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Further fuel for the Horn perspective comes from the extreme vulnerability of Picture Completion (Figure 5.10), the close similarity of the aging pattern for Picture Arrangement to the highly speeded PSI subtests (Figure 5.11), and the maintained pattern for Arithmetic (Figure 5.9). That is to say, Picture Completion and Picture Arrangement are both vulnerable subtests, even though neither WAIS-III subtest utilizes bonus points, and Arithmetic is a maintained subtest even though all items are timed and the more difficult items are scored with bonus points. Whereas Picture Completion and Picture Arrangement items are timed, the time limits for these items, other Performance items (i.e., Block Design and Object Assembly), and Arithmetic items are usually generous enough to permit correct solutions for those adults who are able to solve the problems.

(6-2)

[LinuxPAM]

The sample mean, x, is a reasonable estimate of the population mean, . Therefore, the engineer designing the connector using a 3 32-inch wall thickness would conclude, on the basis of the data, that an estimate of the mean pull-off force is 13.0 pounds. Although the sample mean is useful, it does not convey all of the information about a sample of data. The variability or scatter in the data may be described by the sample variance or the sample standard deviation. De nition If x1, x2, p , xn is a sample of n observations, the sample variance is a 1xi

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182 PART II INDIVIDUAL DIFFERENCES ON AGE, SOCIOECONOMIC STATUS, AND OTHER KEY VARIABLES bonus point apiece for quick, perfect performance. On the WAIS-III, mean values ranged from 9.9 to 10.8 at ages 20 24 to 70 74, peaking at ages 45 54; not until ages 85 89 did the education-adjusted mean Arithmetic scaled score dip below 9.6. And processing speed is rewarded even more on the WAIS-III than the WAIS-R Arithmetic subtest, as the final two WAIS-III items award two possible bonus points for rapid solutions. Clearly, the speeded component of Arithmetic did not impair the performance of elderly adults on this Wechsler subtest. Whereas Zimprich (1998) used WAIS Digit Symbol as a marker of mental speed, Storandt (1976) examined the speed and cognitive components of this Performance subtest. First, Storandt tested the pure motor speed of young and elderly adults by simply having them copy symbols as rapidly as possible without the matched pairs. Younger adults far outstripped the elderly in this task. However, when these groups were also given the standard WAIS Digit Symbol subtest, a clear-cut cognitive differential was evident as well; the superior performance by the younger subjects could not be explained by the speed differential alone. In fact, the cognitive and speed components contributed about equally to the differential. Storandt (1977) studied bonus points as well and discovered that the young earned more bonuses than the elderly on all tasks, with the mean difference relatively small on Arithmetic (1.7 versus 1.2), and striking on Block Design (3.5/0.6) and Object Assembly (7.0/2.2). That analysis might implicate speed as the culprit in the sharp age-related decline in scores, except that even when this advantage in favor of the young is eliminated, the old still exhibit poorer performance than the young (Storandt, 1977, p. 177).

x2 2 1 (6-3)

[Losa97]

The bulk of behavior genetic research from a diversity of methodologies converges on the fact that genetics are an important determinant of IQ, and its role conceivably becomes greater as people age, except, perhaps, among the very elderly. This finding, even in light of the possibility that maternal effects account for a considerable portion of the variance that has previously been attributed to genetics, should not be minimized or underplayed. Plomin and Petrill (1997) state:

The units of measurements for the sample variance are the square of the original units of the variable. Thus, if x is measured in pounds, the units for the sample variance are (pounds)2. The standard deviation has the desirable property of measuring variability in the original units of the variable of interest, x. How Does the Sample Variance Measure Variability To see how the sample variance measures dispersion or variability, refer to Fig. 6-2, which shows the deviations xi x for the connector pull-off force data. The greater the amount of variability in the pull-off force data, the larger in absolute magnitude some of the deviations xi x will be. Since the deviations xi x always sum to zero, we must use a measure of variability that changes the negative deviations to nonnegative quantities. Squaring the deviations is the approach used in the sample variance. Consequently, if s2 is small, there is relatively little variability in the data, but if s2 is large, the variability is relatively large.

EXAMPLE 6-2

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