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In this case, a wise step to take to uncover more information about an adolescent s or adult s abilities is to administer supplementary subtests that measure abilities not well tapped by the WAIS-III (see, for example, Flanagan, McGrew, & Ortiz, 2000)..

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Before we present the details of how to attack the WAIS-III subtest profile, the next section spells out the rational postulates and axioms of the philosophy of profile interpretation inherent in intelligent testing. These tenets are far more important for competent WAIS-III interpretation than any combination of tables or formulas.

where x1 g xi1 n and x2 g xi2 n. (a) Write out the least squares normal equations for this model. (b) Verify that the least squares estimate of the intercept in this model is g yi n y. 0 (c) Suppose that we use yi y as the response variable in the model above. What effect will this have on the least squares estimate of the intercept

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1. Examiners must be detectives, actively attacking subtest profiles in systematic fashion. They need to group the subtests in new ways to best explain each individual s subtest-to-subtest fluctuations. Different theories of intelligence as well as practical and clinical approaches to assessment must be integrated to find the one best synthesis for each person tested. 2. As many subtests as possible should be grouped together to denote a person s areas of strength and weakness. Hypotheses generated from three subtests, for example, are usually more potent than hypotheses generated from two subtests. The more reliable the hypothesized strength or weakness, the more valuable it is for practical recommendations. 3. A corollary of the previous postulate is that subtest-specific hypotheses are usually to be avoided. A strength or weakness in a single subtest reflects a narrow area of asset or deficit, one that will not likely generalize to the real world. Some subtests have a considerable amount of reliable unique variance (e.g., Digit SymbolCoding) and frequently do not pair up with any other WAIS-III task. In such instances, interpret the specific ability as the person s strength or weakness; however, such interpretations should be used only as a last resort. 4. A person who scores significantly high on a subtest does not have a strength in all of the abilities and traits measured by that subtest; a

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person scoring very low does not have a weakness in every test component. The person is likely to be especially strong or weak in one or two abilities that the task assesses; the examiner s job is to determine the specific asset or liability by carefully evaluating the person s performance on other WAIS-III tasks that measure similar abilities. 5. The empirical determination of significant strengths and weaknesses is the starting point of test interpretation, not the end point. In essence, the existence of at least one significant fluctuation in the WAIS-III profile gives the examiner his or her detective s license sanction to enter the profile to make sense out of the significant fluctuations. Without significant deviations, differences in the scaled scores are usually best interpreted as due to chance. When one or more scores deviate significantly from the person s mean, the other (nonsignificant) scaled scores become useful interpretive adjuncts for hypothesis testing, depending on whether they are above or below the individual s mean score. 6. When generating hypotheses, examiners should aggregate tasks. Just as subtest-specific interpretations are discouraged, so too are hypotheses that are derived by pitting one subtest against another. Some psychologists (e.g., Sattler, 1988) encourage this type of interpretation: High Comprehension and low Arithmetic may suggest that reasoning ability is adequate in social situations but not in situations involving numbers (p. 176). High Object Assembly and low Picture Arrangement may suggest that visual inductive reasoning skills are better developed than visual sequencing skills (p. 178). Most WAIS-III subtests, especially unstable tasks like Object Assembly and Picture Arrangement, are just not reliable enough to permit interpretation of differences between subtests. Even reliable subtests like Information and Comprehension cannot support the kinds of diagnostic inferences that are sometimes at-

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In multiple linear regression problems, certain tests of hypotheses about the model parameters are useful in measuring model adequacy. In this section, we describe several important hypothesis-testing procedures. As in the simple linear regression case, hypothesis testing requires that the error terms i in the regression model are normally and independently distributed with mean zero and variance 2.

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