Confirmation of the structural dimensionality of the Stanford-Binet Intelligence Scale (Fourth Edition)

Transcription

1 Bond University From the SelectedWorks of Gregory J. Boyle January 1, 1989 Confirmation of the structural dimensionality of the Stanford-Binet Intelligence Scale (Fourth Edition) Gregory J. Boyle, Bond University Available at:

2 1 CONFIRMATION OF THE STRUCTURAL DIMENSIONALITY OF THE STANFORD-BINET INTELLIGENCE SCALE (FOURTH EDITION) GREGORY J. BOYLE* University of Melbourne *Requests for reprints should be addressed to Dr G. J. Boyle, University of Melbourne, Parkville, Victoria 3052, Australia.

3 2 Abstract The new Stanford-Binet Intelligence Scale (fourth edition) seemingly represents an important advance in design and construction over the earlier form L-M. The latest version of the instrument (SB-IV) is purported to index both crystallized intelligence (Verbal and Quantitative Reasoning Areas) and fluid intelligence (Abstract/Visual Reasoning Area) structural dimensions respectively. Given the prominence of modem information- processing theories of cognition, a separate Short-Term Memory (STM) Area is also provided. The authors provided confirmatory factor analytic (CFA) evidence to support their claim for the construct validity of each of the four cognitive ability areas. However, several inconsistent factor loadings were apparent, for which no reasonable explanation could be provided. To clarify this uncertainty, data in the Technical Manual was refactored using a methodologically sound exploratory (EFA) approach. Many initial inconsistent factor loadings were shown to be essentially artifacts of the particular factor analytic procedures employed by the test authors. The obtained results provided support for the structural dimensionality of the new SB-IV measurement instrument.

4 3 The new Stanford-Binet Intelligence Scale (Thorndike, Hagen and Sattler, 1986), like its forerunners will undoubtedly have a long history of successful usage in the measurement and prediction of human cognitive abilities. In its new expanded format, the fourth edition of the instrument will enable a level of cognitive assessment clearly rivalling, and perhaps even superior to that provided in the Wechsler series of scales. The incorporation of findings regarding the hierarchical structure of intellectual abilities into the design and construction of the latest version of the Stanford-Binet Intelligence Scale is quite evident. A Composite score enables measurement of Spearman's 'g' factor, while separate Verbal Reasoning and Quantitative Reasoning scores give an assessment of crystallized abilities, and an Abstract/Visual Reasoning score provides an index of fluid abilities, respectively. Accordingly, the structural basis of the new Stanford- Binet Intelligence Scale rests solidly on the model of crystallized and fluid abilities proposed by the Cattell-Horn school (cf. Brody and Brody, 1976, pp , Cattell, 1971, 1982a, 1978; Hakstian and Cattell, 1978; Horn, 1976, 1980, 1985, 1986; Stankov, 1983). However, in addition, the importance of cognitive-information processing theories is acknowledged and incorporated in terms of a Short-Term Memory score (cf. Vallar and Baddeley, 1982). As Boyle (1988) pointed out in a recent review, the new instrument may well usher in an exciting era for cognitive measurement, providing therein both more extensive and more refined research and applied findings in various psychological fields including those pertaining to clinical, clinical neuropsychological, vocational and educational domains respectively.

5 4 Thorndike et al. (1986) reported the results of a confirmatory factor analysis based on a combined total sample of some 5000 Ss. On this evidence, they concluded that the fourth edition of the Stanford-Binet Intelligence Scale indexes four major cognitive areas (Verbal Reasoning, Quantitative Reasoning, Abstract/Visual Reasoning, Short-Term Memory, respectively). Nevertheless, several of the obtained factor loadings failed to reach practical significance, raising therefore, the question of the construct validity of some of the 15 subtests in the revised instrument, with respect to the major cognitive areas being assessed. Despite these unexpected inconsistencies in group factor loadings, all subtests exhibited substantial loadings on the general cognitive factor ('g'), indicating thereby their cognitive nature overall. However, examination of Table 6.2 in the Technical Manual for the new Stanford-Binet Intelligence scale indicates that for the entire sample measured across all ages, the Absurdities subtest failed to exhibit a sufficient loading on the Verbal Reasoning factor, despite the claim by the test constructors (p. 54) that "All four verbal tests load on the verbal factor...". As they pointed out, however, the Absurdities subtest exhibited a factor loading of only 0.26, which compared to the other three loadings on the Verbal Reasoning factor was quite low. While this factor loading was statistically significant (by the formula provided in Child, 1970, p. 97), nevertheless, it failed to attain the level needed for practical significance, accounting for only 7% of the variance involved in the Verbal Reasoning factor. As a general rule of thumb, it is generally recognized that factor loadings need to be at least about 0.30 or better to be regarded as being of practical significance. It

6 5 is simply not appropriate to define a factor in terms of a variable which only accounts for some 7% of the total variance. In regard to the Short-Term Memory factor, the Bead Memory subtest exhibited a factor loading of merely 0.13 and loaded simultaneously 0.13 on the Abstract/Visual cognitive factor. Thorndike et al. (p. 54) therefore contended that this factor might better be regarded as a sequential memory factor as the other three subtests (Memory for Sentences, Memory for Digits, Memory for Objects) all exhibited significant factor loadings on this dimension, while the Bead Memory subtest has a simultaneous mode of presentation. Even so, the clearcut memory nature of the Bead Memory subtest should have resulted in a considerably higher factor loading than actually obtained. As for the Quantitative Reasoning area, two of the three subtests purported to index this factor (Quantitative and Number Series subtests) did not exhibit substantial factor loadings (being only 0.21 and 0.26 respectively). Variables accounting for only 4 and 7% of the variance could not realistically be regarded as being particularly predictive of the Quantitative Reasoning dimension. As the three subtests together only accounted for 35% of the total variance for this group factor, it is clear that 65% of the variance was not measured by these subtests. Under these circumstances, the adequacy of the subtests needs to be questioned. Even more problematic was the magnitude of the factor loadings reported for the Abstract/ Visual Reasoning area. Only the Pattern Analysis subtest exhibited a conceptually meaningful factor loading (0.65), while the remaining three subtests (Copying, Matrices, Paper Folding and Cutting) all loaded poorly (0.15, 0.04 and 0.23 respectively) on this factor. As Thorndike et al. pointed out, the Copying

7 6 subtest failed to load demonstrably on any of the group factors. However, it is also apparent that the Matrices subtest similarly failed to exhibit conceptually meaningful loadings on any of the group factors. Therefore, use of other than the Pattern Analysis subtest to measure the Abstract/Visual dimension would seem unwarranted. Moreover, given these findings, the reliability of measurement in regard to the Abstract/Visual Reasoning area must be questioned. Thorndike et al. presented numerous tables in the Technical Manual for the new Stanford-Binet Intelligence Scale indicating that the various subtests were highly internally consistent and therefore reliable. Nevertheless, the numerous KR 20 coefficients reported suggest considerable item redundancy and narrowness of measurement, rather than reliability as claimed. The subtests of the new instrument may indeed be highly reliable, but estimates of internal consistency do not necessarily indicate reliability (cf. Allen and Potkay, 1983; Boyle, 1983, 1985; Cattell, 1978, pp , l982b; Kline, 1979, p. 3; Lachar and Wirt, 1981; McDonald, 1981, p. 113). In terms of test-retest reliability evidence, Thorndike et al. failed to differentiate between immediate retest (dependability) and retest over longer periods of time (stability) estimates (see Cattell, 1973, Table 54, p. 354). In the absence of information concerning the actual time intervals between testing and retesting, it is not possible to evaluate the test-retest reliability data provided by Thorndike et al. in the Technical Manual. METHOD Procedure and methodology Given the above reservations concerning the confirmatory factor analytic findings reported by Thorndike et al., it seemed germane to reconsider the factor

8 7 analytic evidence by starting afresh with the intercorrelation matrix provided in Table 6.1 of the Technical Manual. Of the 190 correlations in Table 6.1, six needed to be estimated using the data provided elsewhere in the Technical Manual. Correlations estimated between Absurdities and Verbal Relations subtests, between Absurdities and Paper Folding/Cutting, and between Absurdities and Equation Building subtests were 0.43, 0.43 and 0.30 respectively. Correlations between Verbal Relations and Copying, between Copying and Paper Folding/Cutting, and between Copying and Equation Building subtests were 0.38, 0.45 and 0.24 respectively. The resulting intercorrelation matrix for all Ss and ages combined served as the starting point for the exploratory factor analysis. The procedures used followed guidelines proposed by Cattell (1973, pp ; 1978), Cureton and D'Agostino (1983), Gorsuch (1983), Kline (1987) and Nunnally (1978, pp ). As well, several other authors have discussed the important decision points in conducting a methodologically sound factor analysis (e.g. Barrett and Kline, 1982; Boyle, 1985; Carroll, 1985). Of fundamental importance is an adequate sampling of both Ss and variables. The first was more than amply satisfied by Thorndike et al. since their total sample exceeded 5000 Ss. While small sample size (especially below 200 Ss) often gives rise to unreliable factor solutions, this clearly was not problematic in regard to the analysis reported by Thorndike et al. for all Ss and ages combined. Likewise, the strategic choice of variables (subtests) is crucial. Thorndike et al. also adequately met this requirement as a total of 15 separate subtests from the new Stanford-Binet Intelligence Scale were all included in their confirmatory factor analysis. While research into the hierarchical structure of cognitive abilities

9 8 has suggested as many as 30 primary abilities (Cattell, 1982a) which can be discerned factor analytically (and which are not merely pseudo-specific or bloatedspecific artifacts of the particular factor analytic methodology employed, as in the case of some of Guilford's structure-of-the-intellect factors-cf. Brody and Brody, 1976), the fourth edition of the Stanford- Binet Intelligence Scale does at least purport to measure considerably more than the seven most prominent primary abilities originally proposed by Thurstone (cf. Brody and Brody). Nevertheless, the question might be raised as to whether the subtests are psychologically meaningful, pure measures of such primary abilities (source traits) or whether they are merely superficial, hybrid combinations of these primary ability dimensions (surface traits). A crucial consideration is to determine the appropriate number of factors using objective tests such as automated versions of the Scree test (Barrett and Kline, 1982; Gorsuch and Nelson, 1981), Revelle and Rocklin's (1979) very simple structure (VSS) criterion, or Velicer's (1976) MAP test. The commonly used eigenvalues greater than unity (Kaiser-Guttman) criterion (Yeomans and Golder, 1981) has been shown to be inaccurate when the number of variables is below about 20 or above about 50 (cf. Cattell and Vogelmann, 1977; Hakstian, Rogers, and Cattell, 1982; Horn and Engstrom, 1979). A wrong decision at the factor extraction stage will undoubtedly produce inaccuracies at each subsequent point in the factor analysis. While the fixing of communality estimates by an iterative procedure is important when dealing with small factor matrices (Lee and Comrey, 1979), this

10 9 issue is essentially irrelevant to the final outcome when working with large matrices as in the case of Thorndike et al. (cf. Nunnally, 1978). More critical, however, is the rotation of extracted factors to oblique simple structure. Use of orthogonal rotation such as Varimax (which is so prevalent in the psychological research literature) cannot be justified a priori in the absence of nonsignificant correlations actually being obtained between the resultant derived factors. Accordingly, random application of orthogonal rotation procedures generally fails to attain maximum simple structure and the arbitrary imposition of orthogonality onto the data may actually fractionate the observed factor loadings among the artificial factor axes in a manner devoid of any rationale (Cattell, 1978; Kline, 1987; Loo, 1979). Indeed, an oblique rotational strategy carried to maximum simple structure will stop at the special orthogonal position if the factors are truly independent (cf. Cattell, 1978). Also the accuracy of the factor extraction number should be checked in terms of the approximation to maximum simple structure of the final rotated solution by examining the ±0.10 hyperplane count. If extraction of an additional factor does not produce a significant increase in the hyperplane count, the simpler solution is the better choice (in accord with Walkey's, 1983, argument about the greater reliability of more parsimonious factor solutions). Moreover, derived factors should be checked for statistical significance as facilitated by the Sine and Kameoka (1978) tables, and factor pattern solutions should be cross-validated where possible. Given all the above considerations for conducting a methodologically sound exploratory factor analysis, it is little wonder that some investigators have viewed exploratory procedures as unreliable and have advocated confirmatory methods. However, provided each of the above

11 10 issues is treated with careful consideration, exploratory factor analytic procedures should give the same results as confirmatory methodology. These various methodological issues are considered below in regard to the present refactoring of the structural dimensionality of the new Stanford-Binet Intelligence Scale. RESULTS AND DISCUSSION An iterative principal factoring procedure was employed in accord with the recommendations of the various authors cited above. In the present instance, only one iteration of the initial factor matrix was possible (at which point communality estimates reached unity for at least two of the subtest variables). While not an important issue in working with large factor matrices as in the present case, nevertheless, the resultant communality estimates were well below unity for almost every subtest variable, apart from those already referred to above. Accordingly, there was little chance that spurious common factor variance would be entered into the factor analysis as typically occurs with the principal components method (Lee and Comrey, 1979, p. 301). Application of the Scree (Cattell, 1966) test suggested at least four significant factors and possibly five significant factors (see Fig. 1). Accordingly, both four- and five-factor solutions were taken out, together with rotation to oblique simple structure via the SPSS direct Oblimin procedure (Nie, Hull, Jenkins, Steinbrenner and Bent, 1975). The resultant factor pattern solutions are presented in Tables 1 and 2 respectively. As is evident, the hyperplane count

12 11 Table 1 Factor pattern solution for Stanford-Binet Intelligence Scale (N= 5013) Factor number Subtest I h2 Vocabulary Comprehension Absurdities Verbal Relations -O.o Pattern Analysis O.ll Copying Matrices Paper Folding and Cutting Quantitative o.:so 0.71 Number Series O.ll O.o Equation Building O.o o.si 0.82 Bead Memory 0. O.Q Memory for Sentences o Mcinory for Digits Memory for Objects Verbal Reasoning Abstract{Visual Reasoning O.M Quantitative Reasoning Short Term Memory Composite o.;u O.:!Q o.jq o.n %Variance: Eigenvalue: Notes. Factor loadings are shown to two decimal places only. Significant loadings are underlined. Factor I correlates 0.56 with Factor 2, 0.49 with Factor 3, and with Factor 4. Factor 2 correlates 0.59 with Factor 3, and with Factor 4, while Factor 3 correlates with Factor 4 respectively. Factor 1 - Abstract{Visual Reasoning, Factor 2 Verbal Reasoning. Factor 3- Short-Term Memory, Factor 4 "'Quantitative Reasoning. Table 2 5-Factor Solution for Stanford-Binet Intelligence Scale (N= 5013) Factor number Subtest hz Vocabulary O.o O.Gl 0.80 Comprehension O.oJ O.!Q Absurdities o.u O.o Verbal Relations Pattern Analysis Copying Matrices O.J Paper Foldins and Cutting 0.35 O.o Quantitative Number Series o.g Equation Building 0.2!! Bead Memory Memory for Sentences o.u o.n Memory for Digits Memory for Objects Verbal Reasoning O.G Abstract/Visual Reasoning Quantitative Reasoning o.u o.io 0.97 Short-Term Memory Composite O.ll_ 1.00 Notes. Factor loadings are shown to two decimal places only.significant loadings are underlined. Factor I correlates 0.51 with Factor 2, 0.45 with Factor 3, with Factor 4, and 0.49 with FactorS. Factor 2 correlates 0.57 with Factor 3, with Factor 4, and 0.59 with Factor s. Factor 3 correlates 0.01 with Factor 4, and O.Sl with Factor 5, while Factor 4 correlates 0.11 with Factor S. Factor I Quantitative Reasoning, Factor 2 "'Verbal Reasoning. Factor 3-Short-Term Memory, Factor 4 Absurdities vs Memory for Sentences, Factor S - Abstract/Visual Reasoning.

13 12 increased as expected in going from the four-factor to the five-factor solution (the extra factor should necessarily increase the percentage of nonsignificant variables loading in the hyperplane bandwidth, even if the more complex solution is not superior to the more parsimonious factor solution). However, in going from a fivefactor solution to a six-factor solution, the ±0.10 hyperplane count actually decreased, indicating thereby that no more than five factors could be legitimately taken out. Moreover, examination of the statistical significance of the obtained factors using the Sine and Kameoka (1978) tables, suggested that the four-factor solution was probably superior to the five-factor solution. Indeed, the five-factor solution included one factor which strictly speaking loaded significantly on only two of the subtest variables. In regard to the four-factor solution, Factor 1 (which accounted for 59.8% of the variance associated with the unrotated principal components) unequivocally defined the AbstractfVisual Reasoning area as claimed by Thorndike et al. All four subtests (Pattern Analysis, Copying, Matrices, Paper Folding and Cutting) were clearly and significantly loaded by this factor, thereby demonstrating the validity of this dimension. While Thorndike et al. reported that the Copying and Matrices subtests in particular failed to exhibit significant loadings in their confirmatory factor analysis, the present findings leave no doubt that these subtests do indeed index the Abstract/Visual Reasoning area. Under these circumstances, it is highly likely that the measurement of this group factor in the new Stanford-Binet Intelligence Scale is also quite reliable, a conclusion not readily sustainable from the data provided by Thorndike et al.

14 13 Factor 2 (accounting for 6.8% of the principal components variance) clearly represented the Verbal Reasoning area as defined by Thorndike et al. Once again, all four subtest variables exhibited significant loadings, despite the fact that Thorndike et al. reported that the Absurdities subtest failed to demonstrate a significant loading on this group factor. Considering only loadings of0.40 or greater, it is evident that only these four variables were loaded significantly by this Verbal Reasoning factor {all four group factors were defined only by the relevant subtest variables on this basis). However, a smaller loading of 0.37 was exhibited for the Memory for Sentences subtest, undoubtedly in view of its verbal component. Factor 3 (6.3% of the variance) definitively marked the Short-Term Memory group factor with all four subtest variables being loaded significantly. No other variables exhibited factor loadings which even approximated statistical significance, let alone conceptual meaningfulness. Despite the finding by Thorndike et al. that the Bead Memory and Memory for Sentences subtests did not exhibit significant factor loadings in their analysis, it is quite clear from the present factor analytic findings that these variables do indeed demonstrate strong relationships with the Short-Term Memory group factor, as expected. Factor 4 (5.5% of variance) also clearly defined the Quantitative Reasoning area as proposed by Thorndike et al. Whereas they had reported inadequate loadings for the Quantitative and Number Series subtests respectively, the present exploratory factor analytic findings unequivocally demonstrate that

15 14 these variables are significant and meaningful predictors of Quantitative Reasoning as claimed. As for the five-factor solution presented in Table 2, all four group factors were again supported, but in addition, the Matrices subtest was shown to load significantly on both the Quantitative and Abstract/Visual Reasoning areas. The Matrices subtest loaded only 0.04 on the Abstract/Visual group factor in the Thorndike et al. confirmatory factor analysis. Furthermore, the extra factor which emerged in the five-factor solution exhibited only two factor loadings which were greater than 0.30 (Absurdities vs Memory for Sentences). On the basis of the present findings, it is readily apparent that the structural dimensionality of the fourth edition of the Stanford-Binet Intelligence Scale is as purported by the test authors. It would seem moreover, that the inconsistencies in several of the factor loadings reported by Thorndike et al. were essentially artifacts of the particular factor analytic methodology they employed. The fact that they utilised a confirmatory factor analytic approach in no way justifies the particular factor solution they presented. There are problems with the application of confirmatory factor analysis, as pointed out for example by Kline (1987). Indeed, the very interpretation of the chi-square test of the significance of the factors is often based on subjective criteria (cf. Maruyama and McGarvey, 1980). On the present evidence, however, the reliability and validity of the revised Stanford- Binet Intelligence Scale (SB-IV) appears to be more than adequate.

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