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adults Males scored slightly higher than females on the three WAIS-III IQs, a finding consistent with the results of previous Wechsler studies but of no practical consequence Across the age range, and based on variables from Wechsler s adult scales and several Kaufman tests, males consistently outperformed females on measures of arithmetic and spatial visualization; on the WAIS-III and other Wechsler scales, females have consistently outscored males on measures of clerical and processing speed, such as Digit Symbol Coding and the PSI The mathematical and visual spatial advantage of males, and the psychomotor speed advantage of females, conform to a wide array of prior investigations; however, researchers disagree on the explanations of these gender differences Across the various Wechsler and Kaufman tests, and on the Binet-4, Caucasians scored substantially higher than African Americans, even when corrections are applied for background variables such as educational attainment.

The contour plots in Fig. 5-17 illustrate that as moves from zero (left graph) to 0.9 (right graph), the ellipses narrow around the major axis. The probability is more concentrated about a line in the (x, y) plane and graphically displays greater correlation between the variables. If 1 or 1, all the probability is concentrated on a line in the (x, y) plane. That is, the probability that X and Y assume a value that is not on the line is zero. In this case, the bivariate normal probability density is not de ned. In general, zero correlation does not imply independence. But in the special case that X and Y have a bivariate normal distribution, if 0, X and Y are independent. The details are left as an exercise.

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However, some tests have yielded quite small differences in the scores earned by Caucasians and African Americans, including tests that are extremely culture-loaded, such as WAIS-III Information and KAIT Famous Faces, as well as a new measure of fluid reasoning on the K-SNAP Caucasians outscored Hispanics by a smaller margin than was found in the Caucasian African American studies, with the largest differences usually observed on verbal, crystallized, and memory tests rather than on nonverbal, fluid, and highly speeded tests However, the traditional P > V profile for Hispanics was not found on the WAIS-III With education controlled, the P > V IQ difference was only about 3 points, and the POI > VCI difference was only 1 point.

When the estimator follows a normal distribution, as in the above situation, we can be reasonably con dent that the true value of the parameter lies within two standard errors of the

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estimate. Since many point estimators are normally distributed (or approximately so) for large n, this is a very useful result. Even in cases in which the point estimator is not normally distributed, we can state that so long as the estimator is unbiased, the estimate of the parameter will deviate from the true value by as much as four standard errors at most 6 percent of the time. Thus a very conservative statement is that the true value of the parameter differs from the point estimate by at most four standard errors. See Chebyshev s inequality in the CD only material. EXAMPLE 7-2 An article in the Journal of Heat Transfer (Trans. ASME, Sec. C, 96, 1974, p. 59) described a new method of measuring the thermal conductivity of Armco iron. Using a temperature of 100 F and a power input of 550 watts, the following 10 measurements of thermal conductivity (in Btu/hr-ft- F) were obtained: 41.60, 41.48, 42.34, 41.95, 41.86, 42.18, 41.72, 42.26, 41.81, 42.04 1n, and since is unknown, we may replace The standard error of the sample mean is X it by the sample standard deviation s 0.284 to obtain the estimated standard error of X as x 41.924 Btu/hr-ft- F 0.284 110

Data from the WAIS-R indicated that urban individuals outscored those living in rural areas by about 2 points, a small difference that reflects a trend toward less urban rural difference over the years The urban advantage was substantial in the 1930s, but has virtually disappeared since then Subtest differences were significant only.

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