ON THE NATURE OF THE PERCEPTUAL SPEED FACTOR

W erdelin , I. & S tjernberg , G. On the nature of the perceptual speed factor. Scand. J. Psychol ., 1969, 10, 185–192.–149 subjects, about 15 years old, were given 25 psychological tests. Some of these defined the reference factors R, S, N , and P , others were designed to study the nature of the P factor. It was found that certain visual tests showed successively higher loadings in the P and N factors the more they were practiced. This effect of practice is probably restricted to tests of a certain kind. Very simple visual tests showed high loadings in the P factor. Hypotheses as to the nature of the P factor are suggested.     

The difficulty of a test and its factor composition

A factor analysis of the ten sub-tests of the Seashore test of pitch discrimination revealed that more than one ability is involved. One factor, which accounted for the greater share of the variances, had loadings that decreased systematically with increasing difficulty. A second factor had strongest loadings among the more difficult items, particularly those with frequency differences of 2 to 5 cycles per second. A third had strongest loadings at differences of 5 to 12 cycles per second. No explanation for the three factors is apparent, but the hypothesis is accepted that they represent distinct abilities. In tests so homogeneous as to content and form, where a single common factor might well have been expected, the appearance of additional common factors emphasizes the importance of considering the difficulty level of test items, both in the attempt to interpret new factors and in the practice of testing. The same kind of item may measure different abilities according as it is easy or difficult for the individuals to whom it is applied.     

THE EFFECT OF PERFORMANCE TIME AND RETESTING UPON THE FACTOR STRUCTURE OF INTELLIGENCE TESTS

Changes in the factor structure of intelligence tests between early and later stages of performance and between testing and retesting were studied. In addition to factor analyses, correlations between the test scores of various time periods and the final factor scores were computed. The principal findings were the powerful influence of the verbal ability in the initial stages of most tests, the gradual 'purification' of the factors, and the occurrence of a shift of the highest factor loadings of some tests from one factor to another, particularly in tests with increasing item difficulty.     

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.     

Changes in common-factor loadings as tests are altered homogeneously in length

Formulas are derived by which, given the factor loadings and the internal reliability of a test of unit length, the following estimates can be made: (1) the common-factor loadings for a similar (homogeneous) test of lengthn; (2) the number of times (n) that a test needs to be lengthened homogeneously to achieve a factor loading of a desired magnitude; and (3) the correlation between two tests, either or both of which have been altered in length, as a function of (a) the new factor loadings in the altered tests or (b) the original loadings in the unit-length tests. The appropriate use of the derived formulas depends upon the fulfillment of four assumptions enumerated.This article is based on a paper read by the authors at the annual meeting of the Western Psychological Association in Eugene, Oregon, June 25, 1949.     

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.     

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.     

Performance of neurotics and stables on the standard progressive matrices

The significance of the role of Neuroticism (N) as an important determiner of learning and performance was investigated. The relation of N to performance on intelligence tests was analyzed and it was predicted that as item difficulty increased high N subjects would perform progressively worse and low N subjects would perform better. This type of analysis was shown to demonstrate the Yerkes-Dodson phenomenon better than a single total test score. In the present investigation, 400 subjects were selected for a 2 × 2 design consisting of two personality groups (neurotics vs. stables) and two sexes. Subjects were administered the Standard Progressive Matrices, an intelligence test having five progressively more difficult stages. The findings were that neurotics performed better on the simpler set, but as items became more difficult the stables performed significantly better than neurotics. A correlational analysis also showed a positive relation between N and the first set of items, and a negative relation between N and the other four sets.     

Longitudinal factor analysis

A model is presented for factor analysing scores on a set of psychological tests administered as both pre- and postmeasures in a study of change. The model assumes that the same factors underlie the tests on each occasion, but that factor scores as well as factor loadings may change between occasions. Factors are defined to be orthogonal between as well as within occasions. A two-stage least squares procedure for fitting the model is described, and generally provides a unique rotation solution for the factors on each occasion.We thank M. W. Browne, R. P. McDonald, R. Pruzek, and the Managing Editor for their constructive comments.     

Are visual-perceptual and visual-motor skills separate abilities?

This study explored the independence of visual-perceptual and visual-motor abilities. Scores on the Motor-free Visual Perception Test were correlated by Pearson's method with scores on tests that weight the visual-perceptual, motor, and visual-motor components differently. Small but significant correlations were found between the Motor-free Visual Perception Test and tests of visual-motor integration, but there was no relationship between the motor-free test and tests of motor ability. These findings support the premise that tests of visual perception, visual-motor integration, and motor ability measure different skills.     

Gender Differences in the Measurement of Creative Problem‐Solving

Despite significant scholarly attention, the literature on the existence and direction of gender differences in creativity has produced inconsistent findings. In the present paper, we argue that this lack of consensus may be attributable, at least in part, to gender‐specific inconsistencies in the measurement of creative problem‐solving. To explore this possibility, we empirically tested assumptions of multiple‐group measurement invariance using samples borrowed from four recent studies that assessed creative problem‐solving (J.D. B arrett et al., 2013; K.S. H ester et al., 2012; D.R. P eterson et al., 2013; I.C. R obledo et al., 2012). Across the four samples, apparent gender differences emerged on all three components of S.P. B esemer & K. O 'Q uin's (1999) three‐facet model of creativity (i.e., quality, originality, and elegance) such that, on average, females appeared to exhibit higher baseline levels of creativity. However, in light of violations of measurement invariance assumptions across genders found in these samples, comparisons such as these may not ultimately be appropriate. Although the underlying factor structure and factor loadings on a unitary creativity factor were consistent across gender (i.e., weak factorial invariance), measurement in‐equivalence assumptions were violated at the subfacet level (i.e., strong factorial invariance). Implications of these findings for understanding gender differences in creative problem‐solving are discussed.     

An item-factor analysis of the Eysenck Personality Questionnaire (E.P.Q.): Will the real personality factors stand up

The study utilised responses to the E.P.Q. from 3 samples of subjects. An initial sample of 239 Independent Study Students, a second sample of 278 student and pupil nurses and an aggregate sample of 617 students of both types. The samples were subjected to principal components analyses followed by varimax and promax rotations. Scree Test, number of significant loadings, replicability across samples and sexes, factor reliability and factor replicability were used as criterion measures to determine the number of real factors present. Nearly all the N, E and L-items were recovered in the analyses of each of the samples. In the two smaller samples, insufficient items were retrieved to indicate the presence of a clear psychoticism factor, but in the aggregate sample one factor contained 19 of the 25 P-items. Scree Test, numbers of significant loadings, replicability over samples and factor reliability criteria indicated that either a 4- or 5-factor solution was a valid possibility. Application of the criterion of factor replicability, using factor comparability coefficients based on factor scores, revealed an exceptionally clear 4-factor structure which was also replicable across sexes. The effects of dissimulation were investigated by dichotomising the male and female samples by L-scores. In both cases the mean scores for P and N for the low L-score group were higher than the corresponding mean scores for the high L-score group, which supports a previous finding that dissimulation tends to artificially lower the P and N-scores. Examination of the effect of dissimulation on the factor structure showed that E and N came out equally clearly in the high and low L-score groups for both males and females. P came out more clearly in the low L-score group for males and in the high L-score group for females, the latter finding being contrary to that of other authors. The investigation confirmed the presence of 4 “real”, replicable factors of P, E, N and L at the first order, showed that P and N are sensitive to dissimulation and illustrated the effectiveness of using factor replicability, measured by factor comparability coefficients based on factor scores, to determine the number of “real” factors in an analysis.     

Determinants of information-seeking behavior

Two studies examined situational determinants of choice among anagram tests that varied both in difficulty and in diagnosticity (the information they provided about one's own ability). In both studies, subjects worked on a preliminary anagram test before making their choices. Study 1 manipulated level of performance on the preliminary test. Results showed that high performance led to preferring more difficult and more diagnostic tests. In Study 2, subjects were either paid or not paid for their performance on the preliminary test. Results showed that pay led to a preference for more diagnostic tests. Unexpectedly, results of both studies showed that although difficulty and diagnosticity were defined independently of one another, they were not perceived as such. Thus, high diagnostic tests were perceived as more difficult; more difficult tests were perceived as more diagnostic; and the difference between high and low diagnostic tests in perceived diagnosticity and choice of items (high diagnostic tests had higher scores on both measures) were more pronounced among more difficult tests. Motivational as well as cognitive interpretations of the results were discussed.     

Multiple rectilinear prediction and the resolution into components: II

Given a battery ofn tests that has already been resolved intor orthogonal common factors andn unique factors, procedures are outlined for computing the following types of linear multiple regressions directly from the factor loadings: (i) the regression of any one test on then?1 remaining tests; (ii) all then different regressions of ordern?1 for then tests, computed simultaneously; (iii) the regression of any common factor on then tests; (iv) the regressions of all the common factors on then tests computed simultaneously; (v) the regression of any unique factor on then tests; (vi) the regressions of all the unique factors on then tests, computed simultaneously. Multiple and partial correlations are then determined by ordinary formulas from the regression coefficients. A worksheet with explicit instructions is provided, with a completely worked out example. Computing these regressions directly from the factor loadings is a labor-saving device, the efficiency of which increases as the number of tests increases. The amount of labor depends essentially on the number of common factors. This is in contrast to computations based on the original test intercorrelations, where the amount of labor increases more than proportionately as the number of tests increases. The procedures evaluate formulas developed in a previous paper (2). They are based essentially on a shortened way of computing the inverse of the test intercorrelation matrix by use of the factor loadings.     

Humphreys's attenuated test of Spearman's hypothesis

Humphreys's test of Spearman's hypothesis (viz., that the size of the standardized black-white differences on various psychometric tests is positively related to the tests' loadings on g, the general intelligence factor) is methodologically weak. It is based on comparison of a fairly representative sample of the black population of U.S. school children with a highly selected sample of the white school population, representing the lowest 15 to 20% of whites in socio-economic status (SES). A fair test of the hypothesis requires that the black and white samples should not be selected on any g-correlated variable, such as SES. Selection attenuates and distorts the relationship between tests' g loadings and the magnitude of the standardized mean black-white differences on the tests. Other unorthodox conditions in Humphreys's study, such as performing factor analysis on the test-score means of various arbitrary demographic groups instead of on individual test scores inflates tests' g loadings and biases the test of Spearman's hypothesis by restriction of reliable variance in g loadings. Humphreys's study cannot be considered a proper replication of Jensen's examination of Spearman's hypothesis in 11 different studies comprising 74 different tests, which consistently bears out Spearman's hypothesis.     

Mental toughness among high school students: a test of its multidimensionality and nomological validity with academic achievement and preference for difficult tasks

Recent studies posit that mental toughness is a relevant construct for predicting achievement outcomes in academic settings. It is a multidimensional construct that encapsulates psychological resources that facilitate consistent performance despite stressors and challenges. However, recent evidence has called into question its multidimensional aspect. The first purpose of this study was to verify, using a bi-factor model, if mental toughness can be operationalized by (a) multiple dimensions, (b) a general factor, or (c) both a general factor and multiple dimensions. The second goal was to test the nomological validity of the construct. Specifically, we verified whether the specific factors predict, beyond the general factor, academic achievement and preference for difficult tasks. Using a correlational cross-sectional design in which 515 high school students (58.8% girls; M age = 15.68; SD = 1.05) were asked to complete a questionnaire, we found that mental toughness is best conceptualized by a general factor. More specifically, most loadings are higher on the mental toughness general factor than on the specific dimensions. Furthermore, the mental toughness general factor predicts better school achievement and preference for difficult tasks than the specific factors. The results are discussed in terms of their implications for theory and practice.     

The factorial interpretation of test difficulty

This paper discusses the influence of test difficulty on the correlation between test items and between tests. The greater the difference in difficulty between two test items or between two tests the smaller the maximum correlation between them. In general, the greater the number of degrees of difficulty among the items in a test or among the tests in a battery, the higher the rank of the matrix of intercorrelations; that is, differences in difficulty are represented in the factorial configuration as additional factors. The suggestion is made that if all tests included in a battery are roughly homogeneous with respect to difficulty existing hierarchies will be more clearly defined and meaningful psychological interpretation of factors more readily attained.     

The contributions of memory and attention processes to cognitive abilities

In two experiments, the contributions of memory and attention processes to the cognitive abilities of reasoning and perceptual speed were investigated. Two measures of speed of information retrieval from long-term and short-term memory (Posner paradigm, Sternberg paradigm) and two attention measures (continuous attention test, attention switching test) were included in the first experiment (N = 220). The memory tests led to correlations with the measures of cognitive abilities, whereas the attention test did not. The same tests as well as one additional memory test and one attention test (working memory test, test of covert orientation) were administered in the second experiment (N = 116). Again, the memory tests led to the larger correlations with the measures of cognitive abilities. Two components were obtained in components analysis, of which the first was characterized by high loadings of the memory tests and the second by high loadings of the attention tests. Only the memory component contributed to the prediction of cognitive abilities.     

无铆题情况下测验分数等值方法探索——构造铆测验法

研究旨在探索无铆题情况下,使用构造铆测验法,实现测验分数等值。研究一和研究二分别探索题目难度排序错误、铆题难度差异对构造铆测验法的影响。结果表明：（1）等组条件下,随着错误铆题比例,难度排序错误程度,铆题难度差异增大,构造铆测验法的等值误差逐渐增大,随机等组法的等值误差较为稳定;不等组条件下,构造铆测验法的等值误差均小于随机等组法;（2）对于构造铆测验法,在不等组条件下,铆测验长度越短,等值误差越大。     

Evaluating the Invariance of the Factor Structure of the EPQ–R–N Among Adolescents

We examined the factor structure of the Neuroticism scale of the Eysenck Personality Questionnaire (EPQ–R–N; S. B. G. Eysenck, Eysenck & Barrett, 1985) and its factor invariance across sex and racial/ethnic groups in a sample of 1,979 adolescents. Using confirmatory factor analyses, we compared a hierarchical model to previous models of the EPQ–R–N and to single-factor and 3-factor structures. The hierarchical factor structure in which a general factor coexists with 3 group factors (depression, social concerns, and worry) was superior to alternative models. The general factor accounted for more than 60% of the variance in EPQ–R–N total scores and was invariant across sex and ethnicity. The 3 group factors varied across ethnicity and sex. We discuss the implications of these findings for conceptualization and assessment of neuroticism using the EPQ–R–N.