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garding their clinical, behavioral, or neuropsychological meaning, that support is indicated. Profile analysis is partitioned into two steps: 8 and 9 in the sections that follow, with emphasis on the identification and not necessarily the clinical interpretation of diverse strengths and weaknesses within the adolescent s or adult s cognitive and behavioral spectrum. This chapter is organized in three sections, two of which reflect different approaches to WAIS-III profile attack, depending on the examiner s preferred processing style: (1) a sequential approach to profile attack Steps 8 and 9 (to follow Steps 1 7 in 11); (2) a simultaneous approach to profile attack; and (3) illustrative case reports, which demonstrate the outcome of the various hypothesis generation methods and the integration of WAIS-III data with background information, test behaviors, and data from other tests.

The statistical properties of the least squares estimators 0, 1, p , k may be easily found, under certain assumptions on the error terms 1, 2, p , n, in the regression model. Paralleling the assumptions made in 11, we assume that the errors i are statistically independent with mean zero and variance 2. Under these assumptions, the least squares estimators , , p , are unbiased estimators of the regression coefficients , , p , . This 0 1 k 0 1 k property may be shown as follows:

E1 2

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Our approach to examining the WAIS-III profile focuses on moving from the most global scores (i.e., the Full Scale IQ in Step 1 and Verbal and Performance IQs in Steps 2 and 3) to scores measuring more specific abilities (i.e., the four Indexes in Steps 4 through 7). As we described in 11, moving down the hierarchy of WAIS-III scores will at times lead you to realize that the most global scores are not necessarily the most meaningful ones to interpret. In fact, in some cases, variability in the subtest scaled scores will necessitate focusing on the pattern of scaled scores during interpretation rather than on the IQs or indexes. Examination of the pattern of subtest scaled scores is our focus in Steps 8 and 9 of the Kaufman-Lichtenberger approach to WAIS-III interpretation.

X 4

Unlike the traditional standard scores with a mean of 100 and SD of 15 that are used for the IQs and indexes, WAIS-III scaled scores are a special kind of standard score that have a mean set at 10 and SD set at 3; scaled scores on the WAIS-III can range from 1 to 19. These simple parameters have allowed clinicians to easily compare a person s performance from one subtest to another; to evaluate fluctuations in a person s scores on the same subtest from one time to another; and to relate the subtest scores of different people, regardless of their ages. The beauty of the scaled score for the WAIS-III, WISC-III, and WPPSI-R is that it always has the same meaning for an individual. No matter what the adolescent s or adult s age, or the particular subtest in question, the examiner has the interpre-

since E( ) 0 and (X X) 1X X I, the identity matrix. Thus, is an unbiased estimator of . The variances of the s are expressed in terms of the elements of the inverse of the X X matrix. The inverse of X X times the constant 2 represents the covariance matrix of the regression coefficients . The diagonal elements of 2 1X X2 1 are the variances of 0, , p , , and the off-diagonal elements of this matrix are the covariances. For example, if 1 k we have k 2 regressors, such as in the pull-strength problem, 1X X2

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Table 12-4 Minitab Multiple Regression Output for the Wire Bond Pull Strength Data Regression Analysis: Strength versus Length, Height The regression equation is Strength 2.26 2.74 Length Predictor Constant Length Height 0 1 2 Coef 2.264 2.74427 0.012528 0.0125 Height SE Coef 1.060 0.09352 0.002798 T 2.14 29.34 4.48 P 0.044 0.000 0.000 R-Sq (adj) VIF 1.2 1.2 97.9%

tive luxury of knowing that 10 is average, 7 is 1 SD below the mean, 16 is 2 SDs above the mean, and so forth Because the W-B I, WAIS, and WAIS-R derived scaled scores for everyone are based on subtest norms for ages 20 34, these earlier versions of Wechsler s adult scale did not enjoy the benefit of uniformity from age to age or from subtest to subtest The farther the person was from the 20 to 34-year-old reference group, the lower the average scaled score was for his or her age group Similarly, the degree to which subtests displayed different aging curves (such as Verbal versus Performance subtests; see 5) marked the degree to which the subtests would yield different mean scores for the same age group Consider ages 65 69 on the WAIS-R.

S 2.288 PRESS 156.163 Analysis of Variance Source Regression Residual Error Total Source Length Height DF 1 1 DF 2 22 24

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