The factorial isolation of primary abilities

This is an experimental study of the isolation, by factor methods, of primary abilities from a battery of tests given to 240 students. The range and nature of the fifty-six tests is briefly described. Tentative interpretations of the twelve orthogonal primary factors are given.     

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.     

Study of some factors related to intelligence

From the factorial analysis of a battery of nineteen individual tests seven factors were obtained, six of them being interpreted. Some of these factors are probably related to similar ones isolated in different batteries and by different authors. The testProgressive Matrices here analyzed is loaded in some of the factors, as was expected according to the nature of its problems and to previous experience with the test. The loadings of the tests and of the factors in the second-order factors are given. It is expected that this extension of factor theory will prove useful for the isolation of more fundamental psychological parameters, although at present it is difficult to evaluate precisely the theoretical and practical implications of this aspect of factor analysis.     

The effects of selection in factor analysis

Factorial results are affected by selection of subjects and by selection of tests. It is shown that the addition of one or more tests which are linear combinations of tests already in a battery causes the addition of one or more incidental factors. If the given test battery reveals a simple structure, the addition of tests which are linear combinations of the given tests leaves the structure unaffected unless the number of incidental factors is so large that the common factors become indeterminate.     

The dependability of the general factor of intelligence: Why small, single-factor models do not adequately represent g

Floyd, Shands, Rafael, Bergeron and McGrew (2009) used generalizability theory to test the reliability of general-factor loadings and to compare three different sources of error in them: the test battery size, the test battery composition, the factor-extraction technique, and their interactions. They found that their general-factor loadings were moderately to strongly dependable. We replicated the methods of Floyd et al. (2009) in a different sample of tests, from the Minnesota Study of Twins Reared Apart (MISTRA). Our first hypothesis was that, given the greater diversity of the tests in MISTRA, the general-factor loadings would be less dependable than in Floyd et al. (2009). Our second hypothesis, contrary to the positions of Floyd et al. (2009) and Jensen and Weng (1994), was that the general factors from the small, randomly-formed test batteries would differ substantively from the general factor from a well-specified hierarchical model of all available tests. Subtests from MISTRA were randomly selected to form independent and overlapping batteries of 2, 4 and 8 tests in size, and the general-factor loadings of eight probe tests were obtained in each battery by principal components analysis, principal factor analysis and maximum likelihood estimation. Results initially indicated that the general-factor loadings were unexpectedly more dependable than in Floyd et al. (2009); however, further analysis revealed that this was due to the greater diversity of our probe tests. After adjustment for this difference in diversity, and consideration of the representativeness of our probe tests versus those of Floyd et al. (2009), our first hypothesis of lower dependability was confirmed in the overlapping batteries, but not the independent ones. To test the second hypothesis, we correlated g factor scores from the random test batteries with g factor scores from the VPR model; we also calculated special coefficients of congruence on the same relation. Consistent with our second hypothesis, the general factors from small non-hierarchical models were found to not be reliable enough for the purposes of theoretical research. We discuss appropriate standards for the construction and factor analysis of intelligence test batteries.     

Orthogonal inter-battery factor analysis

It is the purpose of this paper to present a method of analysis for obtaining (i) inter-battery factors and (ii) battery specific factors for two sets of tests when the complete correlation matrix including communalities is given. In particular, the procedure amounts to constructing an orthogonal transformation such that its application to an orthogonal factor solution of the combined sets of tests results in a factor matrix of a certain desired form. The factors isolated are orthogonal but may be subjected to any suitable final rotation, provided the above classification of factors into (i) and (ii) is preserved. The general coordinate-free solution of the problem is obtained with the help of methods pertaining to the theory of linear spaces. The actual numerical analysis determined by the coordinate-free solution turns out to be a generalization of the formalism of canonical correlation analysis for two sets of variables. A numerical example is provided.This investigation has been supported by the U.S. Office of Naval Research under Contract Nonr-2752(00).     

Experimental study of simple structure

A battery of thirty-six tests was given to a group of high-school seniors. The factorial analysis reveals essentially the same primary factors that were found in previous studies. The test battery reveals a simple structure.     

Expanding the Nexus of Cognitive and Psychomotor Abilities

A study was conducted to expand the nexus of cognitive and psychomotor abilities. A cognitive aptitude battery and a psychomotor battery were administered to 429 military recruits. A confirmatory factor analysis yielded higher-order factors of general cognitive ability (g) and psychomotor/technical knowledge (PM/TK). PM/TK was interpreted as Vernon's (1969) practical factor (k:m). In the joint analysis of these batteries, g and PM/TK each accounted for about 31% of the common variance. No residualized lower-order factor accounted for more than 7% PM/TK influenced a broad range of lower-order psychomotor factors. The first practical implication of these findings is that psychomotor tests are expected to be at least generally interchangeable. A second implication is that the incremental validity of psychomotor tests beyond cognitive tests is expected to be small. These findings should help guide test developers and inform personnel selecting agencies regarding the expected utility of psychomotor tests.     

Introduction: A Festschrift in Honor of Earl A. Alluisi

A battery of 10 traditional paper-and-pencil aptitude tests and a battery of 25 cognitive-components-based tests were administered to 298 men and women to investigate the common sources of variance in those batteries. Earlier confirmatory factor analyses showed each battery to have a hierarchical structure, each with a single higher order factor. The higher order factor in the paper-and-pencil battery had previously been identified as general cognitive ability, or g. The higher order factor from the cognitive-components battery had been identified as working memory. The intercorrelation of the higher order factors from the two batteries was .994, indicating that both measured g. The proportion of common variance because of g was greater in the cognitive-components battery than in the paper-and-pencil battery. The correlations between each factor based on cognitive components and g averaged .946. Despite theoretical foundations and arguments, cognitive components tests appear to measure much the same thing as traditional paper-and-pencil tests.     

Confirmatory factor analysis of the WAIS-IV/WMS-IV

The Wechsler Adult Intelligence Scale-fourth edition (WAIS-IV) and the Wechsler Memory Scale-fourth edition (WMS-IV) were co-developed to be used individually or as a combined battery of tests. The independent factor structure of each of the tests has been identified; however, the combined factor structure has yet to be determined. Confirmatory factor analysis was applied to the WAIS-IV/WMS-IV Adult battery (i.e., age 16-69 years) co-norming sample (n = 900) to test 13 measurement models. The results indicated that two models fit the data equally well. One model is a seven-factor solution without a hierarchical general ability factor: Verbal Comprehension, Perceptual Reasoning, Processing Speed, Auditory Working Memory, Visual Working Memory, Auditory Memory, and Visual Memory. The second model is a five-factor model composed of Verbal Comprehension, Perceptual Reasoning, Processing Speed, Working Memory, and Memory with a hierarchical general ability factor. Interpretative implications for each model are discussed.     

Individual and group differences in intelligence and speed of information processing

A battery of eight different reaction time (RT) tests, measuring the speed with which individuals perform various elementary cognitive processes, and a group test of scholastic aptitude (the Armed Services Vocational Aptitude Battery, ASVAB) were given to 50 black and 56 white male vocational college students. The regression of the general factor scores of the ASVAB on the RT measures yielded a shrunken multiple correlation of 0.465. Although discriminant analyses, when applied separately to the ASVAB subtests and to the RT variables, showed highly comparable overall discrimination (over 70% correct classification) between the black and white groups, factor scores derived from the general factor (labeled ‘speed of information processing’) of the RT battery show only about one-third as large a mean black-white difference as the mean group difference on the general factor scores derived from the ASVAB. Comparisons were also made between the 106 vocational college students and 100 university students of higher average academic aptitude who had previously been tested on the same RT battery (Vernon, 1983a). These groups showed marked differences on the RT variables, the largest differences occuring on the tests that required more complex cognitive processing. The more complex RT tests also correlate most highly with the psychometric measures of ability within each group. The results are consistent with the hypothesis that individual differences and the mean differences between groups in psychometric abilities and scholastic achievement are related to differences in the speed of information processing as measured in elementary cognitive tasks.     

Music ability

Two batteries of music tests were factored by the centroid method. From each battery three oblique factors were extracted and in each case were tentatively identified as tonal sensitivity, retentivity (memory for elements), and memory for form. The correlations of the music tests of one battery with subtests of Cattell's intelligence test and with tests of a literary nature are also reported.Karlin, J. E. A multiple factor analysis of musicality. M. A. thesis, University of Cape Town, 1939.Drake, R. M. A factorial analysis of music tests by the Spearman tetrad-difference technique.J. Musicology, 1939, 1, 1.     

On methods in the analysis of profile data

This paper is concerned with methods for analyzing quantitative, non-categorical profile data, e.g., a battery of tests given to individuals in one or more groups. It is assumed that the variables have a multinormal distribution with an arbitrary variance-covariance matrix. Approximate procedures based on classical analysis of variance are presented, including an adjustment to the degrees of freedom resulting in conservativeF tests. These can be applied to the case where the variance-covariance matrices differ from group to group. In addition, exact generalized multivariate analysis methods are discussed. Examples are given illustrating both techniques.We are indebted to Mrs. Norma French for performing all the calculations appearing in this paper.     

Testing specific cognitive abilities by telephone and mail

The two goals of this research were to develop a brief battery of tests of specific cognitive abilities that can be administered via telephone to adolescents and to assess the psychometric properties of the battery. In a sample of 212 adolescents from 10 to 15 years of age, factor analyses supported the hypothesized structure of verbal, spatial, perceptual speed, and memory abilities, with three tests intended to mark each factor. For a subsample of 62 subjects, retest correlations were .81, .73, .82, and .57, respectively, for the four specific cognitive abilities; scores from telephone testing and face-to-face testing correlated near the reliabilities of the telephone tests. Recommendations are made for shortening the 60-min battery to 35 min by using only two tests to mark each factor.     

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.     

Stepwise Selection of ECATs for Maximum Mean Validity

The problem addressed in this article is how to select a common battery of predictor tests for all armed services schools. A technique was developed for selecting a subset of tests from a larger test pool in order to maximize the mean corrected validity across occupational samples. The method involved adding or deleting tests stepwise to build a battery having a specified number of tests. The method was applied to the combined battery consisting of the Armed Services Vocational Aptitude Battery (ASVAB) and the Enhanced Computer-Administered Test (ECAT) battery. The analyses showed that, if all ASVAB tests were forced in first, validity tended to level off after 3 ECAT tests were added, each test representing a different ECAT factor. The first 3 ECAT tests selected by the procedure were Two-Hand Tracking, Mental Counters, and Assembling Objects. These 3 ECAT tests produced 76% of the validity gain from the full 9-test ECAT battery for preferred (i.e., hands-on performance oriented) school criteria. Also, a combination of 3 ECAT battery tests and 5 ASVAB tests had greater mean validity than did the full ASVAB of 10 tests. A variety of alternative combinations of 3 ECAT tests had nearly the same validity as did the optimal tests, as long as the tests measured the 3 basic ECAT battery factors of Psychomotor Ability, Working Memory, and Spatial Ability.     

On the interpretation of common factors: A criticism and a statement

The concept of simple structure is criticized for lack of objectivity and for failure to produce invariance of (a) factor loadings under change of battery, and (b) individual scores on primary traits under change of tests. It is also criticized on the grounds that simple structure yields at best the factors which were put in and that, by suitable manipulation of tests, any set of factors may be represented in a battery by tests which will yield a simple structure. A procedure for rotation is developed which locates the first rotated axis to pass through a cluster of tests which, by hypothesis, contain a common factor and to project all tests into a hyperplane orthogonal to this factor. The second factor is then located to pass through the projections of a second cluster of tests defining the second factor, and so on, until all hypothecated factors have been located. Any residual interrelations may then be rotated graphically to the most plausible arrangement.     

Use of factor analysis in the study of alcohol-induced strategy changes in skilled performance on a soccer test

The present study was designed to examine how skilled behaviour changes under the effects of two doses of alcohol (0.5 gm/kg and 1 gm/kg). A battery of perceptual-motor reference tests, together with the criterion test of a soccer slalom were given a sample of 48 male volunteers to show how performance strategies changed across the different experimental conditions. Analysis indicated little change between effects of placebo and the lower dose but some change in the composition of performance between placebo and the 1 gm/kg dose. This finding supports further use of factor analysis in the study of skilled behaviour.     

Visual,auditory and reaction time approaches to the measurement of speed of information processing and individual differences in intelligence

A battery of tachistoscopic, auditory, reaction time and microcomputer-generated measures of speed of information processing (inspection time, IT) were administered to 96 college students aged between 18 and 22 yr. In addition, each S was given a battery of tests designed to provide independent evaluations of right- and left-hemispheric functioning. Criterion measures included a verbal (Vocabulary) and a nonverbal (Block Design) measure of intelligence. Results revealed a general processing speed factor in addition to task-specific sources of variability. Moreover, the IT tasks loaded on the same second-order factor as did the traditional measures of intelligence and aptitude. The findings support the theoretical view that processing speed may be a general factor in individual differences in performance on complex intellectual solving tasks. An important objective for future work in this area is to seperate and evaluate the common and specific sources of variability on IT tasks.