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longitudinal WAIS-R P-IQ data (Figure 5.18), the graphs for WAIS-III P-IQ overlap remarkably for most ages (age 72 is an exception). Again, Figure 5.19 is only offered for comparison purposes, as it is inappropriate to evaluate age changes with cross-sequential data (Schaie & Hertzog, 1983). The major developmental inferences come from the 17-year cohort comparisons (Table 5.12): The 10-point P-IQ decrements for the five oldest cohorts denote a fairly constant loss of nonverbal intellectual function over a 17year period for individuals born between 1904 and 1943, and the 7- to 8-point Verbal IQ losses for the two oldest cohorts (those aging from 67 to 84 and from 72 to 89) reflect loss of verbal skills for adults in their 80s. Combining WAIS-III cross-sectional and longitudinal data suggests a loss of about 0.5 points per year in Performance IQ, or 5 points per decade, which is precisely Horn s (1985; Horn, Donaldson, & Engstrom, 1981) best estimate of the adult decline in fluid intelligence

40 400

18 360

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based on his reviews and results of numerous studies. That degree of loss in P-IQ also mirrors precisely the results of Kaufman s (1990) WAIS/ WAIS-R cohort-substitution study, which found an average decrease over a 25-year period of about 121 2 P-IQ points for the four cohorts (see Table 5.12). The two Wechsler cohort-substitution studies provide results that agree remarkably well with the cross-sectional data provided for Wechsler s adult scales and for the Kaufman and Kaufman tests. Taken together, the two cohort-substitution studies offer broad support to the developmental reality of a loss in nonverbal intellectual function (Gf, Gv, Gs) across virtually the entire adult life span as well as a loss in verbal function (primarily Gc) during the decade of the 80s. These meaningful declines on the WAIS-III, in particular, are dramatic in view of the systematic exclusion of so many potentially low-functioning adults from the normative sample, for example, adults who merely went to a doctor or other professional for

30 40

Bundesamt f r Sicherheit in der Informationstechnik: IT Baseline Protection Manual, Bundesanzeiger, 2002 SecurityFocus: Bugtraq Mailing List

75.0 70.0

10 40

Therefore, P1B A2 can be interpreted as the relative frequency of event B among the trials that produce an outcome in event A. EXAMPLE 2-17 Again consider the 400 parts in Table 2-3. From this table P1D F2 P1D F2 P1F2 10 40 ^ 400 400 10 40

Mean reference group (ages 20 34) Performance IQs, by age, on the WAIS-R or WAIS-III for adults ages 22 to 88 years comparison of crosssectional and longitudinal data.

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Note that in this example all four of the following probabilities are different: P1F2 P1D2 40 400 28 400 P1F D2 P1D F2 10 28 10 40

SOURCE: Standardization data of the Wechsler Adult Intelligence Scale: Third Edition. Copyright 1997 by The Psychological Corporation. Used by permission. All rights reserved. Reprinted from Kaufman (2001) with permission.

Here, P(D) and P1D F2 are probabilities of the same event, but they are computed under two different states of knowledge. Similarly, P(F) and P1F D2 are computed under two different states of knowledge. The tree diagram in Fig. 2-13 can also be used to display conditional probabilities. The rst branch is on surface aw. Of the 40 parts with surface aws, 10 are functionally defective and 30 are not. Therefore, P1D F2 10 40 and P1D F2 30 40

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Of the 360 parts without surface aws, 18 are functionally defective and 342 are not. Therefore, P1D F 2 342 360 and P1D F 2 18 360

memory problems or problems with thinking. The consistency in the P-IQ decrease with increasing age for U.S. men and women born during the first half to three-quarters of the twentieth century from cross-sectional and longitudinal data on the WAIS, WAIS-R, and WAIS-III is simply phenomenal. Comparison of Wechsler and PMA Results Taken together, the Wechsler cohort-substitution longitudinal studies suggest that declines in P-IQ with age start at about age 50. In the WAIS/WAIS-R study, the change in P-IQ for the youngest cohort in 1953 was a striking

Random Samples from a Batch Recall that to select one item randomly from a batch implies that each item is equally likely. If more than one item is selected, randomly implies that each element of the sample space is equally likely. For example, when sample spaces were presented earlier in this chapter, sampling with and without replacement were de ned and illustrated for the simple case of a batch with three items {a, b, c}. If two items are selected randomly from this batch without replacement, each of the six outcomes in the ordered sample space Swithout 5ab, ac, ba, bc, ca, cb6

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