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Historically, factor-analytic investigators of Wechsler s adult scales have not agreed on the number of meaningful factors or constructs underlying the batteries. Silverstein (1982a) frequently argued for two, corresponding fairly closely to the intended constructs of verbal and nonverbal intelligence, while others opted for factor solutions that interpret three or more meaningful dimensions (Berger, Bernstein, Klein, Cohen, & Lucas, 1964; Matarazzo, 1972; Wechsler, 1958). With development of the WAIS-III, some differences in the factor structure were expected, as one of the goals for this version of the test was to strengthen the theoretical basis by creating hypothesized third and fourth factors. LetterNumber Sequencing and Symbol Search were added to the WAIS-III with hopes of producing a Working Memory and a Processing Speed factor to supplement the familiar, robust verbal comprehension and perceptual organization dimensions. The issue of the number of meaningful WAIS-III factors and possible theoretical interpretations is treated at length in 7. Whereas the factor analyses of the WAIS-III showed that there are four dimensions comprising the test, three dimensions have emerged

Figure 5-2 Marginal probability distributions of X and Y from Fig. 5-1.

fairly consistently for the W-B I, WAIS, and WAIS-R On these older versions of the test, for a wide variety of normal and special samples using an even greater variety of psychometric techniques, the two main, omnipresent factors were Verbal Comprehension and Perceptual Organization, and the third, smaller dimension was assigned labels like Freedom from Distractibility, Memory, Sequential Ability, and Number Ability The four dimensions of the WAIS-III (Verbal Comprehension, Perceptual Organization, Working Memory, Processing Speed) are similar to those found on the earlier versions of the test, and contain slightly different subtests, as shown in Table 35 Exploratory and confirmatory factor analyses were performed on the WAIS-III standardization data The results of these analyses, which included all subtests but Object Assembly (now an optional subtest), clearly supported a four-factor solution.

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Capture: acquire data about a security event Store: hold data about an event Review: discern information from the data Report: communicate information about an event

0 f X (x) = 0.0001

1 0.0036

The Verbal Comprehension factor had its highest loadings by Vocabulary, Information, Similarities, and Comprehension; Perceptual Organization had its highest loadings by Block Design, Matrix Reasoning, Picture Completion, and Picture Arrangement The third factor, Working Memory, had its highest loadings by Digit Span, Letter-Number Sequencing, and Arithmetic, and the final factor, Processing Speed, was made up of Digit Symbol-Coding and Symbol Search Confirmatory analyses were performed on the WAIS-III standardization sample to determine how well the four-factor model would fare in comparison to one-factor, two-factor, threefactor, and five-factor models (Psychological Corporation, 1997) All of these factor models were evaluated according to a variety of goodness-of-fit indexes The results showed that the four-factor model, indeed, provided the best fit for the data for the WAIS-III sample, although the results for ages 75 89 did not conform to the neat four factors for ages 16 74 (see discussion in 7).

2 0.0486

Event data Security event 1 Detectable data Asset ID:1123 Asset Actor representation representation Asset ID 1123 went missing at 2:00 pm from the main hall Capture

On the Wechsler-Bellevue, the WAIS, and the WAIS-R, when two factors were rotated, the six Verbal subtests tended to load highly on the.

3 0.2916

TABLE 3.5 Comparison of the Verbal Comprehension (VC) and Perceptual Organization (PO)

4 0.6561

The term audit is sometimes used informally to encompass these four functions. In this chapter we use the more formal definition of audit, which is limited to review and analysis of captured information after the fact. The figure illustrates the basic security accounting service in terms of the four functions and their typical sequence. An event occurs and accounting captures detectable data from the event (1), makes representations of the event, actors, and assets (2),

De nition If X and Y are discrete random variables with joint probability mass function fXY (x, y), then the marginal probability mass functions of X and Y are fX 1x2 P1X x2 a fXY 1x, y2

factors of the W-B I, WAIS, WAIS-R, and WAIS-III Rotated Factor Loadings Rank Order of Factor Loadings WAISIII Verbal Comprehension W-B I WAIS WAIS-R WAIS-III W-B I VC PO WAIS Perceptual Organization WAIS-R WAIS-III WB-I WAIS WAIS-R VC PO VC PO VC PO

(5-2) where Rx denotes the set of all points in the range of (X, Y) for which X Ry denotes the set of all points in the range of (X, Y) for which Y y x and

Verbal 63 02 -02 03 -08 04 00 04 70 71 35 38 74 73 4.0 3.0 73 69 34 39 3 4 3 4 35 39 83 61 35 40 84 61 1.0 5.0 84 58 32 47 2 6 1 5 32 40 1.0 5.0 3.0 4.0 79 47 61 27 55 54 79 52 42 34 80 44 2.0 7.0 2.0 6.5 31 37 31 29 1 10 2 6 9.0 10.0 11.0 6.5 8.0 6.5 6.0 11.0 9.5 7.0 9.5 8.0 11 8 10 4 9 7 10.0 11.0 9.0 5.5 8.0 7.0

11

Given a joint probability mass function for random variables X and Y, E(X ) and V(X ) can be obtained directly from the joint probability distribution of X and Y or by rst calculating the marginal probability distribution of X and then determining E(X ) and V(X ) by the usual method. This is shown in the following equation.

(5-3)

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