A factor-analytic study of creative-thinking abilities

Fifty-three tests designed to measure aspects of creative thinking were administered to 410 air cadets and student officers. The scores were intercorrelated and 16 factors were extracted. Orthogonal rotations resulted in 14 identifiable factors, a doublet, and a residual. Nine previously identified factors were:verbal comprehension, numerical facility, perceptual speed, visualization, general reasoning, word fluency, associational fluency, ideational fluency, and a factor combining Thurstone'sclosure I andII. Five new factors were identified asoriginality, redefinition, adaptive flexibility, spontaneous flexibility, andsensitivity to problems.Under Contract N6onr-23810 with the Office of Naval Research. The opinions expressed are our own and are not necessarily shared by the Office of Naval Research. These studies are under the direction of J. P. Guilford. Paul R. Christensen is assistant director. Robert C. Wilson has been principally responsible for the conduct of this particular study. Donald J. Lewis contributed to the development of hypotheses and tests. Raymond M. Berger made substantial contributions to the development of the tests.The authors are very much indebted to the Personnel Research Laboratory, Human Resources Research Center, Air Training Command, Lackland Air Force Base, Texas, for making the testing possible, and in particular to Dr. Lloyd G. Humphreys, Director, and to Mr. William B. Lecznar, Technical Aide.Acknowledgement is made to Gordon Taaffe for the supervision of much of the statistical work connected with this study and to Norman W. Kettner for carrying out the extractions of factors and for valuable assistance on the rotations of axes.A fuller discussion of this factor analysis is given by Wilson (16).     

A study of speed factors in tests and academic grades

Speeded and unspeeded tests of vocabulary, spatial relations, and arithmetic reasoning were factorially analyzed, together with certain reference tests and academic grades. Lawley's maximum likelihood method was used, the computations being carried out on the Whirlwind electronic computer. Four different speed factors were isolated, together with a second-order general speed factor. Consistent small positive correlations between the academic grades and the speed factors were found.The writer is indebted to Dr. John French, to Dr. David Saunders, and especially to Dr. Ledyard R Tucker for helpful suggestions and theoretical advice throughout the course of this study. The active cooperation of Dr. William Shields, Educational Advisor, and of many others at the United States Naval Academy at Annapolis has been invaluable. The author is very grateful to Dr. P. Youtz and Dr. C. W. Adams for the opportunity to use Whirlwind I, a high-speed computer sponsored by the Office of Naval Research, and to Dr. H. Denman for help is programming and in putting the program on the computer. He also wishes to express his deep appreciation to Dr. Hubert Brogden and Miss Bertha Harper of The Adjutant General's Office for the opportunity to use their matrix rotator and for helpful guidance in its operation.     

Percentage points of Wilks'L mvc andL vc criteria

Likelihood ratio tests have been proposed by Wilks for testing the hypothesis of equal means, variances, and covariances (H _mvc) and the hypothesis of equal variances and covariances (H _vc) in ap-variate normal distribution. Using exact distributions of the appropriate likelihood ratio statistics, tables of the .05 and .01 points of these distributions are constructed forp = 4, 5, 6, 7 and sample sizen = 25 (5) 60 (10) 100. A correction factor is recommended for largern. Two numerical examples illustrate use of the tables. A nonparametric test is proposed forH _mvc when the multivariate parent population is known to be non-normal.This research was supported partly by the Office of Naval Research under Contract No. Nonr-855(06) and partly by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. 18(600)-83. Reproduction in whole or in part for any purpose of the United States Government is permitted.     

Full-information item bi-factor analysis

A plausibles-factor solution for many types of psychological and educational tests is one that exhibits a general factor ands − 1 group or method related factors. The bi-factor solution results from the constraint that each item has a nonzero loading on the primary dimension and at most one of thes − 1 group factors. This paper derives a bi-factor item-response model for binary response data. In marginal maximum likelihood estimation of item parameters, the bi-factor restriction leads to a major simplification of likelihood equations and (a) permits analysis of models with large numbers of group factors; (b) permits conditional dependence within identified subsets of items; and (c) provides more parsimonious factor solutions than an unrestricted full-information item factor analysis in some cases. Supported by the Cognitive Science Program, Office of Naval Research, Under grant #N00014-89-J-1104. We would like to thank Darrell Bock for several helpful suggestions.     

A new status index derived from sociometric analysis

For the purpose of evaluating status in a manner free from the deficiencies of popularity contest procedures, this paper presents a new method of computation which takes into accountwho chooses as well ashow many choose. It is necessary to introduce, in this connection, the concept of attenuation in influence transmitted through intermediaries.This work was done under the sponsorship of the Office of Naval Research.     

Application of the concept of simple structure to Alexander's data

A battery of 20 tests originally analyzed by Alexander (1) was reworked according to the principle of simple structure. His results were sustained in general. Both analyses yielded five factors in the first-order domain. Of these, three factors in the re-analysis (v,X andF) have almost exactly the same loadings as the corresponding factors in the original work, and were interpreted in the same way. The loading pattern of a fourth factor,Z, left uninterpreted in the original study, happened to be more clear in the re-analysis, and an interpretation was attempted. It appears to be a factor of perceptual synthesis, and seems to play an important role in intellectual processes. A fifth factor, not present in Alexander's results, appeared in the new analysis: the reasoning factor, involved in inductive and deductive thinking. All four cognitive factors are related to a general factor that can be thought of as representing abstraction and education of relations and correlates, these processes being, therefore, the essential feature underlying intellectual behavior, at least in that sector surveyed by the tests of the present battery.The analysis of the data was done in the Psychometric Laboratory of The University of Chicago, under a fellowship from The University of Madrid (Junta de Relaciones Culturales). The author wishes to express his gratitude to Professor L. L. Thurstone, whose advice as a scientist and kindness as a friend, have been the principal stimulus for this work.     

Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study

In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log (N–1) and log {[n(n–1)/2]–[(i–1)n]}, whereN is the number of observations;n, the number of variables; andi, the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member.     

Organizational reward systems: Implications for climate

This study investigated the role of systematically different organizational reward structures upon individual perceptions of the reward climate. Nurses in a naval hospital worked for the same supervisors but were subject to either tenure-contingent (N=73) or behavior-contingent (N=50) reward systems. No differences in perceived reward climate were found between the two groups. In the tenure-contingent group, job attitudes reflected individual characteristics rather than perceived climate. The opposite relationship was found for the behavior-contingent group.Support for this research was provided under Office of Naval Research Contract RR942-08-01 NR 170-915. Opinions expressed are those of the author. No endorsement by the Department of the Navy has been given, nor should it be inferred. Portions of the study were conducted while the author was at the Naval Health Research Center in San Diego. The author would like to thank R. J. Bullock, Mark C. Butler, L. R. James, and R. D. Pritchard for their helpful comments and assistance.     

A synthesis of two factor analyses of intermediate algebra

A battery of 18 tests of intermediate algebra and 20 reference tests was administered to two successive second-year algebra classes. Each battery was separately factor analyzed by Thurstone methods, and the two analyses were synthesized by the Tucker method. The five congruent factors obtained were identified as: Verbal Comprehension, Deductive Reasoning, Algebraic Manipulative Skill, Number Ability, and Adaptability to a New Task.This paper is a condensation of a thesis. The work was begun while the author was a Psychometrics Fellow of the Educational Testing Service. The work was further supported by Contract N6onr-270-20 of the Office of Naval Research and by Grant NSF G-642 of the National Science Foundation. The writer is indebted to Professors Harold Gulliksen and Ledyard R Tucker for their guidance throughout this study.     

A generalization of Thurstone's learning function

Thurstone's equation giving the probability of a correct response (p) as a function of practice time (t) when punishment and reward have equal effects has been generalized to the case where the effect of punishment is not necessarily equal to the effect of reward. Since the general equation is somewhat unwieldy, three special cases are considered, where reward has no effect, where punishment has no effect, and where these effects are equal. Equations are given together with tables for making a rectified plot for each of the three special cases.This study was supported in part by contract N6onr 270-20 between the Office of Naval Research and Princeton University. The opinions expressed are, of course, those of the author and do not represent attitudes or policies of the Office of Naval Research.     

A proposed index of the conformity of one sociometric measurement to another

An index is proposed to measure the extent of agreement of the data of a sociometric test with another test made at an earlier time or on another test criterion. The index is used to define an index of concordancebetween the two tests. It is shown how the index may be used for either individuals or groups. Tests of the hypothesis that agreement is random are given for all cases and applied to an example.Work done under the sponsorship of the Office of Naval Research.     

Relations of factor score estimates to their use

Considerations of factor score estimates have concentrated on internal characteristics. This report considers external characteristics of four methods for determining factor score estimates; that is, relations of these estimates to measures on attributes not entered into the factor analysis. These external characteristics are important for many uses of factor score estimates. Findings are that different ones of the methods are appropriate for different uses.Supported in part by the Personnel and Training Branch of the Office of Naval Research under contract number 00014-67-A-0305-0003.     

The closure factors related to other cognitive processes

Twenty-five group tests, assembled with certain hypotheses concerning the first and second closure factors in mind, were administered to 154 subjects, mostly graduate students. The intercorrelations were analyzed factorially, yielding eight factors that were rotated to an oblique simple structure. The factors were interpreted as: speed of closure, C₁; flexibility of closure, C₂; verbal closure, C₃; word fluency, W; reasoning, R; perceptual speed, P; the first space factor, S₁; and speed of handwriting, H. Four second-order factors were tentatively described as analytical ability, synthetic ability, speed of perception, and word fluency. Three of the reasoning tests had their highest loadings on C₂ and one on C₃, which seems to be evidence that flexibility of closure generalizes in the cognitive domain and is associated with analytical ability.This paper summarizes part of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Chicago. The writer is deeply indebted to Dr. L. L. Thurstone for his generous advice and guidance. The complete study is obtainable on microfilm, from the University of Chicago library, Film No. T1279 (price $2.15). It includes reproductions of the tests used, score distributions, and plots of the obliqueV-matrices.     

An inter-battery method of factor analysis

The inter-battery method of factor analysis was devised to provide information relevant to the stability of factors over different selections of tests. Two batteries of tests, postulated to depend on the same common factors, but not parallel tests, are given to one sample of individuals. Factors are determined from the correlation of the tests in one battery with the tests in the other battery. These factors are only those that are common to the two batteries. No communality estimates are required. A statistical test is provided for judging the minimum number of factors involved. Rotation of axes is carried out independently for the two batteries. A final step provides the correlation between factors determined by scores on the tests in the two batteries. The correlations between corresponding factors are taken as factor reliability coefficients.This research was jointly supported by Princeton University and the Office of Naval Research under contract N6onr-270-20 and the National Science Foundation under grant NSF G-642; Harold Gulliksen, principal investigator. The preparation of this paper and the accompanying material has been aided by the Educational Testing Service. The author is grateful to Professors Harold Gulliksen and Samuel S. Wilks for their many most helpful comments and suggestions.     

CONSTRUCTING AND DERIVING RECIPROCAL TRIGONOMETRIC RELATIONS: A FUNCTIONAL ANALYTIC APPROACH

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula‐to‐graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula‐to‐graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.     

Evidence and inference in educational assessment

Educational assessment concerns inference about students' knowledge, skills, and accomplishments. Because data are never so comprehensive and unequivocal as to ensure certitude, test theory evolved in part to address questions of weight, coverage, and import of data. The resulting concepts and techniques can be viewed as applications of more general principles for inference in the presence of uncertainty. Issues of evidence and inference in educational assessment are discussed from this perspective.Probability isn't really about numbers; it's about the structure of reasoning.Presidential address to the Psychometric Society, presented June 25, 1994, in Champaign, Illinois.Supported by (1) Contract No. N00014-91-J-4101, R&T 4421573-01, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research, (2) the National Center for Research on Evaluation, Standards, Student Testing (CRESST), Educational Research and Development Program, cooperative agreement number R117G10027 and CFDA catalog number 84.117G, as administered by the Office of Educational Research and Improvement, U.S. Department of Education, and (3) the Statistical and Psychometric Research Division of Educational Testing Service. I am grateful for comments and suggestions from Henry Braun, Drew Gitomer, Richard Patz, Jonathan Troper, and Howard Wainer.     

Object manipulability affects children’s and adults’ conceptual processing

Research on kinds of concepts indicates that children use perceptual and functional information differently to form natural and artifact concepts. Beyond object domain, object manipulability appears to be a decisive factor in adult conceptual processing. Thus, the effect of object manipulability on conceptual processing was tested in 5- and 7-year-olds and adults using a picture matching task. Reaction times for identifying conceptual relations on the basis of perceptual similarity (e.g., jacket-coat) and contextual/functional information (e.g., jacket-hanger) were analyzed according to object manipulability and domain. Both children and adults were faster to identify contextual/functional relations for manipulable than for nonmanipulable objects. Conversely, they were faster to identify perceptual similarity relations for nonmanipulable than for manipulable objects, particularly for natural concepts. Results reveal an early distinction between concepts of manipulable and nonmanipulable objects. Implications for further research on concept formation and for embodied views of concepts are discussed.     

An analysis of Guttman's simplex

Applying a Spearman formula for factor loadings to a variant of the diagonal method, the Guttman simplex model is factored algebraically inton/2 additive factors. The finding that communalities can be discovered such that the rank of a simplex becomesn/2 is contradictory to Guttman's contention that the minimal rank isn — 2. Certain matrices of 4 and 5 variables presented by Guttman as simplexes, can, in general, be considered 2-factor matrices, easily analyzed to simple structure without rotation. One example of 6 variables is factored by the method described to a 3-factor structure.Prepared under Contract 816(02) between the Office of Naval Research and Washington University and presented in part at a meeting of the Southern Society for Philosophy and Psychology, St. Louis, Missouri, March 27, 1959. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

Conceptual change in science and in science education

There is substantial evidence that traditional instructional methods have not been successful in helping students to restructure their commonsense conceptions and learn the conceptual structures of scientific theories. This paper argues that the nature of the changes and the kinds of reasoning required in a major conceptual restructuring of a representation of a domain are fundamentally the same in the discovery and in the learning processes. Understanding conceptual change as it occurs in science and in learning science will require the development of a common cognitive model of conceptual change. The historical construction of an inertial representation of motion is examined and the potential instructional implications of the case are explored.The preparation of this paper was supported in part by the Office of Naval Research Grant N00014-85-K-0337 to the Learning Research and Development Center at the University of Pittsburgh. The opinions expressed do not necessarily reflect the position or policy of the ONR, and no official endorsement should be inferred. I wish to thank Lauren Resnick for her helpful comments and encouragement to pursue this research. I also thank Paul Thagard for introducing me to the technique of concept mapping and Gregory Nowak for his assistance in the preparation of the figures. The paper has benefited from comments by Floris Cohen, Susan Hojnacki, Thomas Kuhn, and Michael Ranney. Any misconceptions are, however, my own.     

Notes on an approximation method for fitting parabolic equations to experimental data

When a numerical transformation of raw data is used only to simplify the arithmetic of curve fitting, the transformation may lead to undesirable and even highly distorted results. This principle is illustrated with an approximation method of fitting parabolic equations to experimental data, as described recently in texts by Johnson and Lewis. Although the approximation method will never yield as good fits as the exact, least-squares method, satisfactory results are in general achieved whenever the transformed scores yield a linear plot as a function ofX. The principal difficulty with the method is that some data which fall along a parabola may not yield a linear plot of the transformed scores versusX, and so cannot be fitted satisfactorily by the approximation method.This study was done in cooperation with the Systems Division, Naval Research Laboratory, under Contract N5-ori-166, Task Order I, between the Office of Naval Research and The Johns Hopkins University. This is Report No. 166-I-156, Project Designation No. NR-507-470, under that contract. The author is indebted to Dr. Hermann von Schelling, of the Naval Medical Research Laboratory, U. S. Naval Submarine Base, New London, Connecticut, for technical advice. Miss Judith T. Parker and Mr. William T. Pollock assisted capably in the tedious computations required for this note.