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Third, as described in the cross-battery section of this chapter, the Wechsler batteries, as well as most other major intelligence batteries, have been unable to shed light on a number of important CHC abilities because of inadequate construct representation. With the exception of the WAIS-III Matrix Reasoning tests, none of the Wechsler batteries have been able to shed valid light on the developmental patterns for Gf. Other constructs that have not been reflected in the extant Wechsler cognitive developmental literature are Glr and Ga. Fortunately, recent analyses of the developmental change in valid Gf and Glr test scores from other nationally normed instruments (viz., K-BIT, K-FAST, K-SNAP, and KAIT) have been reported (Kaufman et al., 1996; Wang & Kaufman, 1993). Fourth, even for the Wechsler tests that are valid indicators of a CHC ability (e.g., Arithmetic as an indicator of Gq), the availability of only one test or indicator for a CHC construct limits the generalizability of some of the research findings (Kaufman et al., 1996). Finally, the lack of an equal-interval measurement scale across the three Wechsler batteries has necessitated some creative methodological trickery to analyze scores across ages. For example, Kaufman (1990) employed a procedure with the WAIS-R data in which the individual test scores for all seven adult age groups in the standardization sample were equated to a reference norm group. All WAIS-R norm subject individual test raw scores were converted to subtest scaled scores (M = 10; SD = 3) using the target norm age group of 25 34. This provided for the ability to analyze the change in standard scores in reference to a common standard. Another creative approach reported by Kaufman et al. (1996) was to convert the raw scores for all norm subjects between ages 15 and 94 on seven tests from the Kaufman family of instruments to z-scores (M = 100; SD = 15) calculated on the entire sample (N = 1,193). The resultant standard scores, which are referenced to the mean and standard deviation of the entire sample, were then analyzed. At the level of individual tests, the latter approach provides for more precision in the measurement of change than the
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WAIS-R approach. The WAIS-R subtest scaled scores only provide for three points of measurement for every standard deviation on the scale, regardless of which normative reference group is used. In contrast, the Kaufman et al. (1996) approach placed the individual tests on a scale that allowed for five times the degree of ability differentiation (15 points are covered for each standard deviation on the scale). All subjects with a scaled score of 12 on a WAIS-R subtest are not all likely to be at the same ability level and would cover a range of scores on a scale with a standard deviation of 15. Regardless of the creative methods used to obtain a score suitable for analyses across age groups, this has only provided a partial withinbattery metric solution. Without a common equal-interval growth scale, the analyses of cognitive change across similar batteries from the same family of tests (e.g., Wechsler or Kaufman family of related instruments) is extremely difficult and fraught with potential error. These measurement limitations result in lost opportunities for more comprehensive and informative analyses of cross-sectional CHC-based data. Advantages of the WJ III in Measuring Growth and Change The WJ III is particularly well suited for the measurement of growth and change both in clinical practice and for developmental research. A number of characteristics of the WJ III address the previously described limitations of measures. First, the WJ III includes the same tests across all developmental age groups. Although only certain tests provide norms below age five, almost all of the 20 WJ III COG and 24 ACH tests provide measurement starting at age 5 or 6 and extending up through 95+ years of age. The use of the same tests across most of the life span removes the potential of method effects (i.e., different test content across tests in different batteries) confounding the interpretation of the resultant change scores. Second, when the focus is on changes in CHC abilities across the life span, the WJ III provides two-test clusters that
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maximize construct relevant variance. As described previously, each WJ III CHC COG cluster is comprised of two tests of qualitatively different narrow abilities (therefore insuring adequate construction representation) within each respective Gf Gc domain. No other individually administered battery provides empirically validated cluster scores for the major cognitive constructs included in contemporary CHC theory. Finally, and probably more important in the context of the current discussion, is the fact that all WJ III tests are grounded in unidimensional and equal-interval growth scales. All WJ III tests incorporate the W-scale, a transformation and application of the Rasch measurement model (Woodcock, 1978; Woodcock & Dahl, 1971). Each test s W-score is centered on a value of 500, which is the approximate average performance of 10-year-olds. Cluster scores represent the arithmetic mean (average) of the tests comprising the cluster. Although the W-scores are testor cluster-specific (W-scores cannot be compared across measures), changes in scores can be compared. That is, a change of 1 W point represents the same amount of unit change within any of the WJ III tests or clusters. More importantly, within a test or cluster, growth can be measured from the preschool years through late adulthood on a single common scale.8 For the above reasons, the WJ III battery is particularly well suited to the measurement and evaluation of cognitive growth and change. Examples of the potential research benefits accrued from using a battery designed like the WJ III have been demonstrated in research with the WJ-R. For example, McArdle and Woodcock (1997; also see test-retest study by McArdle & Woodcock reported in McGrew et al., 1991) presented a series of longitudinal test-retest designs with developmental time-lag components that focused on decomposing the sources of change in test scores over time (e.g., test score variance due to practice and retention, growth or maturation, trait stabil8See Woodcock (1978) for a thorough treatment of the development and application of the Rasch-based W-score metric.
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ity, and test unreliability). Using the WJ-R standardization data, Salthouse (1998a) investigated the extent to which age-related differences in cognitive abilities should be interpreted as reflecting either a general developmental mechanism or an ability-specific mechanism. WJ III CHC Growth Curves The norm-based growth curves for 11 WJ III clusters are presented in Figures 14.5a k.9 Included are the curves for the GIA-Ext (Figure 14.5a), seven CHC cognitive clusters (Gc, Glr, Gv, Ga, Gf, Gs, Gsm, Figure 14.5b h), and three broad achievement clusters (reading, math, and written language, Figure 14.5i k). Each figure includes three smoothed curves (average score and standard deviations) based on the WJ III norms. We believe these figures represent the first time a complete set of Gf Gc growth curves based on measures with strong construct validity (adequate construct representation) have been presented across most of the life span. The following discussion of the curves will be descriptive. Appropriate data-analytic methods need to be applied to these data to empirically evaluate the trends and to compare the results with the extant literature on the development of CHC abilities. These growth curves should be systematically compared to the analyses of the WAIS-III and other measures (WAIS, WAIS-R, Kaufman tests) presented in detail in 5, especially regarding the different aging patterns for different abilities within Horn s expanded Gf Gc framework. However, note that the data are not directly comparable because (1) the WJ III analyses use W-scores and the 5 analyses use
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9See McGrew and Woodcock (2001) for a description of how the growth curves were centered at the same starting point to allow for a comparison of relative changes across the curves. The W-scores on the x-axis do not represent the normative values as a different constant has been subtracted from all values for each curve. Furthermore, ideally it would be optimal to present an additional set of curves of the same data using a logarithmic transformation of the age scale. This would allow for a closer examination of the changes occurring during the early years. Space limitations preclude the presentation of both sets of figures.
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