The WJ III Predicted Achievement (PA) Model for ability-achievement discrepancy calculation is also portrayed in Figure 14.3. A similar model was present in the WJ and WJ-R in which the differential Scholastic Aptitude clusters were used as the predictor measures. The Scholastic Aptitude clusters were used to provide predicted achievement scores based on the best combination of four cognitive tests that predicted different achievement domains (McGrew, 1986, 1994; McGrew et al., 1991; Woodcock, 1978).
As portrayed in Figure 14.3, in the WJ III PA Model the standard seven WJ III COG tests are placed into equations that differentially weight each tests' contribution to the prediction of the target achievement domain. Not only do the weights for the same test differ by achievement
4An additional ability—achievement discrepancy procedure that is identical to the GIA Model, with the exception being the substitution of the WJ III ACH Oral Language (Gc) cluster as the ability measure, is not described here.
domain (e.g., Sound Blending [Ga] has a near zero weight for the prediction of math achievement but a significant weight for the prediction of Basic Reading Skills), but the weights also change systematically as a function of developmental status. For example, although Sound Blending is important in the prediction equation for Basic Reading Skills during the formative years, its contribution drops appreciably past the elementary school ages. In contrast, the Verbal Comprehension (Gc) weight increases with age in the prediction of Basic Reading Skills. The utilization of computer-scoring technology provides the ability to implement this developmental/purpose-focused/optimal test weighting prediction method. This method better captures the complex nuances of human development via predictions that reflect achievement domain, by developmental status, by CHC ability domain interactions.
Similar to the GIA Model, the PA Model also implicitly accounts for regression-to-the-mean. Also, an individual's resultant discrepancy score is compared against real distributions of discrepancy norms. Not surprisingly, the WJ III PA Model provides a better estimate of a person's predicted (expected) achievement than does the GIA Model (McGrew & Woodcock, 2001). The PA Model optimally weights the seven standard COG tests to "wring out" as much variance as possible in the prediction of achievement. In comparison, the WJ III GIA score is developed to "wring out" as much general intelligence variance as is possible from the 7- or 14-test combinations of tests; optimal weighting for the prediction of achievement is not included in the differential GIA g-weighting.5
5Although true, as described by McGrew and Woodcock (2001), one of the major criteria used to select tests for the WJ III COG-Std was which respective CHC test was a better predictor of achievement. For example, both the Analysis-Synthesis and Concept Formation Gf were found to be equally strong indicators of Gf. Concept Formation was found to be a slightly better predictor of achievement across all domains and ages and, therefore, was selected to be the featured Gf test in the WJ III COG-Std. This insured that the GIA-Std score, although not weighted to best predict achievement, included those tests from each CHC ability domain (when all other psychometric factors were judged to be relatively equal) that best predicted achievement.
Given the different design goals and philosophies, the WJ III GIA and PA ability-achievement discrepancy models provide different and complementary information. The calculation of ability-achievement discrepancies with either the GIA-Std or GIA-Ext may be useful when a generalized measure of cognitive functioning or intelligence is required for eligibility purposes (Schrank & Mather, 2001). In contrast, the Wj III PA option is intended to determine if a person is performing as well as one would expect, given his or her measured levels of associated cognitive abilities, not necessarily to diagnose a learning disability (Schrank & Mather, 2001). The PA discrepancy procedure will be particularly useful for making the most accurate predictive statements possible concerning an individual's anticipated levels of current achievement. It should be informative for setting short-term goals.
Because the strong PA prediction is achieved via the inclusion and higher weighting of certain tests that measure cognitive abilities that may be a significant weakness for a person, and that may reflect an intrinsic cognitive or processing disorder, it may not be appropriate (in many cases), nor was it ever intended to be used, for determining a specific learning disability. The PA's predict how an individual will perform, on the average, in a variety of situations requiring that particular subset of abilities, otherwise known as "aptitude."6
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