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is usually assumed that the observations (Xi, Yi), i 1, 2, p , n are jointly distributed random variables obtained from the distribution f (x, y). For example, suppose we wish to develop a regression model relating the shear strength of spot welds to the weld diameter. In this example, weld diameter cannot be controlled. We would randomly select n spot welds and observe a diameter (Xi) and a shear strength (Yi) for each. Therefore (Xi, Yi) are jointly distributed random variables. We assume that the joint distribution of Xi and Yi is the bivariate normal distribution pre2 2 sented in 5, and Y and Y are the mean and variance of Y, X and X are the mean and variance of X, and is the correlation coef cient between Y and X. Recall that the correlation coef cient is de ned as

The initial step in comprehensive analyses of WAIS-III profile fluctuations involves systematic statistical treatment of the most global score, Full Scale IQ Following this initial step, proceed in a stepwise fashion to examination of the other IQs, Indexes, and, finally, specific subtests Because the Full Scale IQ is the most reliable score in the battery (mean split-half coefficient of 98), it is the logical starting point in Wechsler profile interpretation This score should be assigned an intellectual category, using Wechsler s (1997, Table 23, p 25) classification system The purpose of the verbal label is to facilitate communication, not to pigeonhole the subject, and most terms in Wechsler s system (eg, Superior for IQs of 120 129 or Low Average for IQs in the 80s) communicate quite well to the professional and layperson alike.

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Computer Audit, Systems Audit and Information Security Audit Made Easy!, 2002

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However, the terms used for IQs in the 70 79 range can be unclear This range is called Borderline by Wechsler, and IQs of 69 and below are considered Extremely Low (formerly called Mentally Retarded) The term Borderline is indecisive, and may be confused with the DSM-IV psychiatric label of the same name Examiners who are accustomed to Wechsler s classification system may wish to use it with a slight amendment: substituting Well Below Average for Borderline We recommend examining the qualitative description for the confidence interval, not just the IQ alone For example, if a FS-IQ is 108 and the 90% confidence interval is 104 to 113, then the person is functioning in the Average to High Average Range Using such descriptive categories that correspond to the person s range of functioning helps to avoid pigeonholing an examinee, and provides a more accurate description of his or her abilities.

where XY is the covariance between Y and X. The conditional distribution of Y for a given value of X fY 0 x 1 y2 where

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Next, the FS-IQ should be converted to a percentile rank, using Wechsler s (1997, pp 197 198) Table A5, which includes percentile ranks for every IQ Finally, surrounding the Full Scale IQ with a band of error is essential to ensure that the IQ is perceived as a range rather than a specific.

[Coc01] [Coe03]

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number. Table A.5 in the WAIS-III Administration and Scoring Manual (Wechsler, 1997) presents bands of errors for FS-IQ at two levels of confidence (90% and 95%). The confidence intervals provided in the WAIS-III Administration and Scoring Manual were derived from a method that uses the standard error of estimation (Psychological Corporation, 1997). This method uses an estimated true score rather than the observed score, which results in an asymmetrical interval around the observed score. This asymmetry is more noticeable on scores at the extremes of the bell curve (e.g., the 90% confidence interval for a V-IQ of 50 is 47 56) than on scores closer to the normative mean (e.g., the 90% confidence interval for a V-IQ of 100 is 96 104). This asymmetry exists because the estimated true score is always closer to the mean of the scale than is the observed score. Thus, a correction for true-score regression toward the mean is obtained when the confidence interval is based on the estimated true score and the standard error of estimation is used. Regardless of how the confidence intervals are calculated, it is important to utilize them to communicate, even to the novice, that scores on intelligence tests have a certain amount of builtin error. The WAIS-III Interpretive Worksheet presented at the end of 12 summarizes this step as well as all the others that follow.

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