A factor-analytic study of reasoning abilities

A battery of 32 tests was administered to a sample including 144 Air Force Officer Candidates and 139 Air Cadets. The factor analysis, using Thurstone's complete centroid method and Zimmerman's graphic method of orthogonal rotations, revealed 12 interpretable factors. The non-reasoning factors were interpreted asverbal comprehension, numerical facility, perceptual speed, visualization, andspatial orientation. The factors derived from reasoning tests were identified asgeneral reasoning, logical reasoning, education of perceptual relations, education of conceptual relations, education of conceptual patterns, education of correlates, andsymbol substitution. The logical-reasoning factor corresponds to what has been called deduction, but eduction of correlates is perhaps closer to an ability actually to make deductions. The area called induction appears to resolve into three eduction-of-relations factors. Reasoning factors do not appear always to transcend the type of test material used.Under Contract N6onr-23810 with the Office of Naval Research. The views expressed here are not nesessarily shared by the Office of Naval Research. These studies are under the general direction of J. P. Guilford. P. R. Christensen is assistant director. A. L. Comrey was in direct charge of this study during its early stages and R. F. Green during most of its progress.     

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.     

On the Wilson tests

A general critical analysis of the median tests proposed by Wilson for certain analysis of variance hypotheses is presented. Specifically, discrepancies between the purported and actual approximate distributions of some of the test statistics are noted. Validity and power of the resulting tests are discussed.This work was sponsored in part by the Office of Naval Research while the author was at Stanford University. Reproduction in whole or in part is permitted for any purpose of the United States Government. The author wishes to thank Professors Fred C. Andrews, Lincoln E. Moses, and David L. Wallace for their helpful criticisms and suggestions in the writing of this paper.     

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.     

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.     

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.     

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.     

Organization of the bilingual lexicon: Categorical versus alphabetic cuing in Russian-English bilinguals

The mechanism by which Russian native speakers store and retrieve Russian and English words from lexical memory was investigated in two experiments in which fluency of retrieval was compared for categorical and alphabetic cues. We hypothesized that fluency in Russian would be higher for categorical cues but that fluency in English would be higher for alphabetical cues because native language words would have been stored by meaning, while second-language words would have been stored according to dictionary usage. Subjects retrieved more Russian than English words with categorical cues, but their retrieval was the same for the two languages with alphabetic cues. In addition, fluency was greater overall with alphabetical than categorical cues. We attributed the greater fluency in Russian with the categorical cues to the early age at which the concepts were acquired, which made them more accessible in the native language. These findings support the idea that access codes for words may vary depending upon how they are originally learned.This research was supported by Research Grants AFOSR 89-0442 and F49620-92-J-0119 from the U.S. Air Force Office of Scientific Research to Joan Gay Snodgrass. We are indebted to an anomymous reviewer for constructive comments on an earlier version of this article.     

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.     

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.     

An automated test development of parallel tests from a seed test

Binary programming models are presented to generate parallel tests from an itembank. The parallel tests are created to match item for item an existing seed test and match user supplied taxonomic specifications. The taxonomic specifications may be either obtained from the seed test or from some other user requirement. An algorithm is presented along with computational results to indicate the overall efficiency of the process. Empirical findings based on an itembank for the Arithmetic Reasoning section of the Armed Services Vocational Aptitude Battery are given.The Office of Naval Research, Program in Cognitive Science, N00014-87-C-0696 partially supported the work of Douglas H. Jones. The Rutgers Research Resource Committee of the Graduate School of Management partially supported the work of Douglas H. Jones and Ing-Long Wu. A Thomas and Betts research fellowship partially supported the work of Ing-Long Wu. The Human Resources Laboratory, United States Air Force, partially supported the work of Ronald Armstrong. The authors benefited from conversations with Dr. Wayne Shore, Operational Technologies, San Antonio, Texas. The order of authors' names is alphabetical and denotes equal authorship.     

Notes on the Horizon Illusion: II

O.S.S. Assessment Staff. The Assessment of Men. New York: Rinehart, 1948. Reviewed by H. J. Eysenck.

Army Air Forces. Aviation Psychology Program Research Reports. Washington, D. C.: Goaernrnent Printing Office, 1947. Reviewed by H. J. Eysenck.     

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.     

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.     

Two models of group behavior in the solution of eureka-type problems

A study by Shaw (7) some twenty years ago is frequently cited by social scientists to support the generalization that groups are superior to individuals in problem-solving. Shaw suggests that personal interaction within the group is responsible for the superior performance of groups. This article re-examines her data in the light of two models which propose that the difference in quality of solution between group and individual performance is solely a matter of ability. It is shown that Shaw's data may be considered to have been an outcome of behavior postulated by the models. Since Shaw's observations relate to a special population and to special kinds of problems, the proposed models may not be appropriate under differing experimental conditions. In fact, Lorgeet al. (4) have indicated that experimental demonstration of the superiority of groups over individuals in problem-solving depends not only on the kind of group but also on the kind of problem to be solved. In addition, the diversity of transfer of training for groups and for individuals is considered.Supported in part by the Office of Naval Research under Contract N6 onr 266 (21) and the Air Force Personnel and Training Research Center under Contract AF 18(600)-341.     

Higher‐order factors of creativity within Guilford's structure‐of‐intellect model: A re‐analysis of a fifty‐three variable data base

Both exploratory factor analyses (varimax and promax solutions) and confirmatory maximum likelihood factor analyses were used to re‐examine a correlation matrix of 53 tests from a battery administered to a sample of more than 400 Air Force officers. The data base originated in a report from the University of Southern California Aptitudes Research Project (Guilford, Wilson, & Christensen, 1952), which was intended to identify factors of creative thinking. The major objective of this study was to ascertain whether the covariation among the test variables that were conceptualized as first‐order factors within the structure‐of‐intellect model could be explained parsimoniously in terms of a number of higher‐order creative abilities. Application of a relatively objective oblique exploratory factor analytic technique (promax) afforded a replication of four of Guilford's creativity factors—two divergent production constructs of ideational fluency and word fluency, one construct representing sensitivity to problems, and another identified as redefinition or flexibility of closure typically involving transformations. Although substantial support was found for higher‐order factor models which distinguished among five types of psychological operations and three kinds of test content, statistical indicators of closeness‐of‐fit suggested that a mixed model of both first‐order and higher‐order factors was required to describe creativity thinking, perhaps within some form of hierarchical ordering. In addition to recognition of divergent production as a key component of creative endeavor, it appeared that a higher‐order convergent production factor involving primarily semantic and symbolic transformations constituted a dimension of potential importance to the creative thinking of mathematicians, scientists, engineers, and inventors. It was hypothesized that in creative thinking a variety of psychological operations within a dynamic interactive system is employed almost simultaneously in a forward and backward manner.     

Tests of hypothesis in a repeated measures design from a permutation viewpoint

Repeated measures designs have been widely employed in psychological experimentation, however, such designs have rarely been analyzed by means of permutation procedures. In the present paper certain aspects of hypothesis tests ina particular repeated measures design (one non-repeated factor (A) and one repeated factor (B) withK subjects per level ofA) were investigated by means of permutation rather than sampling processes. The empirical size and power of certain normal theoryF-tests obtained under permutation were compared to their nominal normal theory values. Data sets were established in which various combinations of kurtosis of subject means and intra-subject variance heterogeneity existed in order that their effect upon the agreement of these two models could be ascertained. The results indicated that except in cases of high intra-subject variance heterogeneity, the usualF-tests onB andAB exhibited approximately the same size and power characteristics whether based upon a permutation or normal theory sampling basis.This research prepared under Contract No. 2593 from the Cooperative Research Branch of the U. S. Office of Education.     

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.     

Sampling fluctuations resulting from the sampling of test items

Sampling fluctuations resulting from the sampling of test items rather than of examinees are discussed. It is shown that the Kuder-Richardson reliability coefficients actually are measures of this type of sampling fluctuation. Formulas for certain standard errors are derived; in particular, a simple formula is given for the standard error of measurement of an individual examinee's score. A common misapplication of the Wilks-Votaw criterion for parallel tests is pointed out. It is shown that the Kuder-Richardson formula-21 reliability coefficient should be used instead of the formula-20 coefficient in certain common practical situations.Most of the work reported here was carried out under contract with the Office of Naval Research. The writer is indebted to Professor S. S. Wilks, who has checked over certain critical portions of a draft of this paper.