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Interestingly, the later decline for the PMA Space and Reasoning subtests is consistent with the relatively late decline (after age 54) observed for the Gf tasks on the Kaufman adult tests (KAIT, K-BIT, and K-SNAP) Subsequent analyses (eg, Schaie & Hertzog, 1983) revealed Schaie s responsiveness to the criticisms and the concomitant efforts by his research team to refine their methodologies and analyses Schaie and Hertzog (1983) admitted that their original cross-sequential design was ill-suited to evaluate age changes; further, the results of the two 14-year longitudinal studies they reported indicated earlier declines in intelligence (ie, prior to age 60) than were previously observed in Schaie s laboratory In Schaie and Hertzog s (1983) analysis, however, the pattern of decline for the 14-year longitudinal samples was quite similar for both verbal and nonverbal PMA subtests.

That is, the upper 5 percentage point of F5,10 is f0.05,5,10 3.33. Table V contains only upper-tail percentage points (for selected values of f ,u,v for 0.25) of the F distribution. The lower-tail percentage points f1 ,u,v can be found as follows.

Schaie and Labouvie-Vief s (1974) generalization about aging and intelligence, that most of the adult life span is characterized by an absence of decisive intellectual decrements (p 15), summarizes well the overall results of their many PMA studies..

(10-28)

Required security properties (continued)

For example, to nd the lower-tail percentage point f0.95,5,10, note that f0.95, 5,10 1 f0.05,10, 5 1 4.74 0.211

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The best integration of the numerous analyses appears in Schaie s (1983b) thorough treatment of the 21-year Seattle project Among other syntheses of the data, he organized the findings of the three 7-year longitudinal studies into two tables, each comparing the performance of every age group to age 25; the average score was set at 100 The first table showed these comparisons without correction for potentially confounding variables, while the second one corrected all values for timeof-measurement effects, attrition, and cohort differences (Schaie, 1983b, Tables 417 and 418) Figure 517 depicts Schaie s results for Verbal Meaning, Space, and Reasoning, where these values are corrected for the three variables noted previously For these three tasks, the uncorrected and corrected values were quite similar for each age, usually disagreeing by only 1 to 3 points In Figure 5.

10-5.2 10-5.3

REQUIRED SECURITY PROPERTIES Confidentiality Integrity Availability Accountability BUSINESS FACTOR Accounting

17, Verbal Meaning increases steadily until age 53, with a notable decline occurring between ages 67 and 74 Space peaks earlier than Verbal Meaning (age 46), but has its first sizable decline between the same 67- to 74year period Nonetheless, its decline is more dramatic than that of the vocabulary test Reasoning declines substantially after age 60, plunging to 73 by age 81 These results are basically in agreement with the differential results for the measures of maintained abilities (Gc, Gq) versus vulnerable abilities (Gf, Gv, Gs, Gsm) on the various Wechsler and Kaufman scales Unlike the popular interpretations of the initial findings reported by Schaie and his colleagues, intelligence does, indeed, decline with chronological age, and that decline becomes precipitous; however, the use of longitudinal data juxtaposed with cross-sectional results on the PMA suggest that the decrements may not begin until relatively late in life.

Let X11, X12, p , X1n1 be a random sample from a normal population with mean 1 and variance 2, and let X21, X22, p , X2n2 be a random sample from a second normal pop1 ulation with mean 2 and variance 2. Assume that both normal populations are 2 2 independent. Let S 1 and S 2 be the sample variances. Then the ratio 2 F has an F distribution with n1 inator degrees of freedom.

1 denom-

SHOULD CORRECTIONS BE MADE FOR COHORT EFFECTS We have excluded Number from Figure 517, despite its similarity to Wechsler s Arithmetic subtest, because its corrected and uncorrected values were so disparate Prior to correction, peak performance on Number was at age.

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This result is based on the fact that (n1 1)S 2/ 2 is a chi-square random variable with n1 1 1 1 degrees of freedom, that (n2 1)S 2 2 is a chi-square random variable with n2 1 degrees 2 2 of freedom, and that the two normal populations are independent. Clearly under the null 2 hypothesis H0: 2 S 2 S 2 has an Fn1 1,n2 1 distribution. This is the basis of 1 2 1 2 the ratio F0 the following test procedure.

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