A factor analysis of the original Stanford-Binet scale

From the original Stanford-Binet scale, those items passed by between 10 and 90 per cent of a group of ten-year-old children were analyzed by the centroid method. Upon rotation, there appeared a common factor, for which two explanatory hypotheses are offered, the more tenable being that it is an effect of maturation. Primary factors tentatively identified are Number, Space, Imagery, Verbal Relations and Induction. A sixth factor apparently involves a reasoning ability and a seventh can not be interpreted.The writer is indebted to Dr. L. L. Thurstone for his interest and assistance throughout this study and to Dr. Andrew W. Brown, who made possible the collection of data at the Institute for Juvenile Research, Chicago, Illinois.     

A factorial study of the reasoning and closure factors

A battery of 46 tests was given to 237 college men. A factor analysis using the Thurstone technique revealed eight clearly interpretable first-order factors, one dubious factor, and a residual factor. The factors were interpreted as induction, deduction, flexibility of closure, speed of closure, space, verbal comprehension, word fluency, and number. Four second-order factors were abstracted from the matrix of first-order correlations. The presence of induction, deduction, and flexibility of closure on the first second-order factor, interpreted as an analytic factor, confirmed previous indications of relationships between the reasoning and closure factors. A second bipolar factor is interpreted as a speed of association factor. The third factor is interpreted as facility in handling meaningful verbal materials—perhaps an ability to do abstract thinking. The fourth factor is possibly a second-order closure factor—perhaps an ability to do concrete thinking.The author is grateful to Professor L. L. Thurstone for his encouragement and invaluable advice and for permission to use many tests originally prepared in the Psychometric Laboratory of the University of Chicago, to Mr. James Degan for assistance in rotations, and to the Social Science Research Committee of the University of Chicago for a grant to this study.     

A factorial study of fluency in writing

A factorial study of fluency was undertaken to test an hypothesis that at least two fluency abilities would be measured by a battery composed both of word fluency tests used by Thurstone and tests of fluency described by several British investigators. Twenty-eight tests, including ten reference tests for five primary mental abilities, were administered to 181 high-school seniors. Ten centroid factors were extracted, a simple structure was found, and eight factors were interpreted. Five factors defined were the following reference abilities: memory (M), number (N), reasoning (R), verbal comprehension (V), and perceptual speed (P), the last one being somewhat tentatively identified. The main finding is the analysis of fluency into two factors: word fluency (W) and ideational fluency (F). Word fluency is defined as a facility in producing single, isolated words that contain one or more formal restrictions, without reference to the meaning of the words. Ideational fluency is described as a facility in expressing ideas by the use of words and their meanings. Another verbal ability indicated is tentatively interpreted as verbal versatility, the ability to express essentially the same idea by means of several different words or combinations of words.The writer wishes to express his appreciation to Dr. L. L. Thurstone for his guidance throughout the study and for providing facilities and materials needed; to Miss Jessie LaSalle and the Washington, D. C., high schools for providing the subjects; to Ledyard Tucker, Frank Medland, and Mrs. Virginia Brown for computational assistance; and to others who gave aid during the study.     

THELMA GWINN THURSTONE

This paper examines the life and career of Thelma Gwinn Thurstone—her career strategies and her contributions to psychological testing, intelligence theory, and instruction—based on her publications and a series of personal interviews with her and her colleagues. Thurstone's contributions, with her husband, L. L. Thurstone, included the development of the American Council on Education's Psychological Examinations and the Primary Mental Abilities test batteries. Her own work included the development of instructional materials using the common factor theory of intelligence. Thurstone, wife of a preeminent scholar and mother of three sons, pursued career strategies that facilitated her continued professional activity for six decades. Further research on measurement history and also on women's career strategies are suggested.     

Psychology as a quantitative rational science (excerpts)

The purpose of the Psychometric Society is to encourage mathematical psychology. This article justifies the emphasis on quantification, and upon rationalization in science, as well as the Society's conception of the fundamental nature of science.Editor's Note: On September 4, 1936, L. L. Thurstone gave the presidential address at the first annual meeting of the Psychometric Society in Hanover, NH. Uncertainties about the viability of the new journal,Psychometrika, led his colleagues to urge him to publish his address inScience. Excerpts from that paper are reprinted here. Thurstone's examples are now quite dated, and have been omitted, thus thwarting his major intent of providing examples of quantification. But his point of view towards the goals of the new Society is remarkably fresh, and is expressed with typical Thurstone clarity. The reference to the complete paper is:Thurstone, L. L. (1937). Psychology as a quantitative rational science.Science, 85, 227–232. (Copyright 1937 by the American Association for the Advancement of Science.)     

Centroid orthogonal transformations

An initial transformation for facilitating the analysis of a factor problem is discussed. Such a transformation is used in the rotational procedure developed by L. L. Thurstone in an accompanying article.     

The effect of difficulty and chance success on item-test correlation and on test reliability

An equation is derived for predicting the effect of chance success, relative to item difficulty, on item-test correlation. The values predicted by this equation and by equations derived by Guilford and Carroll for predicting the effect of chance success on item difficulty and test reliability are compared with empirical values in an experiment which used identical test items in multiple-choice and answer-only form.Condensation of a dissertation presented in partial fulfillment of the requirements for the Ph.D. degree to the University of Chicago. Grateful acknowledgment is made to Professor Harold Gulliksen for his guidance as thesis advisor and to Professor L. L. Thurstone and Dr. D. W. Fiske of the University of Chicago who served as members of the thesis committee. The author is also indebted to Professor S. S. Wilks for review of the derivations and development of statistical tests used in the thesis, to Dr. L. R Tucker for technical advice, and to Dr. W. G. Mollenkopf for critical comments on the derivations and interpretations. The writer expresses appreciation to the Educational Testing Service for making available its technical facilities, and to the University of Chicago for the flexible administrative arrangement which made this thesis possible.     

Some properties of the communality in multiple factor theory

Several theorems concerning properties of the communaltiy of a test in the Thurstone multiple factor theory are established. The following theorems are applicable to a battery ofn tests which are describable in terms ofr common factors, with orthogonal reference vectors.1. The communality of a testj is equal to the square of the multiple correlation of testj with ther reference vectors.2. The communality of a testj is equal to the square of the multiple correlation of testj with ther reference vectors and then—1 remaining tests. Corollary: The square of the multiple correlation of a testj with then—1 remaining tests is equal to or less than the communality of testj. It cannot exceed the communality.3. The square of the multiple correlation of a testj with then—1 remaining tests equals the communality of testj if the group of tests containsr statistically independent ests teach with a communality of unity.4. With correlation coefficients corrected for attenuation, when the number of tests increases indefinitely while the rank of the correlational matrix remains unchanged, the communality of a testj equals the square of the multiple correlation of testj with then—1 remaining tests.5. With raw correlation coefficients, it is shown in a special case that the square of the multiple correlation of a testj with then—1 remaining tests approaches the communality of testj as a limit when the number of tests increases indefinitely while the rank of correlational matrix remains the same. This has not yet been proved for the general case.The author wishes to express his appreciation of the encouragement and assistance given him by Dr. L. L. Thurstone.     

AN INVESTIGATION OF COMPLIANCE-GAINING AS POLITENESS

This study considers an alternative perspective on the compliance-gaining phenomenon, specifically the theory of politeness articulated by Brown and Levinson (1978). They posit that all interaction is characterized by concern over the other person's autonomy needs and his or her desire to be liked, manifested in message behavior that addresses these needs (i.e., politeness). Brown and Levinson's typology of politeness strategies was translated into 32 items to which 155 respondents indicated likelihood of use and perceived politeness. Respondents assessed the items while imagining themselves in one of eight hypothetical scenarios created to manipulate the three situational factors posited as significant by Brown and Levinson: relationship distance, relationship power, and the magnitude of the request. A factor analysis reduced the 32 tactics to four underlying factors, which in turn served as one variable set for a canonical correlation whose second variable set was the situational factors and the agent's gender. Results indicated that females and persons in close relationships use more polite tactics than males and persons in more distant relationships. Secondarily, results also indicated that persons with power use less politeness than less powerful persons.     

An empirical comparison of methods of communality estimation

This paper shows the formulation of nine methods of estimating the unknown communalities. Each of these methods has been used on experimental data and the results tabulated for comparison. The results show that the most accurate approximations are obtained from the Centroid No. 1 and theGraphical methods.The author wishes to express his appreciation to Professor L. L. Thurstone for his advice and for providing the facilities of the Psychometric Laboratory for this investigation.     

A non-graphical method for transforming an arbitrary factor matrix into a simple structure factor matrix

The most commonly used method of factoring a matrix of intercorrelations is the centroid method developed by L. L. Thurstone. It is, however, necessary to transform the centroid matrix of factor loadings into a simple structure matrix in order to facilitate the interpretation of the factor loadings. Current methods for effecting this transformation are chiefly graphical and require considerable experience and personal judgment. This paper presents a new method for transforming an arbitrary factor matrix into a simple structure matrix by methods almost completely objective. The theory underlying the method is developed and approximation procedures are derived. The method is applied to a matrix of factor loadings previously analyzed by Thurstone.     

An analysis of random and systematic changes with practice

Six motor tests and six nonverbal tests were administered four times to the same subjects. Subjective reports of the subjects are discussed, changes in mean scores and in variability and score correlations from trial to trial are surveyed, and factor analyses of results on the first and fourth trials are presented and compared. Implications of the findings with respect to correction for attenuation are pointed out.Thanks are due to Mr. Searles and his staff at the Henry Ford Trade School, who gave both suggestions and aid in completing this work; to Dr. L. L. Thurstone, who gave suggestions for certain aspects of the analysis; and to L. R. Tucker and Robert Blakey, who made the final factorial analyses and suggested various conclusions.     

L. L. Thurstone: A new assessment

Most psychologists have heard of Thurstone, and know him as a pioneer of mathematical psychology and factor analysis. But his appearances in history books are rare and peripheral, as a man of technical prowess rather than intellectual achievement, and at best he is seen as a link in the tradition culminating in signal detection and mathematical learning theory. Nineteen eighty-seven is the centenary of his birth, so it is a timely moment to correct this picture. Thurstone was influenced by G. H. Mead, and his work is best placed within the pragmatist movement, not as moving towards the mechanistic psychology that now dominates psychology. Viewed in this way, his true status and the reasons for his relative neglect become apparent. This is illustrated by a detailed consideration of his mathematical learning models.     

Pattern variants on a square field

A quantitative approach to the psychology of pattern recognition requires knowledge of the number of possible variants of any particular pattern. The general solution for the number [p/m ²] of pattern variants thatp counters can form on a square network ofm ² positions is obtained by elementary group theory. The exact solution is given in terms of the different types (symmetric, asymmetric, etc.) of patterns possible and an approximate formula for the total number of patterns is also developed.The author is indebted to Mr. J. Sandiford for his invaluable assistance on the theoretical aspects of the problem and to Mr. J. L. Griffith for his helpful criticism.     

Methylphenidate and cognitive therapy with add children: A methodological reconsideration

The present doubleblind study examined the effects of methylphenidate, cognitive therapy, and their combination in attention deficitdisordered (ADD) children. Four treatment groups were compared on measures of attentional deployment and cognitive style, tests of academic achievement, and behavioral rating scales. In contrast to a previous study conducted in this laboratory, children in this study were not receiving medication during posttesting. Results were interpreted to suggest that measurable effects of stimulant medication dissipate rapidly upon discontinuation of pharmacotherapy. The combination of methylphenidate and cognitive therapy was not found to be any more efficacious than either of the treatments studied alone. Discussion suggests that medication status at follow-up is an essential feature of research design.This research was supported in full by U.S. Public Health Service Grant No. MH 37-628 from the National Institute of Mental Health, Psychopharmacology Branch, and by Biomedical Research Award No. RR 0715807 from the National Institutes of Health, each awarded to R. T. Brown. Placebo and methylphenidate were supplied by CIBA-GEIGY, Summit, New Jersey. The authors are grateful to Dr. Rute Medenis and the entire staff at the University of Illinois Pediatrics Clinic for their valuable assistance and kind support throughout the project. The authors would also like to thank Avery L. Spunt, R.Ph., College of Pharmacy, University of Illinois, for his assistance in packaging the medication and monitoring compliance; Arthur I. Neyhus, Ph.D., Coordinator of Child Study Facility, University of Illinois at Chicago, for his assistance in evaluation; and J. Scott Allen, Jimmy Bruce, Robert Miller, Michael Mazius, and Steven Orenczuk, for their assistance in training of the children.The contributions of these authors are equal.     

A factorial study of number ability

In order to investigate certain hypotheses concerning the nature of number ability, and, secondarily, the nature of perceptual speed, a battery of thirty-four tests was given to 223 Chicago high school seniors and the data were factored by the centroid method. Seven primary factors were identifiable upon rotation. Several deductions are made relative to the interpretation of the factors and relative to the consistency of the data with the hypotheses which were to be tested. I wish to express my great appreciation of the aid of Professor L. L. Thurstone whose generosity made this study possible. Grateful acknowledgment is made of the aid of Mr. Ledyard Tucker in the use of the I.B.M. machines for obtaining the intercorrelations and the centroid factor loadings, and to both him and Mr. Harold Bechtoldt for aid in the testing of subjects.     

Thurstone's analytical method for simple structure and a mass modification thereof

The analytical method for simple structure proposed by Thurstone is applied to four separate cases and found to yield satisfactory results. The simple structure obtained by Thurstone's method is found to match closely that obtained by other methods and corresponds to the true structure of the matrix in those cases where true structure is known. Difficulties about the choice of the correct trial vector led the writer to develop a modification of Thurstone's method, useful where high speed computational facilities are available. Instructions are given for this so-called mass modification, and the procedure is illustrated with a 5-factor, 14-variable example. While the results do not fully correspond to a previous graphical solution, it can be argued that the results obtained by the new method show an improved simple structure. The modified method is applied to three other correlation matrices, yielding in each case a satisfactory simple structure.Contribution No. 961 from the Department of Entomology, University of Kansas, Lawrence, Kansas.Most of the work on which this paper is based was performed during the summer of 1956 when the author was the holder of an Elizabeth Watkins Faculty Scholarship granted by the Kansas University Endowment Association. The work was carried out at the University of Illinois, where the author was privileged to spend the tenure of this scholarship. The writer is indebted to Professor L. H. Lanier, the Chairman of the Psychology Department, who graciously placed space and equipment at his disposal, and to Professor Raymond B. Cattell for his continuing encouragement of and interest in the author's work. Some of the computations were performed on the ILLIAC digital computer. The many courtesies extended by Professor J. J. Nash, Director of the Digital Computer Laboratory of the University of Illinois, are gratefully acknowledged. The writer is indebted to Mr. John R. Hurley for much assistance during the development of the computational routines and for a critical reading of this paper. Expenses in connection with the work were met by a General Research Grant of the University of Kansas.     

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.     

Studies in the learning function

The error function of the theoretical learning curve developed by Thurstone has been fitted to maze data from rats that have been subjected to cerebral cortical insult. There is a high degree of relationship between the number of errors necessary to complete learning as predicted from the curve and the experimental measure of learning, total-errors-minus-errors-first-trial. The procedure provides a method of analysis for individual learning records and it may be used to shorten the training period. The goodness of fit indicates that the underlying logic of the learning curve is plausible.A grant-in-aid from the National Research Council has made the present analysis possible. We are indebted to Professor L. L. Thurstone for aid and encouragement.