to other divergent-production
factors
The parallelism of abilities across contents
seems to be well supported in the unit products of the
divergent-production matrix where figural fluency (DFU)
emerges as a cognate to factors previously identified as
word (or symbolic) fluency (DSU) and ideational (or
semantic) fluency (DMU) (Guilford et al., I960).
At the classes level evidence for DFC and for
DSC confirmed the fact that spontaneous flexibility
209
composes at least part of the description of these
classification abilities as it has for DMC in the semantic
content column.
At the relations level only DSR is found as a
symbolic corollary to associational fluency (DMR) since
a figural relations factor (DFR) still remains to be
investigated.
Similarly, since DST was not investigated, no
summary statement across products can be advanced for
the transformation row. The present findings confirm the
fact that figural adaptive flexibility (DFT) appears to be
well defined by the ubiquitous match-problems tests.
Although supportive evidence from Dot Systems has been
added to that of Planning Air Maneuvers.
The parallelism that might be anticipated for a
factor of figural originality was not ascribed to DFT
in this study, but rather to DFS since Making Objects
did not significantly saturate DFT as originally
hypothesised.
The present study tends to support the postulation
that divergent-production abilities most likely enter
into productions ascribed to a more global concept of
210
creative thinking (Guilford, 1959) . Although past
studies have associated the putative phrase originality
with creativity (Guilford et al., I9603), when precisely
applied the semantic“originality factor is best described
as divergent°production of semantic transformations
(DMT). The reinterpretation or redefinition of given
information to produce a variety of clever or unusual
responses is the best description of the ability involved.
When the task or problem is relatively difficult and
trial“and-error production is required to produce
acceptable responses, the term adaptive flexibility is
applied. DFT as defined in this study seems to subscribe
to the specifications of figural adaptive flexibility but
not to those of figural originality. The latter is
possibly more descriptive of DFS (as defined by the Making
Objects test). Since the evidence for DSS is somewhat
tenuous, the systems row across the three contents will
emerge more clearly as additional studies explore the
types of synthesis required to produce complex systematic
relationships.
In the implications row figural elaboration (DFI)
and semantic elaboration (DMI) now are joined by symbolic
211
elaboration (DSI). Future investigations will determine
how closely the present measures of DSI are allied to
alphanumeric manipulation and a knowledge of algebra.
The symbolic"elaboration ability involved should prove
to be of importance for investigations of mathematical
thinking. Further clarification will be required,
however, to determine which items of the DSR tests
(Name Grouping and Number Rules) enter into defining DSI.
Figure 2 presents the status of factors in the
divergent-production matrix after placement of the seven
newly described factors in cells parallel to previously
confirmed factors.
The foregoing results and their interpretation
support the primary hypothesis of this investigation,
, that primary mental abilities in empty cells of the
divergent-production matrix can be predicted by the
theoretical model and the tests to measure such abilities
can also be developed by operational specifications
derived from the model.
Relation of the results to the other hypotheses
A direct disconfirmation of the Garrett (1946)
developmental theory of intelligence was predicted. It
Products
212
Figure 2
Divergent-production matrix
Content
Figural Symbolic Semantic
Unites X R R
Classes Y X R
Relations ? X E
Systems ‘ X R R
Transformations XR ? R
Implications R X R
Diagram of the divergent-production matrix showing
the positions of the factors that were under investi
gation. X = a hypothesised factor confirmed in the
two samples, Adults and Adolescents. Y = a hypothe
sised factor confirmed only in the Adolescent, sample.
R = divergent-production factors previously confirmed.
The ? indicates the cell remains to be investigated.
was stated in Chapters I and II that Garrett (et al.,1935)
had presented factor analytical evidence that primary
abilities were more differentiable as age increased.
Part of the evidence presented was that the principal
components distributed variances more evenly when tests
were given to older age-groups. The batteries of tests
they administered at age-levels 9, 12, and 15 were the
same for each group.
The present analyses with ninth-grade boys and
girls and with navy pilot trainees indicate that the
number of factors defined by a fixed battery of tests
administered to the two populations is essentially the
same. In the Adolescent sample the number of factors
and their separation was found to be even more distinct
than that in the Adult solution. When factors, identified
as being the same abilities in the two separate solutions,
x*?ere compared they accounted for almost the same propor
tions of variance in each matrix, respectively. Three
matched pairs of factors differed by three per cent of
the variance, five pairs differed by two per cent, and
four pairs differed by one per cent; one pair was the
same.
214
Finding most of the variance on one or tv?o factors
can be anticipated when comparing principal-component
solutions (unrotated axes). The amounts of variance,
however, such as that accounted for by the rotated axes
in the Adult matrix (Table 10) ranged from three to ten
per cent of the total variance. In the Adolescent matrix,
separate axes accounted for amounts itfhich ranged from
three to twelve per cent of the variance.
The range of correlations was greater in the
Adolescent sample (Table 4) than in the Adults (Table 5).
This was attributed to the heterogenity in the sample of
boys and girls as compared to the relatively select and
homogeneous group of navy office-candidates. This was
further reflected in the proportions of variance accounted
for by the first five principal components in each
unrotated matrix (Tables 6 and 7): in the Adult sample
these were .43, .18, .08, .06 and .05 and in the
Adolescent sample, .53, .16, .07, .04, and ,03 of the
total variance. In the Adult sample, five principal
components accounted for ,80 of the total variance and in
the Adolescent sample five principal components accounted
for .83 of the total variance. Wo statistical test is
215
believed necessary to support a conclusion concerning the
similarity represented by these two sets of proportions.
With reference to the interpretation of the
factor matrices in the two solutions, configurational
invariance (Thurstons, 1947) was the basic premise for
assigning similar factor names to matched pairs of axes
in the two solutions. Butler (1961) describes Thurstone1s
concept of configurational invariance as based upon
similarity of factor patterns. Following this rationale,
the factor patterns for the two graphic orthogonal
solutions in Table 12 indicate that an interpretation
of similarity would follow from the two observed patterns.
It is noted that only variables hypothesized to load
significantly on the factors are indicated. If a loading
was .30 or greater, unity is entered; if the predicted
measure of the factor had an insignificant loading, zero
is entered. Again, using Thurstone's term, the solution
is "compelling.”
The second hypothesis, H£ , specified that a
fixed battery of tests would measure similar mental
abilities in two such diverse populations as young, male
adults and adolescent boys and girls. Although Thurstone
216
(1947) had Indicated that numerical inyariance could
not be expected with such different populations, but
". . . that the configuration may remain invariant for
different populations . . (p. 361). On the basis of
comparison of factor patterns, the abilities represented
in the two rotated factor matrices appear to be equally
well defined by the same battery of tests, one exception
being for factor DFC.
In general, the previously unverified divergent-
production abilities emerged as clearly in the
Adolescents as it did In the Adults, if not better. A
similar set of results was obtained with the reference
factors which had been defined only in studies with adults.
The Garrett theory remains without support in this study,
and bodes to further disconfirm the application of his
developmental hypothesis to younger groups as well (Meyers
et al.,1962).
With reference to the third experimental hypoth
esis, Hg, inspection of the factor results was superseded
by other modes of comparison. The indications for
similarity of factors by inspection of the pattern of
tests loading significantly on factors was ascribed to
217
logical and intuitive considerations. H3 hypothesized
that the matching of factors would also be supported by
more rigorous, statistically objective, measures of
comparability.
The coefficients of congruence (Tucker, 1951) in
Table 10 generally did not support the high degree of
similarity indicated by non-mathematical comparisons.
Although Tucker does not indicate a precise level for
the significance of 0r, he accepts .93 as significant and
as an indication of the congruence of two factors.
Factors with coefficients of congruence of .45 are rele
gated to the noncongruent factor space. Kline (1956)
vews Tucker's 0r as related to levels of reliability
coefficients for tests. He states that .90 would be
considered high, and that .80 would indicate considerable
congruence: "Values between .70 and .80 will probably
lie in the twilight range, accepted by some workers and
rejected by others" (p. 44).
When a standard of .75 was applied to the rotated
graphic solutions (Tables 8 and 9) four matched pairs of
axes were termed "significantly" congruent. When a
comparison was made with the analytically rotated
218
solutions (Appendices E and F) five significant 0r's x^ere
obtained between corresponding varimax axes. The low
degree of congruence, then, cannot be ascribed to the
subjective aspects of graphic rotational procedures.
The results in Table 12 suggest that substituting
unities and zeros in lieu of the actual loadings in the
graphic and in the varimax solutions would result in more
than four or five significant 0r's. In using the
continuous scale values in Tables 8 and 9, it appears
that only those axes interpreted as DFU, DFS, DFT, and
CSR could be termed congruent with their respective
counterparts. Not in all instances, however, were the
highest coefficients obtained with axes defined by similar
names. DSI in Adults had a higher 0r (.75) with CSR in
the Adolescents, EFU in the Adult solution was paired
with a 0r of .77 with CFG; it was paired to the extent
of .64 with its EFU counterpart in the Adolescent solution,
when the two solutions compared DFU, 0r was .84, but it
was .86 when the Adult DFU x-7as compared to the Adolescent
DFS. Werdelin (1962) suggests that "‘The lack of perfect
congruence may depend on experimental errors, or on the
fact that we use too few tests . . . to obtain a good
219
determination of the factors" (p. 154). In the present
study, the factors were usually not overdetermined; how
ever, this should not be taken to represent an error of
omission. The paucity of tests loading significantly
on DSI was one exception. It seems rather than the low
degree of congruence obtained represents error of
commission. In a sense, this may be the sort of experi
mental error to which Werdelin alludes. It is suggested
that with better test ideas and better construction of
test measures a higher level of congruence x-jould be
obtained..
Recommended tests for newly discovered factors
The following tests demonstrated a sufficient
degree of univocality in at least one of the solutions
to merit further dependence upon them:
DFU 24. Sketches; 12. Make a Mark
DFC 2. Alternate Letter Groups
DFS 13. Making Obj ects
DSC 17. Name Grouping; 26. Varied Symbols
DSR 19. Number Rules; 18. Number Grouping
DSI 25. Symbol Elaboration
From this suggested list, one aspect of
220
measurement of the divergent-production abilities is most
evident: none of the tests is in a multiple-choice
format; none of them can be machine-scored with any
facility. Each response in Sketches, Making Objects, and
in Symbol Elaboration requires separate evaluation.
Although the other five tests can be keyed with sets of
the most probable responses, the possibility is such
that the scoring criteria is relatively sensitive to the
educational background of the groups sampled, although
the items do not represent any particular body of knowl
edge or mode of classroom training commonly found in
school curricula.
The tests that have been recommended in relation
to the results obtained in this study represent the
writer's confidence that the two major hypotheses, and
H2, have been confirmed, although the evidence supporting
is somewhat equivocal.
Implications for future research
1. The findings in the present study have
confirmed previous results relative to the separation
of factors in the three content areas. It can be
anticipated that future research will direct primary
221
emphasis in test construction to differentiating products
within operations and contents. The divergent-production
abilities show clear separation from the factors in other
operations which indicates that future investigations
will concentrate upon clarification of the product
categories. The current conceptualization of the model
with six product rows in all five operations has worked
reasonably well tox^ard facilitating the discovery of new
or hypothesized abilities. In the divergent-production
matrix only two cells remain to be explored (DFR and DST).
One area requiring further refinement in the present
study centers about the complexity and low reliability
of the test measures. Symbolic elaboration (DSI), a
doublet factor, is insufficiently determined. Some of
its tests are confounded with other symbolic factors.
Additional measures of this factor should be developed.
The determination x^hether DFU and DFS are better
described by an oblique solution should be resolved. It
is suggested that revised scoring criteria for some of the
hypothesized measures of these two factors may provide
clear orthogonal solutions.
2. A major question for developmental psychology
222
is posed by the present findings in relation to the
concept of changes in intelligence with increases of age.
Bayley (1955) had demonstrated in the Berkeley Growth
Study that ' ’constancy1 1 of IQ over long periods is a
questionable concept. In the present investigation the
counter indications presented to the Garrett theory,
covering the span of years from early adolescence to
young adulthood present the question s t How young must the
child be before differentiations of abilities are
manifest?” The exploration of this problem also leads
to further information concerning the use of the present
test forms at younger age levels. The question arises
whether the present tests, appropriately modified for
vocabulary and difficulty, would continue to identify
relatively distinct factors at ages 12, 9, and younger?
Finally, would these factors be interpreted as similar
to the cognate abilities in older age groups? It would
seem that the "non-verbal” factor-unique tests in the
present battery and others from the structure of Intellect
would provide more precise identification of basic
abilities than the more factorially complex Weehsler or
Stanford-Binet measures commonly employed with investi
gations of younger samples. Such studies would then be
223
rephrased to ask what kinds of intelligences change with
age.
3. Since the sample of ninth-grade students in
the creative-adolescent study and in the present study
x^ere the same it would be desirable to re-explore the
common-factor domain with the benefit of the hind-site
from the two separate factorial solutions. Although this
procedure had been originally planned, the formal
experimental design for the treatment of the data had not
been specifically set forth. It would be of experimental
interest to determine which of the analytical, orthogonal
rotational procedures provides the factor pattern in
closest agreement to the graphic orthogonal rotations for
the combined test batteries, especially since the factor
domain is apparently so well defined; sixteen out of
eighteen cells in the three content categories of the
divergent-production matrix of the model have been
verified.
4. Other benefits that could be derived from
analyzing the combined batteries in the determination of
the factor structure in the subsamples of boys and girls.
One implication to be tested would be that greater
224
dimensionality (qua°°differentiation) would be found in a
more mature female sample. This result, of-course, would
lend support to the developmental theory otherwise
rejected on the basis of the results of the present study.
It is suggested that the combined battery xrould provide
a more comprehensive determination of the divergent-
production factor space. The one consideration mitigating
against such an analysis based upon already tested cases
is that the sample of approximately 100 girls is less
than the numbers required for satisfactory factor
analyses.
5. With respect to the factors obtained in the
present study, it is of interest that the numerical-
facility factor (MSI) was found distinct from DSR al
though both factors were defined by tests that required
simple number operations. It would seem that some of
the traditional phrases such as the “verbal factor5 8 which
at times refers to CMU (verbal comprehension) and at
times may be taken as a general term involving several
verbalisation or semantic abilities can be abandoned.
By the same token, the use of numerical symbolic notation
in several factors can lead to a general term of “number1*
f
ability whereas at times only numerical facility (MSI) as
the number factor is intended. It would follow then, that
present results indicate that more than one number ability
exists. In this respect, future inquiry should clarify
whether some of the items of the DSR tests involve
implications, while others involve relations; it would
be of interest to determine whether the number vehicle
upon which these tests ride is unrelated to other factors
in which tests involving the manipulation of numbers are
employed. If faulty test construction can be assigned as
the cause for the clustering of number-content tests,
then the logical solution would be to devise symbolic
tests of DSR and DSI that do not depend on numerical
notation.
6 . Artistic abilities and aesthetics are topics
that have not yielded themselves easily to objective,
eimpirical research. Although the present battery of
figural tests has contained the caveat "artistic ability
is unimportant" it is possible that the same tests using
their present scoring criteria could serve to differ
entiate the artistically gifted from a general population.
The abilities to manipulate forms in visual space in a
variety of ways (under speeded conditions) may represent
fluency of imagery on the one hand and freedom from rigid
ity on the other. It may be that “good1 1 ' figural thinking
and poverty of figural Ideas may be the discriminanda
for those who possess the dynamic attributes required of
artists, architects, or designers. The critical analysis
of the shapes and forms produced would involve figural
evaluative abilities, nevertheless, the capacities to
generate many figural ideas may also lie at the base of
artistic creativity. By this, it should not be concluded
that art is limited to the convergence upon only one
figural solution. The artist shapes a variety of spatial
forms from the same idea. He may “see1 1 such ideas in his
“mind’s eye," but it is often the quick thumb-nail
sketches that provide him the solutions that result in
the final "masterpiece." The cartoons by Rembrandt and
DaVinci that preceded their final works give valuable
indications of the genesis of ideas of which some became
the works we view today. The xvriter is given to specula
tion, however, as to whether a "cubist" would not score
higher on the Making Objects tests than xrould Goya or
Renoir were they alive today.
227
7. One final conjecture is made concerning the
present sets of data: The Navy pilot trainees have since
completed (or failed) their flight training and have
obtained some levels of success in their military
specialities. Also, many of the ninth-grade students
tested in the winter of 1959-60 will soon be applying for
admission to college and will no doubt be tested on some
form of college entrance examination. It would seem that
from testing based upon the structure of intellect we
can quickly proceed from the exploratory phase to provide
predictive validation information with practical criteria.
Such work is -programmatic, but it is a matter more for
the technicians in psychology and in related fields,
while the basic research with model continues to explore
the parameters of the thought processes, the construct
validity that will point the way to studies of predictive
validity. To understand and thereby describe behavior in
scientific terras is one objective, to predict behavior
is another phase or level of inquiry.
CHAPTER VIII
SUMMARY
The problem
The study was designed to test and extend the
empirical foundations underlying structure-of"intellect
theory. Factors of figural and symbolic content in the
divergent^production matrix of the unified model were
selected for investigation. Abilities in these categories
had been hypothesised to be important for artistic
creativity (figural) and mathematical abilities (symbolic).
Five major objectives of the study were:
(1) demonstration of factors suggested by empty cells in
the model.
(2) clarification of a previously confirmed factor.
(3) determination of the configurational invariance of
similarity of factor pattern when a fixed test battery
is administered to two population samples.
(4) determination of the metric invariance or congruence
of factor structure in the two samples.
223
229
(5) evaluation of the theoretical model as a basis for
developing tests of hypothesized factors.
The hypothesised factors
Six factors, previously unverified, representing
empty cells in the Guilford model were selected for
investigation:
The divergent production of figural units
The divergent production of figural classes
The divergent production of figural systems
The divergent production of symbolic classes
The divergent production of symbolic relations
The divergent production of symbolic implications
Reference factors
Six reference factors, previously confirmed in
adult populations were included as experimental controls:
Cognition of Figural Classes CFG
Cognition of Symbolic Units CSU
Cognition of Symbolic Relations CSR
Cognition of Semantic Units CMU
Evaluation of figural units „ EFU
Memory for Symbolic Implications MSI
DFU
DFC
DFS
DSC
DSR
DSI
230
In addition confirmation was sought for the
previously confirmed figural adaptive flexibility factor:
Divergent production of figural transformations DFT
In order to accomplish the experimental objectives
twenty-nine test measures were constructed, adapted, or
selected to compose a battery requiring six hours of
administration time. Twenty-one tests were newly designed
for this study. Thirteen of these were of figural content
designed to measure the four divergent-production figural
factors DFU, DFC, DFS, and DFT. Eight new measures were
designed to define three divergent-production, symbolic
factors DSC, DSS., and DSI. Nine marker tests were
included to measure well-known reference factors CFG, CMU,
CSR, CSU, EFU, and MSI.
The battery was administered to two samples:k A
young adult male population (N = 238) of Navy pilot
trainees and a ninth-grade student sample of boys and
girls in a Southern California junior high school(N = 205).
The responses of the two samples were evaluated by the
same scoring criteria. The correlation matrix for each
sample was factor-analyzed separately. Principal-component
231
factors were rotated to the three criteria of simple
structure, positive manifold, and psychological meaning"
fulness. The Zimmerman graphic orthogonal procedure
was used for rotation. For comparative purposes a Kaiser
varimax orthogonal analytic rotational solution was also
inspected.
The Results
In the younger sample (Adolescents) all six
hypothesised factors emerged defined largely by the tests
designed to measure them. In addition, a singlet factor
was defined by a presumed DFC test with a unique loading.
All reference factors emerged, even in those instances
where only one test was included in the battery.
In the adult sample, one factor DFC, did not
emerge. Two of the four tests hypothesized to measure
it were loaded on the measures of CFG. A third DFC
measure was also loaded on an undefined, singlet factor.
In the two matrices a residual factor accounted for the
remaining variance. Seventeen factors had been extracted
in each matrix, 15 of the axes had been rotated, but only
the 13 hypothesized factors emerged for the Adolescents
and one less for the Adults.
232
Interpretation of Factors
A figural fluency DFU) and a divergent figural
systems (DFS) factor were found in each sample. Sketches
was the least ambiguous measure of DFU, which represents
an ability to produce a variety of figural units under
relatively unrestricted conditions. For DFS, the Making
Objects test required synthesizing figural elements to
construct a named object. Aside from these two measures
the DFU and DFS axes appeared best defined by an oblique
simple structure since the other measures for the two
factors were loaded on both.
The emergence of DFC gave indication of either a
spontaneous flexibility factor across the three contents
in the classes row, as evidence was also obtained for DSC.
The latter was defined primarily by letter or syllable
tests, whereas some of its hypothesised measures were
loaded on DSR, which appeared to be in the category of
’'number” factors. The symbolic elaboration factor (DSI)
appeared to be defined primarily by an algebraic-manipula
tion test. The results were also somewhat confounded by
the complexity of the DSR tests which also were loaded
on DSI. Here again, oblique simple structure may prove
233
to be more precise although the assumption of independent
abilities was maintained since a number of the test
variables had low reliabilities, possibly indicating that
the seeming oblique structure would not have resulted had
better tests been developed for the study.
DFT was again confirmed but it still was largely
defined by match-problems tests with only a minimal
loading on the axes by Dot Systems, not hypothesised to
measure figural adaptive flexibility.
The well-known reference factors, CMU (verbal
comprehension), MSI (numerical facility), EFU (perceptual
speed), and CFG (figure classification), assisted by
measures of two lesser knoxm symbolic factors CSU and
CSR, helped indicate the basic distinction between
measures of discovery (or cognition) and those of
divergent-production where emphasis is upon a variety of
responses.
Clear separation of abilities according to
operation, and according to content was well established
in this study. The separation of products was not as
distinctly achieved and provided problems for future
research. Many of these problems would possibly be
234
clarified by refinement of items in the present battery
of new experimental tests.
With respect to experimental objectives of achiev
ing invariance, it appeared from the logical or intuitive
appraisal of factor patterns in the two matrices that
the same abilities were defined in Adults and in Adoles
cents with the exception of one factor. The more
rigorous test, using coefficients of congruence, indicated
that only four of the 13 axes in either sample could be
defined as statistically, although not geometrically,
congruent. Values between .75 and unity were arbitrarily
accepted as indicators of congruent factors.
The results generally have supported the theory
that factor patterns can be identified in younger persons,
analogous to adult capacities. Adolescents do not
appear to have a more amorphorous mental organisation
than adults. Whether these conclusions can be extended
to age groups younger than early adolescence must await
empirical verification. It appears, however,. that the
present test forms are adaptable to these age levels
without major modification in instruction or level of
difficulty.
235
The value of the unified theoretical model of the
structure of intellect as a hypothetico-deductive
construct for generating predictions about unverified
factors and the kinds of tests to measure them seems
augmented by the results of the present investigation.
With the exception of six factors of behavioral content
all but two of the remaining 18 divergent-production
abilities have been isolated, although the present study
and previous ones indicate that evidence is tenuous for
some of the abilities that have been demonstrated.
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APPENDIX A
DESCRIPTION OF THE
STRUCTURE OF INTELLECT CODE
APPEND DC A
250
DESCRIPTION OF THE STRUCTURE-OF-INTELLECT CODE3
Each factor has a three-letter designation. The
first letter refers to the operation, the second
to the content, and the third to the product.
For example: ’ ’ Convergent thinking about symbolic
material resulting in a relationship” would be
coded NSR.
OPERATIONS
Cognition C
Memory M
Divergent D
Production
Convergent N
Production
Evaluation E
CONTENTS
Figural F
Symbolic S
Semantic M
Behavioral B
PRODUCTS
Units U
Classes C
Relations R
Systems S
Transformations T
Implications I
aGuilford, J.P. and Merrifield, P.R. The struc
ture of intellect model: its uses and implications. Rep.
psychol. Lab., No. 24. Los Angeles: Univ. Southern
Calif., 1960. (Reproduced by permission of the authors).
APPENDIX B
THE HYPOTHESIZED FACTOR STRUCTURE
OF THE TEST BATTERY
252
APPENDIX B
THE HYPOTHESIZED FACTOR STRUCTURE
OF THE TEST BATTERY
The experimental tests were classified according
to their hypothesised placement under factor designations
in the structure-of-intellect model as follows:
DFU--Divergent production of figural units (figural
fluency). Rapid production of a variety of figures
having specified common perceptual elements.
10. Make A Figure Test (fluency)--DFUQ2A
12. Make A Mark--DFU03A
24. Sketches--DFUQ1A
DFC"“Divergent production of figural classes (figural
spontaneous flexibility). Production of many
categories of figures of designs appropriate to
common properties.
2. Alternate Letter Groups-“DFC03A
11. Make A Figure Test (shifts)--BFU03A
5. Figural Similarities--DFC01A
26. Varied Figural Classes--DFC02A
DFS--Divergent production of figural systems. Production
253
of a variety of figural patterns in visual space.
3. Designs--DFS01A
4. Dot Systems--DFS02A
16.. Monograms--DFS03A
DFT--Divergent production of figural transformations
(figural adaptive flexibility). Production of a
number of changes of interpretation in perceptual
material redefined in terms which are neither
immediate nor obvious, but are commensurate to a
general requirement.
13. Making Obj ect s--DFT06B
14. Match Problems III--DFT03B
15. Match Problems IV--DFT04A
DSC--Divergent production of symbolic classes (symbolic
spontaneous flexibility). Production of a number of
categories of symbolic information appropriate to
common properties.
17. Name Grouping— DSC02A
18. Number Grouping--DSC01A
27. Varied SymbolS--DSC03A
DSR--Divergent production of symbolic relations (multiple
symbolic correlates). Production of many relation
ships appropriate to given sets of symbols.
254
1. Alternate Additions--DESR01A
8. Letter Group Relations--DSR03A
19. Humber Rules--DSR03A
t
DSI---Divergent production of symbolic implications
(symbolic elaboration). Production or elaboration
of a number of antecedents, concurrents, or
consequents of given symbolic information.
9. Limited Uords--DSI02A
25. Symbol Elaboration--DSI01B
CPC--Cognition of figural classes (figural classification).
The ability to classify perceived objects (Guilford,
1957, p. 24).
6. Figure Classification--EF01A
22. Picture Classification--EF03A
CMU--Cognition of semantic units (verbal comprehension).
Awareness of the meaning of words or ideas.
28. Verbal Comprehension, Form A--Part I, Guilford-
Zimmerman Aptitude Survey.3
CSU--Cognition of symbolic units (symbolic recognition).
Awareness of the structure of symbolic units
aPublished by the Sheridan Supply Company, Beverly
Hills, California, 1955.
255
(Guilford et al., 1960, p. 20).
7. Four-Letter Word--CSU01A
CSR--Cognition of symbolic relations (education of
structural relations). The ability to discover
relations involving letter patterns (Guilford, 1957,
p. 23).
22. Seeing Trends II--CSR01B
29. Word Relations--CSR02A
EFU--Evaluation of figural units (perceptual speed).
Deciding upon the identity of a given figure among
similar figures (Guilford, 1957, p. 24).
21. Perceptual Speed, Form A--Part IV, Guilford-
Zimmerman Aptitude Survey.
MSI--Memory for symbolic implications (numerical facility).
Rapid recall of well-practiced implications, e.g.,
sums and products of numbers (Guilford et al., 1961,
p. 7).
20. Numerical Operations, Form A--Part III, Guilford-
Si
Zimmerman Aptitude Survey.
£
Published by the Sheridan Supply Company, Beverly
Hills, California, 1955.
APPENDIX C
DESCRIPTION OF TESTS
257
APPENDIX C
DESCRIPTION OF TESTS
1. Alternate Additions--DSRQ1A. Show how numbers in a set may be
related in obtaining the same total with any or all of the
given numbers, when only addition is permitted and only the
given numbers may be used to obtain the same total in different
Ways.
Sampl.e: Given: 1, 2, 3, 4. Obtain: 7 as a sum.
Possible responses: 3 * £ * V = 7
\+2l +
3 ^ = 7 (not acceptable)
Score: one point for each different solution within items.
Parts: . 2; items per part: 8; working time: 6 minutes.
2. Alternate Letter Groups--DFC03A. Find letters of the alphabet
that belong to a class because of a commonality of shape or form.
Sample: Given j\ H V T" C.
Possible Groups:
(a) A H (all letters made of straight lines)
(b) AHT (all letters have horizontal lines)
co A & T (not acceptable; letters form a word)
Score: one point for each group that contains all the members
of the class.
Parts: 3; items per part: 3'; working time: 9 minutes.
258
3. .Designs.--DFS01A. Combine any or all of a given set of simple
figural elements into many different patterns.
Sample: Given: ° •=■=■
Possible answers:
vAv vAy
Score: one point for each design that is subjectively judged
different from the others in that part. Instances where
two or more designs appear to have been organized along
similar principles are resolved by applying criteria of
similarity of orientation,contiguity, and sequence.
Parts: 2; items per part: 1; working time: 6 minutes.
Dot Svstems--DFS02A„ Draw two copies of a given letter in many
different, relative positions within a matrix of equally spaced
dots.
Sample: Draw two T's in different ways.
Rule 1. Only two letters per matrix.
Rule 2. Each letter connects exactly four dots.
Rule 3. Letters must not touch or cross.
Possible answers:
JL
Score: one point for each different arrangement that adheres
to certain simple restrictions.
Parts: 2; items per part: 1; working time: 6 minutes.
259
5. Figural Similarities--DFCOLA. Determine whether figural aspects
of six complex figures can be used to form class sets of three
figures each, based on some common feature.
Sample: Given:
A
Q
B
/
c
£
Decide whether the three figures in each of the
groups listed below has a common property. Circle the
Yes if they do; Circle the No if they do not. If you
cannot decide, circle the question mark.
Probable Responses:
1. A B C Yes ? tfNo^ 4. B C E ? No
2. A B D (jesj ? No ■ B C F Yes ? f No
3. A B E /Yes^ ? No 6. D E F Yes ?
&
Probable answers: 2. yes (three part figures);
3. yes (contains triangles);
4. yes (shaded or filled-in)
Score: one point for each triad that is correctly identified as
forming a class among all 20 possible triads.
s
Parts: 2; items per part: 1; working time: 8 minutes.
260
6. Figure Classification--EFOIA. Discover classes of figures and
assign, other figures to the correct classes.
Sample: Assign the numbered figure at the left to one of the
five classes of figures at the right.
SAMPLE
ITEM NUMBER
XI
ill
IV
( (
A
5
C
D
E
o
Y
/ V ,
w/??m
o o
o
Answers: Item I and class A (solidness); Item II and
D (closed and shaded); Item III and E (each
figure includes parts of a circle); Item IV
and B (straight lines).
Score: one point for each correct choice.
Parts: 1; items: 15; working time: 6% minutes.
a
261
a
7. Four-Letter Words--CSU01A. In lines of pied type, find four-
letter words and encircle them.
Sample: A M. G Ehl I N d)t E Y K Q C iCR O C KJW Z E(H 0 W L
B E L T O F H U L L)V A Y F S M IfP L A NifF 0 U R)Y
Score: one point for each word found.
Parts: 1; items: 55; working time: 3 minutes
8- Letter Group Relations--DSR03A. Determine whether a given triad
of letters is related in different ways to each group in a list
of three-letter groups.
Sample: Given: the triad ABC, show to which numbered groups
it belongs.
Answers:
(yes^
------
yes
yes
yes
yes
Numbered Grouos:
no 1. G H I
no 2 . T T E
no 3. S A ■ U
©
4. B R R
/no'') 5. E M A
Answer 1 is "yes" because of alphabetical order of GHI.
Answer 2 is "yes" because the group contains two
consonants, one vowel. Answer 3 is "yes" because of
alphabetical order with one letter skipped.
Score: one point for each correctly determined relation.
Parts: 4; items per part: 4; working time: 10 minutes
Adopted from a test by H. A. Bechtoldc
262
9* Limited Words--DSI02A. Given two words, make up additional pairs
of words (anagrams) using all the letters in the given pair.
Sample: Given: SHIRT BEAN
Possible answers: 1- A-e/nfl
2-
Score: one point for each acceptable pair produced. Proper
names and slang are-not acceptable.
Parts: 2; items per part: 4; working time: 10 minutes.
10. Make A Figure Test (fluency)--DFU02A. Use all and only the
given lines to draw many different figures in a series of blank
squares.
Sample: Given these lines:
1 2 3
Figure 3 is not acceptable because one of the given
lines is used twice.
Score: one point for each acceptable response. Responses were
subjectively judged different by criteria of orientation,
contiguity, overlapping, and pattern.
£ >
Parts: 2; items per part: 1; working time: 6 minutes.
263
11. Make A Figure Test (shifts). This is the same test as Number 10,
alternatively scored by a subjective judgement whether the
examinee spontaneously shifted or altered his style of responses
by using different orientations and spatial relationships of the
givens to each other.
The examinee performed on the MAKE A FIGURE TEST only
once but two scores were obtained with the same series
of responses.
1 2 ' 3 4
Score: one point for each shift between successive squares.
12. Make A Mark--DFU03A. Draw many different marks in a series of
squares. Marks are to subscribe to some simple specification,
such as "’ draw dotted lines."
Sample: Make different marks using only DOTTED LINES.
Possible responses:
1 2 3 4
i
Score: one point for each mark subjectively judged different
from other responses within the item.
Parts: 2; items per part: 1; working time: 4 minutes.
264
13. Making 0biects--DFD06B. Combine the same given simple figural
elements in various ways to form certain named objects. All of
the elements need not be used.
Sample: Given: Figures a, b, c, d make objects named in each
scuare.
Examinee is show, how only a and b can be used to make
the face; how b, c, and d can make the lamp; the
examinee is told to practice'making the clown.
C l o w n
Score: one point for each element used differently within an
object that is recognizable.
*
Parts: 2; items per part: 9; working time: 6 minutes.
I
265
14. Hatch Problems X1I--DFT03B. Obtain a specified number of
squares, from the same given set of squares in different
patterns, by removing a specified number of matches. A
different rule must be used for each solution within an item.
Sample: CROSS OUT 3 MATCHES
LEAVING 4 SQUARES
EVERY MATCH LEFT MUST BE PART OF SOME SQUARE.
G i v e n A ttemp!
( a - )
_ P _
— 4 -
New Pattern
(*>)
0 1
f \ i
n I
Score: one point for each accepted solution. In addition to
the more common solutions in terms of adjacent squares,
there are some squares that overlap or are included in
larger squares.
Parts: 2; items per part: 5; working time: 12 minutes.
266
15. Match Problems IV--DFT04A. Obtain the same number of squares
in different patterns by removing any number of matches. A
different rule or principle must be followed in each solution
within items.
Sample: CROSS OUT ANY NUMBER OF PATCHES
LEAVING 2 SQUARES
SHOW AS MANY DIFFERENT SOLUTIONS AS YOU CAN
EVERY MATCH LEFT MUST BE PART OF SOME SQUARE.
G iven A tte m p t New P a t t e r n
---
J 1
n I
J u 1
1 „ r
t j
u
Score: one point for each different acceptable solution.
Examinee must be able to produce some squares with
sides greater chan one match length in order to
obtain a superior score.
Parts: 2; items per part: 2; working time: 8 minutes.
16. Monograms--DFSQ3A. Combine three initials in various complex
interrelationships to form different monograms.
Sample: Given the initials A V L, make many different monogram
designs.
Score: one point for each monogram that is subjectively judged
different from the others in that part. Instances in
which two designs appeared similar were judged different
on a basis of shape, sequence, arrangement, or
orientation.
Parts: 2; items per part: 1; working time: - 4 minutes.
267
17. Name Group ing--DS CQ2A. Classify a group of common names into
several groups based upon the different symbolic (alphabetical
or grammatical) principles they have in common.
Sample: Given the name list: 1. GERTRUDE ■ > 2. BILL, 3. ALEX,
4. CARRIE, 5. BELLE, 6. DON*
Possible groups:
1 , 3, ¥
(two syllables)
- S '
(double consonants--LL, RR, LL)
/, L K S
(begin with consonant, end with vowel)
S.core: one point for each group formed. A prepared key
indicates all the members of the most probable groups.
The examinees must write all members in order to show
the class property involved.
Parts: 2; items per part: 3; working time: 6 minutes.
18. Number Grouping;--DSC01A. Given a group of one- and two-digit
numbers, group them in several different classes based upon
properties they have in common, e.g., odd/even, multiples of
three, perfect squares, etc.
Sample: Given: 2 3 4 6 17 23 36
Possible groups:
a. 2. , ^ ^ i 3 £ (even numbers)
C. 3. 17, 2 3 (odd numbers)
Score: one point for each acceptable solution. A prepared
key indicates all the members of the most probable
groups. The examinees must write all members in order
to show the class property involved.
Parts: 2; items per part: 3; working time: 6 minutes.
268
19. Number Rules--DSR02A. Starting with one given number, arrive
at a second given number by means of simple arithmetical
operations.
Sample: Starting with 2, get 6 in a variety of ways.
Possible answers:
a.
9
f s
V V______ = 6 (add 4)
b. 2
V
= 6 (multiply by 3)
c. 2
% J • < 5 «
n
^ * 5 C 7 - * > 9
= 6 (multiply by 2, then add 2)
d. 2
v 5 "- /
= 6 (add 5, then subtract 1)
Response d is not acceptable because it is not
different enough from response a (add 4).
Score: one point for each solution that uses different rules
for obtaining the same relationship between the two
given numbers.
Parts: 2; items per part: 10; working time: 10 minutes.
20. Numerical Operations, Form A--Part III Gui1ford-Zimmerman
Aptitude Survey. Solve a number of simple computational
exercises.
Score: one point for each problem that is correctly added,
subtracted, multiplied or divided.
Parts: 1; items: .132; working time: 8 minutes.
21. Perceptual Speed, Form A--Part IV, Gui1ford-Zjmmerman Aptitude
Survey. Find the pictured form that appears the same as the
given one.
Score: one point for each correct identification.
Parts: 1; items: 72; working time: 8 minutes.
269
22. Picture Classification--EF03A. Assign pictures to classes each
defined by a group of three pictures.
Sample:
II
A
B
;n
Answers: I-B (receptacles); II-A (feathered things).
Score: one point for each correct assignment.
Parts: 2; items per part: 15; working time: 13 minutes.
23. Seeing Trends II--CSRQ1B. Describe a trend based upon relations
of letters in a group of words.
.Sample: rated crate morning dearth separate
Answer: Letter "r" moves one place to the right.
Score: one point for each trend or relation recognized as
depending upon some alphabetical or spelling property.
Parts: 2; items per part: 12; working time: 16 minutes.
270
24. Sketches--DFUQ1A. Add figural details to several replications
of the same basic design ,to produce a variety of recognisable
objects.
Sample: Given these blank figures:
Y our s k e tc h e s m ig h t look like these:
Score: one point for each different but recognizable object
produced.
Parts: 4; items per part: 12; working time: . 8 minutes.
271
25. 5-71111301 Elaboration--DSI01A. Given pairs of simple algebraic
equations, write new equations derived from the given ones.
Sample: Given: B - C = D
Z = A + D
Possible responses:
(B minus C equals D)
(C equals A plus D)
s- c . = Z - 4
A = Z-
Score: one point for each algebraically correct solution.
Only the more common arithmetical operations are-
accepted.
Parts: 3; items per part: 2; working time: 9 minutes.
26. Varied Figural Classes--DFC02A. Assign the same figure to a
number of different sets of figures, based upon different
principles of perceptual quality and form.
Sample: Circle the letters for figures forming classes based
upon common properties, with the figure triad.
F I G U R E S
Probable responses: A B © < 2 )
C (filled-in); D (closed).
s
o
A
B
D
Score: a weighted key assigns one or two points to each
acceptable grouping. A prepared key lists the most
probable groups-.
Parts: 2; items per part: 5; working time: 4 minutes.
Varied Symbols --DSC03A. Indicate the different common properties
that sets of letter combinations may have in common.
Sample: Hie set EPZT APCTO UMDT is like which of these
groups?
1. ACBE
2 . ROS
3. COH
4. GAIH
5 . ZMOD
Possible responses: 1 (begin with a vowel)
5 (contain three consonants)
Score: one point for each indicated group that shares common
symbolic properties. A prepared key lists the most
probable responses.
Parts: 2; items per part: 5; working time: 8 minutes.
t
Verbal Comprehension, Form A--Guilford-Zimmerman Aptitude Survey.
Select from a group a word that means about the same as a given
word.
Sample: EARTH
A. Sugar B. farm C. sun D. soil E. horse
Score: one point for each correct response; a correction for
chance success is applied.
Parts: 2; items: 40; working time: 12 minutes.
Eord Relations--CSR02A. Apply a rule discovered from the
relations of two given pairs of words to select the second
member of a, third pair.
Sample: on no top pot part • 1" ar!:
2. pat
3. rapt
4. tar
5. trap
Answer: 5. trap (part spelled backwards).
Score: one point for each correct response.
Parts: 2; items per part: 15; working time: 10 minutes.
APPENDIX D
ORIENTATION STATEMENT
TO STUDENTS
APPENDIX D
ORIENTATION STATEMENT
TO STUDENTS
(Examiner:) GOOD MORNING AND HAPPY NEW YEAR. I AM GLAD
TO BE HERE WITH YOU AGAIN AND TO TELL YOU WHY WE ARE
ASKING YOUR HELP WITH SOME NEW KINDS OF TESTS.
YOUR COOPERATION IN DECEMBER PROVED TO US
THAT YOU WERE INTERESTED ENOUGH IN SCIENTIFIC PRO
GRESS TO REALLY TRY.
YOU WILL RECALL THAT WE ARE INTERESTED IN
DISCOVERING MORE ABOUT HOW PEOPLE THINK; HOW
NINTH GRADERS LIKE YOU APPLY YOUR IMAGINATION TO
NEW PROBLEMS.
IN MOST OF THESE TESTS YOU WILL HAVE A
CHANCE TO USE YOUR IMAGINATION. IN MANY YOU WILL BE
ASKED TO DRAW SIMPLE DESIGNS; IN SOME OTHERS YOU WILL
WRITE WORDS OR SHORT SENTENCES; IN OTHERS YOU CAN
SHOW US WHAT YOU KNOW ABOUT LETTERS AND NUMBERS.
AS BEFORE, ON MOST OF THE TESTS YOU ARE TO
274
275
PUT YOUR ANSWERS IN SPACES IN THE BOOKLET. WRITE
CLEARLY ENOUGH SO WE CAN READ YOUR ANSWERS. DO NOT
WORRY ABOUT SPELLING OR PUNCTUATION. IF YOU CANNOT
REMEMBER HOW TO SPELL A WORD WRITE IT LIKE IT SOUNDS.
IF YOU DO NOT KNOW WHETHER AN ANSWER FITS, PUT IT
DOWN ANYWAY AND GO ON. IF YOU WANT TO CHANGE AN
ANSWER DO NOT WASTE TIME ERASING; JUST PUT DOWN THE
NEW ANSWER. YOU MAY WRITE IN THE MARGINS IF
NECESSARY.
EACH OF YOU SHOULD FEEL FREE TO PUT DOWN ALL
OF YOUR IDEAS. IF YOU THINK OF AN IDEA WHICH IS
FUNNY, STRANGE, OR UNUSUAL, PUT IT DOWN IF YOU THINK
IT FITS THE INSTRUCTIONS.
YOU ALL HAVE MANY ABILITIES THAT ARE NOT
USUALLY USED IN YOUR SCHOOL WORK. THESE TESTS MEASURE
SOME OF THOSE ABILITIES.
MOST IMPORTANT OF ALL IS THAT YOU TRY YOUR
BEST.
(Pass out booklets and pencils)
(Examiner): I WILL READ THE INSTRUCTIONS ALOUD WHILE YOU
READ THEM SILENTLY. I WILL TELL YOU EXACTLY WHEN TO
TURN EACH PAGE, WHEN TO BEGIN WORK, AND WHEN TO STOP.
276
YOU MY FIND THAT YOU HAVEN'T FINISHED THE
PAGE WHEN I SAY "STOP." THIS IS BECAUSE WE WANTED
TO LEAVE PLENTY OF ROOM FOR YOU TO DO AS MUCH AS YOU
COULD.
IF YOUR PENCIL DOESN^T WORK, HOLD IT UP AND
WE WILL TRADE IT FOR ANOTHER ONE.
ARE THERE ANY QUESTIONS? NOW TURN OVER
THE TEST BOOKLET.
(Have you wound your stop watch?) (Proceed
to instructions.)
APPENDIX E
VARXMAX ROTATED FACTOR
MATRIX* ADULTS
APPENDIX E
VARIMAX ROTATED FACTOR MATRIXj, ADULTS
a T d G d e f
s
h
1. -61 -08
13
Ob 06 13 -10 04
2 . -18 -12
09 17 -05
00 -11
09
3. -09 -53
10 09
-09
-14 02 -08
4.
-05
-24 16 16 00
07
-04
-03
5.
-21 -04
09 15 05
00
-43
-01
6.
-15
06 07
25 -09
02
03 34
7. -30 -10 04 16
15
00 -02
-03
8. -07
-03 03 05
44 00
-03 -03
9.
-41 -02 11
33
06 -01 00 06
10. -11 -58
17 02 02 11 -04 10
11. 04 -24 02
-03
01 -01 08 02
12.
05
-56 -12 12
03
11
-17
00
13.
-06
-59
18
05
02 -11 -03 -13
14. -23 -08 58
17
02 01
-13
10
15. -23
17 11 01 02 -05 -07 14
16.
-12 -66
-09 -08
-03
04
03
04
17.
-30
-13 -13
21
27
-00
-03
-04
18.
-15 -05
-01 06 14 01
-03
00
19.
-30 -18 16
17 17
18 08
05
20 . -64 -11 -01
05
-01
-07
-08 -01
21. -31 -19
21 18
-07
-01 -12 24
22. -05 -04 11
53 -03 -03 -25 17
23. -33 -05 22 38 07
-10 -12 -06
24. -04 -61 -04 -14 16 -08 12 00
25-
-17 -06
29
04
03
-14
-07 05 .
26. ■
-03 -05
-04 -01 10 00 04 -04
27. -51
-04
15
08
13
-08 -12
23
28. -11
03
-01 60 10 04 01 -01
29.
-36 06
33 32
09
12
-13
06
(Continued)
278
APPENDIX E-Continued
279
X k 1 m n 0 h2
1 . -16
-19 07 17
02 08 -01 54
2.
-17 -00 -12 21 36 11 -02
33
3.
-18 -14 -04
17 -03 -07 -03
44
4.
-39 07 -15 09 13 09
-02 3^
5. -07 -03 -07 03
04 10 -01 28
6. -08
05
-14 06 06 -04 02 26
7. -03 -47
-02 -00 -00 00 -00
37
8 . 01 -06 12
13
-02 -02 01 24
9.
-06
03
-02 00 10 02 08 32
10. -11
09
-02 11
05
11 -02 46
11.
01 01
-07 -05 -04 -42 01 24
12. -07
.08 00 -02
-05 -01 08 40
13.
-06
-03
12 08 08 -18
-17
52
14. ■ -29 -07
-13
16
03
-06 -01 56
15.
-49
-11
03 27
00 -06 01
45
16.
00
-15
-02 08 06
-13 07 52
17.
-13 -13
-02 16 11 12
-19 37
18. -09 -06 12 50
03 03
-04 34
19.
-07 -06 -01
47
10 10
07 52
20.
-04 00
-03 19
02 -06
-03
40
21.
-20 -24
03
11 04 -24 -10 49
22.
-04 01
05
01 06 -06 04 42
23.
03
-19
-04
19
12
05 03 45
24 . 00
-05 10 -08 01 -10
-03
46
25.
-17 18 -08 46 04 -04 00
43
26. 03
01 50
05 -03
04 -00 27
27.
-08 -20 10
13
-01 06 -04
47
28. -06 -11
-03
08
-03
06
-07 43
29.
-01 -14 10 21 12
09 07 53
APPENDIX F
VARXMAX ROTATED FACTOR
MATRIXs ADOLESCENTS
281
APPENDIX F
VARIMAX ROTATED FACTOR MATRIX, ADOLESCENTS
i
ii ill iv V vi vii viil
1.
69
-18 -20 04 16
03 -17
-00
2. ' 54 -27 -17 13
08
15
10 -07
3.
34 -60 -07 -06 16 -00 14 01
4. 17 -46
-23 19
-01 -02 14
07
5. 33 -03 -18
07
04 -02
05 05
6. 38 02 -16 -08
05 07
01 04
7.
28 -10 -06 -14 02 08 08 54
8. 11 -11 -01
27 39
08
03
-06
9.
40 -08 -02 -00 06
09 39 17
10. . 16
-69 05 24
07
12 02 -05
11. 05 -19 -13
08
07 -03
01
03
12.
-08 -54 -08 12 11 -01 -06
09
13-
16
-49
-11 02 24 -18
03
17
14. 38
-15 -53 03
02
09
-04 01
15-
25
-20
-55 13
10 10
05 07
16. 04 -70 -01 02 -00 12 -02
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(Continued)
APPENDIX F-Continued
282
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Asset Metadata

Creator Gershon, Arthur (author)

Core Title Figural And Symbolic Divergent-Production Abilities In Adults And Adolescents

Degree Doctor of Philosophy

Degree Program Psychology

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

Tag OAI-PMH Harvest,psychology, experimental

Format dissertations (aat)

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Guilford, Joy P. (committee chair), Cliff, Norman (committee member), Michael, William B. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-308856

Unique identifier UC11358780

Identifier 6403097.pdf (filename),usctheses-c18-308856 (legacy record id)

Legacy Identifier 6403097.pdf

Dmrecord 308856

Document Type Dissertation

Format dissertations (aat)

Rights Gershon, Arthur

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