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inasmuch as proper WAIS-III, KAIT, and WJ III interpretation demands understanding of normal, or expected, differential fluctuations in a person s ability spectrum from late adolescence and young adulthood to old age. Distinguishing between normal and pathological development is often the essence of competent diagnosis in clinical and neuropsychological assessment. Probably the most comprehensive and cleverly conceived set of studies has been the life s work of K. Warner Schaie (e.g., 1958, 1983b, 1994) in collaboration with numerous colleagues (e.g., Hertzog & Schaie, 1988; Schaie & Labouvie-Vief, 1974; Schaie & Strother, 1968; Schaie & Willis, 1993). His results have transformed the preconceptions of professionals throughout the world regarding the inevitability of declines in mental functioning along the path to old age. Although some of Schaie s findings are controversial, it is incontestable that his clever sequential combination of cross-sectional and longitudinal research designs has shown the importance of considering

7-8. Let three random samples of sizes n1 20, n2 10, and n3 8 be taken from a population with mean and variance 2. Let S 2, S 2 , and S 2 be the sample variances. 1 2 3 Show that S 2 120S 2 10S 2 8S 2 2 38 is an unbiased 1 2 3 estimator of 2. 7-9.

(a) Show that g i 1 1Xi X 2 2 n is a biased estimator of 2 . (b) Find the amount of bias in the estimator. (c) What happens to the bias as the sample size n increases

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128 PART II INDIVIDUAL DIFFERENCES ON AGE, SOCIOECONOMIC STATUS, AND OTHER KEY VARIABLES cohort (generational) effects when conducting research on aging Further, Schaie s research program suggests that, when declines in intelligence do occur with age, they do so at far later ages than was formerly believed But Schaie consistently used the group-administered, speeded Primary Ability Tests (PMA; Thurstone & Thurstone, 1949), based on Thurstone s theory of intelligence and normed only through age 18 years As valuable as his findings are, they cannot replace research results based directly on the WAIS-III, its predecessors (Wechsler, 1939, 1955, 1981), and other intelligence tests for adults in helping clinicians understand the kinds of changes to anticipate during clinical, neuropsychological, or psychoeducational assessment Evaluation of adolescents and adults depends on the WAIS-III or other individually administered clinical instruments as its primary or exclusive measure of intellectual functioning.

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7-10 Let X1, X2, p , Xn be a random sample of size n from a population with mean and variance 2 (a) Show that X 2 is a biased estimator for 2 (b) Find the amount of bias in this estimator (c) What happens to the bias as the sample size n increases 7-11 Data on pull-off force (pounds) for connectors used in an automobile engine application are as follows: 793, 751, 782, 741, 739, 750, 776, 773, 738, 746, 755, 740, 747, 759, 729, 738, 742, 781, 754, 763, 753, 762, 749, 780, 751, 768 (a) Calculate a point estimate of the mean pull-off force of all connectors in the population State which estimator you used and why.

Age changes on the PMA, Army Alpha (Yoakum & Yerkes, 1920), or other group instruments do not necessarily generalize to the profile changes to anticipate when testing the same person several times during his or her lifetime, or when comparing the subtest profiles of individuals or groups who differ in chronological age For these reasons, the studies conducted on the WAIS-III (Heaton, Manly, Taylor, & Tulsky, 2001; Kaufman, 2000a, 2001; Kaufman & Lichtenberger, 1999, pp 187 200; Manly, Heaton, & Taylor, 2000), WAIS-R (Kaufman, 1990, pp 212 222; Kaufman, Reynolds, & McLean, 1989), WAIS (Birren & Morrison, 1961; Botwinick, 1967, 1977), and Kaufman tests (Kaufman & Horn, 1996; Kaufman, Kaufman, Chen, & Kaufman, 1996; Wang & Kaufman, 1993) provide the most valuable research findings for the clinical interpretation of aging and intelligence.

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