Selection of Factor-Based WAIS-Ⅲ Tetrads in the Taiwan Standardization Sample: A Guide to Clinical Practice

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MS No.: 07005; Received: March 19, 2007; 1st_{revision: June 26, 2007; 2}nd_{revision: August 20, 2007; Accepted: January 8, 2008} Correspondence Author: Mau-Sun Hua, Department of Psychology, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, 106, Taiwan.（E-mail: huams@ntu.edu.tw）

Selection of Factor-Based WAIS-III Tetrads in the Taiwan Standardization Sample:

A Guide to Clinical Practice

1 _{Department of Special Education, National Taiwan Normal University} 2 _{Department of Psychology, National Taiwan University}

3 _{The Psychological Corporation, U.S.A} 4 _{The Chinese Behavioral Science Corporation}

Hsin-Yi Chen

1

_{, Mau-Sun Hua}

2

_{, Jianjun Zhu}

3

_{and Yung-Hwa Chen}

4

Factor-based WAIS–III tetrads were investigated with the Taiwan WAIS–III standardization sample of 888 normal adults, ages 16 to 84 years old. Various psychometric characteristics, time constraints, as well as qualities of estimation among prorating and linear equating procedures, were compared among 54 tetrads. Our results supported the use of the linear equating procedure. The Similarities-Matrix Reasoning-Arithmetic-Digit Symbol form exceeded others with respect to validity, content representation, and time saving. Kaufman,s (1990) Similarities-Picture Completion-Arithmetic-Digit Symbol combination, and the Information-Picture Completion-Arithmetic-Digit Symbol short forms were both among the most efficient estimations. For clinicians who highly value the clinical information of Block Design, two other forms, Similarities-Block Design-Arithmetic-Digit Symbol and Information-Block Design-Arithmetic-Design-Arithmetic-Digit Symbol, were found providing better estimation quality. Nonetheless, current findings revealed that even preferred tetrads had substantial misclassification rates, and these factor-based tetrads tend to show under-estimation for people with top abilities. Users are cautioned to use these short forms for screening purposes only. Results of this study are consistent with literature and assist in choosing among WAIS-III factor-based tetrads by providing their relative psychometric quality.

Keywords: WAIS–III, short form, Taiwan norm

Introduction

The Chinese version of the Wechsler Adult

Intelligence Scale—Third Edition (WAIS–III)

was recently released (Chen & Chen, 2002). Administration of the 11 WAIS–III core subtests requires, on average, 86 minutes for normal adults

from Taiwan (Chen, 2002), and possibly longer in clinical populations. When administering a full battery is not possible under some practical constraints, though not preferred, utilization of short form could be one solution when only a quick intelligence screening is required, given that not much reliability and validity are sacrificed

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while saving time (Donder, 2001). Owning to the lack of proven short form utilities for the Chinese population, corresponding validity studies are needed.

This study selected short forms based on reducing the number of subtests for the advantages of higher reliability (Kulas & Axelrod, 2002; Paolo & Ryan, 1993), and ease of completing a full battery at a later time if needed. Traditionally, four-subtest combinations are the popular option for brief intelligence estimation (Kaufman, Isihikuma, Kaufman-Packer, 1991; Wechsler, 1997). Several WAIS-R tetrads have been proposed. For example, Silverstein,s (1982) Vocabulary-Block Design-Arithmetic-Picture Arrangement form, and Reynolds, Willson, and Clark,s (1983) Information-Block Design-Arithmetic-Picture Completion form both have been reexamined frequently (Robiner, Dossa, & O,Dowd, 1997; Ryan, 1985; Ryan, Larsen, & Prifitera, 1983; Silverstein, 1985a). However, they both are criticized for being relatively more time-consuming than other possible options. Meanwhile, Kaufman and associates (Kaufman, 1990; Kaufman, Ishikuma, and Kaufman-Packer, 1991) proposed the Similarities-Picture Completion-Arithmetic-Digit Symbol combination as the “_{extremely brief tetrad”which they found both}

time-saving (roughly 19 minutes) and good with respect to predictive accuracy. The merits of this combination (short administration time, ease of scoring, and good psychometric qualities in various clinical populations) have been evaluated extensively (Allen et al., 1997; Boone, 1992; Cravens, 1999; Grossman, Mednitsky, Dennis, Scharff, & Kaufman, l993; McCusker, 1994; Missar, Gold, & Goldberg, 1994; Nagle & Bell,1995; Ward & Ryan, 1996, 1997). Recently, several compelling features of the newly available WAIS-III Matrix Reasoning subtest are recognized (Tulsky, Saklofske, & Zhu, 2003; Tulsky, Zhu, & Prifitera, 2000), including reliable measure of fluid ability, high g loading, cultural-fairness, ease of administration and scoring, and no need for hand manipulation. Researchers soon recommended this new subtest for inclusion in short forms (Sattler, 2001). For example, Wechsler

(1997) developed the Vocabulary-Similarities-Block Design-Matrix Reasoning tetrad, mainly owing to the high correlations of these subtests with g. A number of investigators have also noted that, for short-form combinations, Matrix Reasoning is a better and an appropriate logical substitution for Block Design (Axelrod, Ryan, & Ward, 2001; Ryan & Ward, 1999; Sattler, 2001; Schopp, Herrman, Johnstone, Callahan, & Roudebush, 2001; Tam, 2004; Wechsler, 1997).

Simultaneously consideration of multiple factors is necessary when deriving short forms. The magnitude of the validity is the main concern (Silverstein, 1985b). Other factors, such as reliability, clinical utility, ease of administration and scoring, and efficiency are all important criteria (Cyr & Brooker, 1984; Kaufman, et al, 1991; Kaufman, Kaufman, Balgopol, & McLean, 1996; Ward & Ryan, 1996). Some researchers claimed that maintaining the factor structure of the parent instrument is crucial (Donders, 1997, 2001; Smith, McCarthy, & Anderson, 2000). Blyler, Gold, Iannone, and Buchanan (2000) selected a WAIS-III short form by including one subtest from each of the four WAIS-III factors. It is believed that if the short form samples from all domains assessed by the full battery, similar constructs from those tapped by the full battery of the WAIS-III are estimated, and therefore the possibility of over- or under-estimating Full Scaled IQ (FSIQ) for individuals with strengths or weaknesses in differential cognitive domains is minimized. Another issue concerns the subtest order in the full battery. The administration order affects the final estimate accuracy for two- and three-subtest short forms because it influences the level of examinees, motivation and attention. However, previous research proved that administration orders had no impacts on the estimation accuracy of short forms with four or more subtests (Thompson, 1987; Thompson, Howard, & Anderson, 1986; Thompson & Plumridge, 1999).

For the current study, all four-subtest short forms were predetermined to include one subtest from each of the four WAIS-III factors: verbal comprehension (VC), perceptual organization (PO),

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working memory (WM), and processing speed (PS). Therefore, three subtests not used in the calculation of index scores (Comprehension, Picture Arrangement, and Object Assembly) were dropped from the consideration for reasons of both content coverage and psychometric qualities. Some of the traditionally popular tetrads, such as Silverstein,s (1982) and Reynolds, Willson, and Clark,s (1983) short forms, were thus not investigated in this current study, for not providing coverage of all four WAIS-III factor domains.

Besides, regardless of the lengthy administration time for Block Design and Vocabulary subtests (Chen, 2002; Ryan, Lopez, & Werth, 1998), we decided to retain both in this study for complete comparison purpose. Block Design has long been recognized for its rich diagnostic value, such as being a good index for visual-motor organization, and is amenable to qualitative analysis (Kaufman & Lichtenberger, 2002). Our previous study also found that Vocabulary was the verbal subtest selected for the most valid WAIS-III dyad (Chen, Hua, & Zhu, 2007). There might be some occasions where these subtests are needed.

W h e n s e l e c t i n g t h e m e t h o d o l o g y f o r computation of the FSIQ estimates, we first considered linear scaling for its well recognized psychometric qualities (Sattler, 2001; Silverstein, 1990; Tellegen & Briggs, 1967). Other methods, such as prorating procedures have a tendency to inflate the normative variation and to generate estimated FSIQ values that are too extreme (Tellegen & Briggs,1967), whereas regression procedure was found tending to do the opposite (Chen et al., 2007). Nonetheless, comparisons among computation procedures continue (Axelrod et al., 2001; Iverson, Myers, & Adams, 1997). Engelhart, Eisenstein, Johnson, and Losonczy (1999) proposed that as the number of subtests in the short form increases, the problem of inflated variances become less of a concern. In their study, inflated variance was a problem for two- and three-subtest combinations, but not the case for four-subtest short forms. Engelhart and his associates claimed that prorating is a viable procedure which could increase an examiner,s

flexibility in constructing short forms based on practical needs. In this study, their hypothesis was tested.

The present research was designed to compare the quality of all possible combinations of WAIS-III factor-based tetrads. Various validity criteria based on both linear equating and prorated procedures were compared. Reliabilities and administration time estimates (Chen, 2002) were included in order to make intact information available for evaluation.

Method

Participants

The Taiwan WAIS–III standardization sample (Chen & Chen, 2002) of 888 adults who reported no history of significant medical illness or psychiatric problem, aged 16-84 years, was used as the database. The sample was stratified on the variables of age, geographical region, and level of education. Equal numbers of men and women were included in each of the 11 age groups. Apart from the eldest age group that contained 88 individuals, each of the remaining 10 age groups were composed of 80 adults.

Procedure

Fifty-four tetrads were established based on all possible combinations of 11 subtests (Vocabulary, Similarities, Information, Matrix Reasoning, Picture Completion, Block Design, Arithmetic, Digit Span, Letter-Number Sequencing, Digit Symbol, and Symbol Search); every short form includes one subtest from each of the four WAIS-III index domains. Table 1 presents the abbreviations for each short form.

Psychometric data were obtained for the estimated FSIQs of all short forms for each of the 11 age groups and the average of all age groups in the standardization sample. Reliabilities and corrected part-whole correlations of the composite scales for each age group were determined by using Tellegen and Briggs, (1967) formula. The overall

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Table 1 Abbreviations and definitions for 54 WAIS–III four-subtest short forms

Abbreviation Definition

VMADs Vocabulary, Matrix Reasoning, Arithmetic, Digit Symbol-Coding

VMASs Vocabulary, Matrix Reasoning, Arithmetic, Symbol Search

VMDDs Vocabulary, Matrix Reasoning, Digit Span, Digit Symbol-Coding

VMDSs Vocabulary, Matrix Reasoning, Digit Span, Symbol Search

VMLDs Vocabulary, Matrix Reasoning, Letter Number Seq, Digit Symbol-Coding

VMLSs Vocabulary, Matrix Reasoning, Letter Number Seq, Symbol Search

SMADs Similarities, Matrix Reasoning, Arithmetic, Digit Symbol-Coding

SMASs Similarities, Matrix Reasoning, Arithmetic, Symbol Search

SMDDs Similarities, Matrix Reasoning, Digit Span, Digit Symbol-Coding

SMDSs Similarities, Matrix Reasoning, Digit Span, Symbol Search

SMLDs Similarities, Matrix Reasoning, Letter Number Seq, Digit Symbol-Coding

SMLSs Similarities, Matrix Reasoning, Letter Number Seq, Symbol Search

IMADs Information, Matrix Reasoning, Arithmetic, Digit Symbol-Coding

IMASs Information, Matrix Reasoning, Arithmetic, Symbol Search

IMDDs Information, Matrix Reasoning, Digit Span, Digit Symbol-Coding

IMDSs Information, Matrix Reasoning, Digit Span, Symbol Search

IMLDs Information, Matrix Reasoning, Letter Number Seq, Digit Symbol-Coding

IMLSs Information, Matrix Reasoning, Letter Number Seq, Symbol Search

VPADs Vocabulary, Picture Completion, Arithmetic, Digit Symbol-Coding

VPASs Vocabulary, Picture Completion, Arithmetic, Symbol Search

VPDDs Vocabulary, Picture Completion, Digit Span, Digit Symbol-Coding

VPDSs Vocabulary, Picture Completion, Digit Span, Symbol Search

VPLDs Vocabulary, Picture Completion, Letter Number Seq, Digit Symbol-Coding

VPLSs Vocabulary, Picture Completion, Letter Number Seq, Symbol Search

SPADs Similarities, Picture Completion, Arithmetic, Digit Symbol-Coding

SPASs Similarities, Picture Completion, Arithmetic, Symbol Search

SPDDs Similarities, Picture Completion, Digit Span, Digit Symbol-Coding

SPDSs Similarities, Picture Completion, Digit Span, Symbol Search

SPLDs Similarities, Picture Completion, Letter Number Seq, Digit Symbol-Coding

SPLSs Similarities, Picture Completion, Letter Number Seq, Symbol Search

IPADs Information, Picture Completion, Arithmetic, Digit Symbol-Coding

IPASs Information, Picture Completion, Arithmetic, Symbol Search

IPDDs Information, Picture Completion, Digit Span, Digit Symbol-Coding

IPDSs Information, Picture Completion, Digit Span, Symbol Search

IPLDs Information, Picture Completion, Letter Number Seq, Digit Symbol-Coding

IPLSs Information, Picture Completion, Letter Number Seq, Symbol Search

VBADs Vocabulary, Block Design, Arithmetic, Digit Symbol-Coding

VBASs Vocabulary, Block Design, Arithmetic, Symbol Search

VBDDs Vocabulary, Block Design, Digit Span, Digit Symbol-Coding

VBDSs Vocabulary, Block Design, Digit Span, Symbol Search

VBLDs Vocabulary, Block Design, Letter Number Seq, Digit Symbol-Coding

VBLSs Vocabulary, Block Design, Letter Number Seq, Symbol Search

SBADs Similarities, Block Design, Arithmetic, Digit Symbol-Coding

SBASs Similarities, Block Design, Arithmetic, Symbol Search

SBDDs Similarities, Block Design, Digit Span, Digit Symbol-Coding

SBDSs Similarities, Block Design, Digit Span, Symbol Search

SBLDs Similarities, Block Design, Letter Number Seq, Digit Symbol-Coding

SBLSs Similarities, Block Design, Letter Number Seq, Symbol Search

IBADs Information, Block Design, Arithmetic, Digit Symbol-Coding

IBASs Information, Block Design, Arithmetic, Symbol Search

IBDDs Information, Block Design, Digit Span, Digit Symbol-Coding

IBDSs Information, Block Design, Digit Span, Symbol Search

IBLDs Information, Block Design, Letter Number Seq, Digit Symbol-Coding

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averages were then transformed by Fisher,s r to z technique. Prorated short form FSIQs were obtained by multiplying the mean of two verbal subtest scaled scores by 6 and the mean of two performance subtest scaled scores by 5. The two prorated standard scores were then summed and the total was converted to the WAIS–III FSIQ, using Table 5 in the Taiwan WAIS– III manual (Chen & Chen, 2002, p.363). Tellegen and Briggs, (1967) formula was used for linear equating to compute a Deviation Quotient with a mean of 100 and standard deviation of 15.

For both linear-equating and prorated estimations, various types of validity indices were calculated (Resnick & Entin, 1971; Silverstein, 1985b; Thompson & Plumridge, 1999), such as paired sample student t- tests for mean and variance differences of the estimated and actual FSIQs, correlations between estimated and actual FSIQs, percentages of people with estimated scores falling within the 90% and 95% confidence intervals for

his/her estimated true FSIQ, and correspondence between estimated and actual FSIQ qualitative categorizations.

Results

Table 2 summarizes the basic characteristics of investigated subtests. The loadings on the first unrotated factor in the principal-axis factor analysis were used to estimate the g loadings. The results indicated that majority of VCI and POI subtests (except Picture Completion) and Arithmetic subtest have g loadings above .70, which indicates a good measure of g (Kaufman & Lichtenberger, 2002, p 234). All other g loadings were fair (above .60). Reliabilities for these subtests were good, ranging from .80 to .91. Adjusted correlations with FSIQ were all significant (p < .001). Administration time estimates based on Chen (2002) revealed that Vocabulary and Block Design were lengthy for

Table 2 Basic characteristics for each considered subtes

Adjusted Average Administration Subtests g loading rxxa r with FSIQ b Time (mins) estimatesc Verbal Comprehension Index

Vocabulary (V) .78 .91 .76 15.0

Similarities (S) .81 .87 .79 6.0

Information (I) .79 .90 .78 6.0

Preceptual Organizational Index

Picture Completion(P) .64 .87 .64 6.0

Matrix Reasoning(M) .70 .90 .69 6.0

Block Design(B) .71 .88 .68 11.0

Working Memory Index

Arithmetic (A) .78 .88 .76 6.6

Digit Span (D) .64 .92 .61 5.0

Letter-Number Seq (L) .65 .87 .64 6.0

Processing Speed Index

Digit Symbol-Coding (Ds) .66 .80 .62 4.0

Symbol Search (Ss) .64 .86 .65 4.0

a_{Data derived from Chen & Chen (2002, p.234).} b_{Data derived from Chen & Chen (2002, p. 267).} c_{Data derived from Chen (2002, Table 2).}

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Table 3 Psychometric characteristics and estimated time for 54 tetrads

Corrected Average

Part-Whole Administration

Tetrads rxxa r b Time (mins.) estimatesc

VMADs .95 .92 31.6 VMASs .96 .92 31.6 VMDDs .95 .91 30.0 VMDSs .96 .92 30.0 VMLDs .94 .92 31.0 VMLSs .95 .92 31.0 SMADs .95 .92 22.6 SMASs .95 .92 22.6 SMDDs .95 .91 21.0 SMDSs .95 .92 21.0 SMLDs .94 .92 22.0 SMLSs .95 .92 22.0 IMADs .95 .92 22.6 IMASs .96 .92 22.6 IMDDs .95 .91 21.0 IMDSs .96 .92 21.0 IMLDs .94 .92 22.0 IMLSs .95 .92 22.0 VPADs .94 .92 31.6 VPASs .95 .91 31.6 VPDDs .94 .91 30.0 VPDSs .95 .91 30.0 VPLDs .94 .92 31.0 VPLSs .94 .92 31.0 SPADs .94 .92 22.6 SPASs .95 .92 22.6 SPDDs .94 .91 21.0 SPDSs .95 .91 21.0 SPLDs .93 .91 22.0 SPLSs .94 .92 22.0 IPADs .94 .92 22.6 IPASs .95 .91 22.6 IPDDs .94 .91 21.0 IPDSs .95 .91 21.0 IPLDs .94 .91 22.0 IPLSs .94 .92 22.0 VBADs .95 .92 36.6 VBASs .95 .92 36.6 VBDDs .95 .92 35.0 VBDSs .95 .91 35.0 VBLDs .94 .92 36.0 VBLSs .95 .92 36.0 SBADs .94 .92 27.6 SBASs .95 .92 27.6 SBDDs .94 .92 26.0 SBDSs .95 .92 26.0 SBLDs .94 .92 27.0 SBLSs .94 .92 27.0 IBADs .95 .92 27.6 IBASs .95 .92 27.6 IBDDs .95 .92 26.0 IBDSs .95 .91 26.0 IBLDs .94 .92 27.0 IBLSs .95 .92 27.0

a_{Composite reliability based on formula from Tellegan and Briggs( 1967, p.500).} b_{Including all 13 subtests (except Object Assembly) for calculating the whole.} c_{Estimated by summing corresponding subtest administration time from Chen (2002).}

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administration, whereas the other subtests were comparatively more time-efficient.

For each tetrad, reliabilities, corrected part-whole correlations with the full battery, and the administration time estimates appear in Table 3. All combinations demonstrate excellent reliabilities, ranging from .93 to .96. After correcting for possible inflation due to overlapping variation, the correlation of each tetrad with full battery were also promising, ranging from .91 to .92. It means that roughly 83% to 85% of the full battery variance can be explained by these short-form estimates. As expected, the short forms that included Vocabulary or Block Design required much more time to administer (range from 26 to 36 minutes); the other combinations reduced administration time up to one-third and could therefore be completed efficiently within 21 to 22.6 minutes. Unless short forms with Vocabulary or Block Design presented impressive estimation accuracies which far exceed performances by others, or any specific clinical consideration is required, these lengthier tetrads would not present an immediately obvious advantage. Short forms that excluded both Vocabulary and Block Design, and included Digit Span had the shortest administration time (roughly 20 minutes). Administration of these presented tetrads saves approximately 58% to 76% of the time it takes to administer the standard 11 WAIS–III subtests (an average of 86 minutes for normal adults).

Table 4 contains the prime index of estimation accuracy based on linear equating procedures. Various types of validity evidence are presented, such as the mean and standard deviation of the difference between the estimated and actual FSIQ; correlations between estimated FSIQ and the actual FSIQ ; paired sample student t- test for significant mean (tm) and variance (tv) differences between

the actual and estimated FSIQ; percentages of individuals with estimated FSIQ within the 90% and 95% levels of confidence of the estimated true FSIQ (within approximately ± 3.43 and ± 4.07 IQ points of the estimated true FSIQ score); and accuracy relative to the correspondence between seven qualitative intelligence categorizations based on Wechsler,s

criteria (1997, Table 2.3): (1) extremely low (FSIQ 69 and below); (2) borderline (FSIQ 70–79); (3) low average (FSIQ 80–89); (4) average (FSIQ 90–109); (5) high average (FSIQ 110–119); (6) superior (FSIQ 120–129); (7) very superior (FSIQ 130 and above).

Results in Table 4 reveal that all tetrads yielded estimated FSIQs that correlate highly with actual FSIQ, ranging from .90 to .95 (all p < .01). Combinations that included Arithmetic and Digit Symbol seem to correlate stronger compared with their corresponding tetrads that did not. The central tendency and variation of all estimated and actual FSIQ distributions match closely (almost all p > .01). Although short forms containing Arithmetic and Digit Symbol tend to show larger score variations, the significance level of 1 % Type I error was not reached.

While comparing estimation quality among all tetrads, SMADs exceeded all others for almost all psychometric properties. It not only possessed a high reliability of .95, but also correlated highly with actual FSIQ which explains about 88% of the full variance. Furthermore, there were 65% of SMADs FSIQ estimates fell within the 95% confidence interval (approximately ± 4.07 points) of the known estimated true FSIQ, and the accurate FSIQ classification hit rate was also among the highest, at 70%. The SMADs combination took roughly 22.6 minutes to administer. Impressively, the estimation quality of the SMADs short form exceeded all tetrads that take more than 30 minutes to administer. Thus, though VMADs and VPADs both demonstrated good properties of validity, the better performance of SMADs and briefer testing time makes it more favorable.

Apart from the best solution of SMADs, other forms, such as SPADs (Kaufman, 1990) and IPADs also performed well in both psychometric and time-efficient domains. Both took 22.6 minutes to administer, and demonstrated strong reliability and validity. Roughly 63% of the estimated FSIQs from these tetrads fell within the known true 95% confidence interval, and the accurate FSIQ classification hit rate of both was around the highest (70%).

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Table 4 Comparing FSIQ estimating quality of 54 tetrads by Linear Equating Procedure

Dyads Difference_{M (SD)}a _r _t(m)b _t(v)c _90%% Within CI d_95%e % Within the Same_{IQ Category}

VMADs -0.02 (5.07) .94 -0.13 1.71 57 64 69 VMASs -0.01(5.64) .93 -0.04 1.45 52 58 68 VMDDs 0.07(5.58) .93 0.37 1.30 54 60 67 VMDSs -0.01(5.98) .92 -0.03 0.98 49 57 68 VMLDs -0.38(6.03) .92 -1.76 -0.04 44 50 58 VMLSs -0.35(6.46) .90 -1.51 -0.25 41 47 60 SMADs 0.01(5.12) .94 0.04 1.81 57 65 70 SMASs 0.05(5.62) .93 0.27 1.72 53 59 68 SMDDs 0.04(5.60) .93 0.22 1.61 55 60 70 SMDSs 0.10(5.94) .92 0.49 1.35 51 57 66 SMLDs -0.22(6.21) .91 -1.01 0.03 44 49 60 SMLSs -0.17(6.63) .90 -0.71 0.02 43 48 57 IMADs 0.08(5.26) .94 0.45 1.83 55 61 68 IMASs 0.05(5.70) .93 0.24 1.42 48 56 66 IMDDs 0.21(5.67) .93 1.10 1.46 53 60 69 IMDSs 0.21(6.00) .92 1.06 1.23 49 55 66 IMLDs -0.35(6.18) .91 -1.57 0.40 44 50 61 IMLSs -0.37(6.59) .90 -1.57 0.20 41 47 58 VPADs -0.08 (5.03) .94 -0.45 1.56 55 63 69 VPASs -0.03(5.74) .93 -0.14 1.37 53 59 68 VPDDs 0.00(5.73) .93 0.00 1.49 50 58 67 VPDSs 0.09(6.26) .91 0.41 1.19 48 56 66 VPLDs -0.47(6.24) .91 -2.10 -0.11 43 49 58 VPLSs -0.41(6.73) .90 -1.72 -0.30 38 43 58 SPADs -0.05(4.96) .95 -0.31 2.20 55 63 71 SPASs -0.08(5.58) .93 -0.40 1.66 53 61 69 SPDDs 0.22(5.62) .93 1.18 1.74 53 59 68 SPDSs 0.08(6.04) .92 0.38 1.38 51 57 67 SPLDs -0.23(6.24) .91 -1.05 -0.03 43 48 58 SPLSs -0.20(6.65) .90 -0.83 -0.05 38 44 58 IPADs 0.05(5.23) .94 0.28 2.03 56 63 70 IPASs 0.07(5.82) .93 0.38 1.58 52 58 68 IPDDs 0.15(5.81) .93 0.79 1.73 54 59 67 IPDSs 0.12(6.23) .92 0.55 1.26 49 56 67 IPLDs -0.39(6.34) .91 -1.73 0.40 44 49 58 IPLSs -0.23(6.78) .90 -0.95 0.33 37 44 57 VBADs 0.33(5.24) .94 1.90 2.75** 54 62 67 VBASs -0.09(5.87) .92 -0.47 1.42 52 57 67 VBDDs 0.03(5.58) .93 0.16 1.56 54 62 66 VBDSs 0.03(6.23) .92 0.14 1.29 51 57 66 VBLDs -0.34(6.06) .92 -1.56 0.10 43 48 58 VBLSs -0.33(6.70) .90 -1.39 -0.02 39 45 57 SBADs 0.08(5.17) .94 0.44 2.15 56 62 67 SBASs 0.01(5.90) .92 0.01 1.47 51 57 64 SBDDs 0.07(5.63) .93 0.38 1.85 51 58 65 SBDSs 0.09(6.20) .92 0.41 1.53 48 54 64 SBLDs -0.21(6.16) .91 -0.96 0.17 43 47 59 SBLSs -0.14(6.73) .90 -0.58 0.14 39 45 55 IBADs 0.06(5.29) .94 0.34 2.05 54 61 67 IBASs 0.08(5.96) .92 0.39 1.57 50 57 66 IBDDs 0.07(5.68) .93 0.38 1.62 53 58 66 IBDSs 0.18(6.23) .92 0.86 1.46 49 55 66 IBLDs -0.28(6.20) .91 -1.27 0.66 42 48 58 IBLSs -0.32(6.72) .90 -1.33 0.43 41 46 55 ** p < .01.

a_{difference between estimated and actual FSIQ.} b_{paired sample student t test for mean differences.} c_{paired sample student t test for variance differences.} d_{approximately ± 3.43 IQ points of the estimated true FSIQ.}

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Table 5 Comparing FSIQ estimating quality of 54 tetrads by Prorated Procedure

Dyads Difference_{M (SD)}a _r _t(m)b _t(v)c _90%% Within CI d_95%e % Within the Same_{IQ Category}

VMADs 0.19 (5.11) .95 1.10 6.88** 56 63 69 VMASs 0.19(5.62) .94 1.02 5.61** 52 59 68 VMDDs 0.23(5.55) .93 1.26 2.44 54 60 69 VMDSs 0.22(5.86) .93 1.10 1.67 51 57 69 VMLDs -0.26(5.99) .92 -1.22 0.09 43 50 59 VMLSs -0.26(6.38) .91 -1.13 -0.45 42 48 58 SMADs 0.28(5.31) .95 1.58 8.57** 54 61 69 SMASs 0.23(5.67) .94 1.21 6.98** 52 58 67 SMDDs 0.31(5.63) .93 1.66 4.20** 53 59 70 SMDSs 0.28(5.90) .93 1.39 2.97** 51 57 67 SMLDs -0.04(6.30) .91 -0.16 1.73 43 50 59 SMLSs -0.01(6.62) .90 -0.05 0.95 42 47 58 IMADs 0.34(5.47) .94 1.87 7.63** 53 61 68 IMASs 0.32(5.80) .93 1.62 6.89** 48 54 65 IMDDs 0.35(5.73) .93 1.83 3.78** 53 61 69 IMDSs 0.34(5.94) .92 1.69 2.55 48 55 67 IMLDs -0.14(6.30) .91 -0.63 1.81 43 49 60 IMLSs -0.16(6.57) .90 -0.69 1.11 40 47 59 VPADs 0.10 (4.89) .95 0.65 5.19** 55 63 70 VPASs 0.09(5.56) .94 0.47 4.36** 52 61 70 VPDDs 0.14(5.52) .93 0.76 1.47 52 61 69 VPDSs 0.13(6.01) .92 0.62 0.69 51 59 68 VPLDs -0.33(6.10) .91 -1.50 -1.01 45 51 58 VPLSs -0.32(6.50) .90 -1.39 -1.54 39 46 58 SPADs 0.19(4.85) .95 1.15 6.41** 56 63 73 SPASs 0.14(5.42) .94 0.79 5.21** 54 61 70 SPDDs 0.24(5.47) .94 1.30 2.75** 55 61 70 SPDSs 0.20(5.85) .93 1.02 1.63 53 59 69 SPLDs -0.06(6.18) .91 -0.29 0.19 42 49 59 SPLSs -0.09(6.52) .90 -0.40 -0.36 39 45 57 IPADs 0.24(5.21) .95 1.39 6.68** 56 63 70 IPASs 0.23(5.74) .93 1.19 5.13** 52 59 67 IPDDs 0.31(5.72) .93 1.64 2.62** 52 60 68 IPDSs 0.28(6.06) .92 1.39 1.57 51 58 68 IPLDs -0.17(6.33) .91 -0.74 0.69 44 51 59 IPLSs -0.20(6.64) .90 -0.86 -0.04 39 45 58 VBADs 0.15(5.09) .95 0.86 6.87** 55 62 68 VBASs 0.15(5.82) .93 0.77 5.51** 52 58 66 VBDDs 0.15(5.48) .94 0.83 2.61** 55 62 67 VBDSs 0.17(6.04) .92 0.84 1.70 51 57 66 VBLDs -0.25(5.98) .92 -1.17 -0.11 45 50 59 VBLSs -0.25(6.51) .90 -1.10 -0.26 40 47 58 SBADs 0.24(5.25) .95 1.36 8.22** 55 61 66 SBASs 0.21(5.89) .93 1.05 6.73** 50 57 66 SBDDs 0.27(5.59) .93 1.44 3.69** 52 58 67 SBDSs 0.25(6.09) .92 1.22 2.98** 49 54 65 SBLDs 0.01(6.16) .92 0.01 1.43 43 48 58 SBLSs -0.01(6.68) .90 -0.04 0.95 40 45 56 IBADs 0.30(5.46) .94 1.65 7.63** 53 63 67 IBASs 0.27(6.05) .93 0.18 6.84** 49 55 65 IBDDs 0.35(5.68) .93 1.81 3.52** 51 57 68 IBDSs 0.31(6.12) .92 1.52 2.78** 50 55 66 IBLDs -0.13(6.23) .92 -0.58 1.81 44 50 58 IBLSs -0.12(6.67) .90 -0.49 1.27 42 47 57 ** p < .01.

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Among the aforementioned three suggested short forms (SMADS, SPADS, and IPADS), both Picture Completion and Matrix Reasoning were selected to represent performance subtests. Some considerations reminded us that that there might be verbal comprehension element embedded in the Picture Completion subtest; and verbal abstract reasoning ability might be involved in processing the Matrix Reasoning work. Besides, the length of Matrix Reasoning administration time could be long if some special clinical patients did unusually take the limit of 2 minutes to answer each item (notice that this subtest is un-timed in the US version). Clinicians who consider these above as crucial issues and prefer the pure visual-motor organization information which Block Design can provide, current data suggested that both SBADs and IBADs demonstrate better estimation accuracy, comparatively.

Table 5 presents the validity information for the same 54 tetrads based on prorating procedures. A majority of the values was quite similar to results from Table 4; however, half of these prorated estimates demonstrated significantly inflated

variances (p < .01). Though they remain the best estimates, the variances of the estimated FSIQs for the previously suggested SMADs, SPADs, IPADs, SBADs, and IBADs significantly deviate from the real distribution, and tend to generate more extreme estimated scores.

Generally, the distribution of the linear equating estimates fit the actual FSIQ distribution better. Results suggest the linear equating procedure may be the better solution for constituting four-subtest short forms estimates. As a result, we selected short forms based exclusively on the linear equating information.

Collectively, evidence indicated that the SMADs combination is the best solution of all WAIS-III tetrads. It is the one with the best estimation accuracy, and only takes approximately 22.6 minutes to administer. Table 6 presents detailed reliability and validity information for this tetrad. Data are provided for each of the 11 age groups and the average of all age groups in the standardization sample. The linear equating formulas are also presented for practitioners, references.

The SPADs and IPADs tetrads are good also options. Estimation accuracy for these two tetrads

Table 6 Psychometric properties, estimation accuracies, and formula for calculation

of estimated FSIQ for SMADs tetrad

Age Range _r Part-Whole % Within CI % Within the Same Linear Equating xx r 90% 95% IQ Category Formulaa 16−17 .91 .89 49 54 64 (1.70X) + 32.00 18−19 .93 .93 61 68 79 (1.57X) + 37.12 20−24 .94 .93 58 66 74 (1.57X) + 37.22 25−29 .95 .92 58 60 60 (1.52X) + 39.38 30−34 .95 .92 59 64 70 (1.57X) + 37.10 35−44 .95 .91 55 69 73 (1.48X) + 40.89 45−54 .95 .91 49 59 68 (1.51X) + 39.40 55−64 .95 .91 66 70 78 (1.52X) + 39.21 65−69 .95 .94 64 74 73 (1.51X) + 39.60 70−74 .95 .94 51 61 72 (1.54X) + 38.25 75−84 .96 .91 56 67 60 (1.49X) + 40.33 ALL .95 .92 57 65 70

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were among the best as discussed, and they save roughly 74% of the administration time. Tables 7 and 8 show detailed psychometric and estimation accuracy information for both tetrads, including data for each of the 11 age groups and the average of all age groups in the standardization sample, as well as the linear equating formulas for each age range.

Same psychometric information were also provided in Tables 9 and 10 for the other two tetrads, SBADs and IBADs, which may be better options when the clinical meaning of Block Design is highly valued. These two forms presented better estimation quality while compared to all the other forms with Block Design subtest. These two tetrads save roughly 68% of the administration time.

For each of the five suggested tetrads, the percentages of people fell into three score discrepancy categories were presented in Table 11. Discrepancy was defined as the difference between the actual and estimated FSIQs. Difference within ±5 IQ points ( roughly close to the 95% confidence interval) was considered as a match; under-estimation was considered when the estimated FSIQ is 6 or more IQ points lower than the actual FSIQ; on

the country, over-estimation was suggested when the estimated FSIQ is 6 or more IQ points higher than the actual FSIQ. These percentages reveal essential base rate information.

Data from Tables 11 demonstrates that, for ability group with FSIQ less than 120, roughly 70% to 80% of these estimated FSIQs were within ± 5 IQ points of the actual FSIQs, and the percentages of either over- or under-estimation were distributed relatively much even. However, for group with FSIQ above 120, the percentages of estimations within ± 5 FSIQ points went down to 50% to 70%, and an unbalanced trend was discerned where much more underestimation was shown, while the percentages of overestimation get unevenly lower. Moreover, besides the uneven distribution for the highest ability group, SMADs, IPADs, and IBADs seem to provide much balanced estimation for all the remaining ability groups.

For each tetrad, we further examined whether the mean discrepancies were statistically significant from zero within each ability group. Figure 1 plots the mean discrepancies by ability level. Results showed that, in the highest ability group (FSIQ

Table 7 Psychometric properties, estimation accuracies, and formula for calculation

of estimated FSIQ for SPADs tetrad

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Table 8 Psychometric properties, estimation accuracies, and formula for calculation

of estimated FSIQ for IPADs tetrad

a_{X = The sum of the Similarities, Matrix Reasoning, Arithmetic, and Digit Symbol age-corrected scaled scores.}

Table 9 Psychometric properties, estimation accuracies, and formula for calculation

of estimated FSIQ for SBADs tetrad

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Table 11 Percentage of people fell in each discrepancy category for five selected tetrads

Tetrad Discerpancya_category Overall

By Full-scaled IQ ability level group

IQ ≤_– 79 80-89 90-109 110-119 IQ ≥_– 120

(N = 886) (n = 77) (n = 150) (n = 440) (n = 135) (n = 84)

SMADs Under-estimates ( ≤_– -6 IQ points) 13.66 14.29 10.67 10.46 14.81 33.33 within ± 5 IQ points 72.01 76.62 73.33 73.86 69.63 59.52 Over-estimates ( ≥_– +6 IQ points ) 14.34 9.09 16.00 15.68 15.55 7.71 SPADs Under-estimates ( ≤_– -6 IQ points) 12.99 15.59 12.67 9.55 12.59 29.76

within ± 5 IQ points 73.25 75.32 76.00 72.05 77.78 65.48 Over-estimates ( ≥_– +6 IQ points ) 13.77 9.09 11.33 18.41 9.63 4.76 IPADs Under-estimates ( ≤_– -6 IQ points) 14.22 7.8 13.33 13.64 14.81 23.81

within ± 5 IQ points 72.23 81.82 76.67 68.41 72.59 75.00 Over-estimates ( ≥_– +6 IQ points ) 13.54 10.39 10.00 17.95 12.59 1.19 SBADs Under-estimates ( ≤_– -6 IQ points) 14.33 14.29 12.00 12.05 17.78 25.00

within ± 5 IQ points 71.33 80.52 70.67 70.23 71.85 69.05 Over-estimates ( ≥_– +6 IQ points ) 14.33 5.19 17.34 17.73 10.37 5.95 IBADs Under-estimates ( ≤_– -6 IQ points) 14.45 6.49 11.34 13.86 17.03 26.19

within ± 5 IQ points 71.33 84.42 73.33 69.77 69.63 66.67 Over-estimates ( ≥_– +6 IQ points ) 14.22 9.09 15.34 16.37 13.33 7.14 a_{Discrepancy = (Estimated IQ – Full scaled IQ).}

Table 10 Psychometric properties, estimation accuracies, and formula for

calculation of estimated FSIQ for IBADs tetrad

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≧_{120), all five tetrads generated statistically} significant lower estimations (t = -2.95 to -6.49, p < .01). Based on these findings, it is important for practitioners to be aware that, while utilizing these factor-based tetrads, under-estimations tend to occur when estimating IQs for people with top abilities (the top 10% smartest people, roughly). Considering other short form combinations might be a better solution for this target population.

Discussion

The purpose of this investigation was to evaluate the potential utility of factor-based WAIS– III tetrads. The linear equating procedure was confirmed as the better choice, and the prorating method tended to generate more dispersed distribution for some short form combinations.

The points made by Tellegren and Briggs (1967), as well as Engelhart and colleagues (1999) that“inflated variance is less a concern for four-subtest short form”were not confirmed by the

current study. In our work, half of the 54 four-subtest prorated FSIQ estimates showed significantly inflated variances, indicating that the quality of prorating estimates is highly sensitive not only to number of subtests, but also to the specific subtests selected. Results revealed that combinations with Arithmetics or Digit Span subtests tended to generate more inflated variances while prorating FSIQ. It could be due to the fact that both subtests are known to have“ample specificity”(Kaufman & Lichtenberger, 1999), which could makes the mean value deviate more from the overall intellectual functions, and thus tended to generate more dispersed prorated FSIQ distributions.

The linear equating procedure generated reasonably stable distributions for almost all tetrads: For fifty-three of all the studied fifty-four tetrads, means and variances generated by this method were not significantly different from their corresponding actual values. The only exception was the VBADs short form where a significant dispersed variation was observed. Evidence supported using the linear

Figure 1.

Mean discrepancies between estimated and actual FSIQ for each selected tetrad by five ability leve.

SMADs SPADs IPADs SBADs IBADs 5 4 3 2 1 0 -1 -2 -3 -4 -5 M ea n D is cr ep an cy ≤ – 79 80-89 90-109 110-119 ≥– 120

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equating procedure, but not the prorating method, to generate four-subtest short form estimates.

Regarding short form selection, five tetrads were recommended in this study: they are SMADs, SPADs, IPADs, SBADs, and IBADs. Among these tetrads, the Similarities-Matrix Reasoning- Arithmetic-Digit Symbol combination performed the best in terms of overall estimation qualities. Similarities-Picture Completion-Arithmetic-Digit Symbol form is a traditionally popular tetrad suggested by Kaufman (Kaufman, 1990; Kaufman, et al, 1991). It performed well in this study and further confirmed its well-recognized predictive utility when considering administration time and psychometric properties simultaneously (Allen et al., 1997; McCusker, 1994; Ward & Ryan, 1997). We also recommended Information-Picture Completion-Arithmetic-Digit Symbol Coding for its good predictive accuracy. On the average, administer these three tetrads would require merely 22.6 minutes, which is 26% of the regular administration time, and provide almost 70% of the accuracy rate when using the matching FSIQ categories as criteria.

Besides, whenever Block Design is considered more appropriate than other performance subtests, such as Picture Completion or Matrix Reasoning, results suggested Similarities-Block Design-Arithmetic-Digit Symbol and Information-Block Design-Arithmetic-Digit Symbol be the options. On the average, they take 27.6 minutes to administer, and provide roughly 67% of the accuracy rate when using the matching FSIQ categories as criteria. Actually, our suggestion of using IBADs was consistent with Blyler et al. (2000),s recommendation where they reported this factor-based short form accounts for the greatest amount of variance in FSIQ for both people with schizophrenia and control subjects (excluding Vocabulary and Matrix Reasoning subtests). Our work cross-validated their finding.

Donders and Axelrod (2002) outlined three criteria for short form selections: Reliability higher than .90, correlation higher than .82, and at least 81% of the estimated scores lie within the 90% confidence interval of the full-length predicted

score. In this study, all factor-based four-subtest short forms met the first two criteria, but not the third one. Even with the best tetrad, the proportion of misclassifications is substantial. Merely 65% of estimated FSIQs were within ± 4 points of their estimated true FSIQ, and only 70% of cases corresponded with actual FSIQ categorizations. Taking together with Chen and co-workers, (2007) findings for WAIS-III dyads, if the prediction accuracy was the main concern, considering the number of subtests in short forms beyond four seems a logical next step. For example, Ward,s (1990) popular seven-subtest short form has been found to provide a comparatively more accurate estimate of the actual FSIQ and misclassifies fewer individuals (Allen et al., 1997; Benedict, Schretlen, & Bobholz, 1992; Guilmette et al., 1999; Satterfield, Clinton, & Leiker, 1994), though it also may take twice the time compared to Kaufman,s tetrad. Obviously, the issue of how to balance the necessity between validity and time-efficiency awaits further investigation. Accordingly, these tetrads should be considered valid measures for a mere screening purpose, rather than a substitute for WAIS-III FSIQ (Ryan & Ward, 1999).

Some inevitable limitations of the present study deserve attention. First, the WAIS–III short forms do not have independent norms, and the way the examinees perform on a short form and a full battery is different (Thompson et al., 1986; Thompson & Plumridge, 1999). Over- or under-estimates of the FSIQ based on the short form thus could occur. Besides, the correlation between the estimated and actual FSIQ are inflated due to overlapping error variances (Kaufman & Lichtenberger, 2002). Users better view these short forms as preliminary, convenient screening tools. Second, research findings based on a normal population do not necessarily fully generalize to patient populations with various neurocognitive deficits. Further validity studies in these populations are necessary. Finally, our results show that these factor-based tetrads did generate significant under-estimations of the FSIQ for the top ability group (the top 10 % in the population). It might be due to the fact that we selected one subtest from each

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factor for these tetrads, and thus the weight of each of the four cognitive domains (VCI, POI, WMI, PSI) for accounting for the variance of the FSIQ was equally treated as 25%. Subsequently, the overall weights of the third plus fourth factors contributing to the variance of the FSIQ are 50% for the tetrads. However, in the WAIS-III full battery, the real weights of the third and fourth factors together accounting for the variance of the FSIQ are only 27%. Accordingly, our tetrads apparently over-weighted the third and the fourth factors for interpreting the variance of the FSIQ, and thus these tetrads might not measure the same construct as the full battery does. In fact, Wechsler (1991, 2003) did find that gifted individuals obtained lower the third- and fourth-factor scores than the other twos. These findings have brought researchers, attention and subsequently an action to increase the loadings of the third and fourth factors accounting for the variance of the FSIQ has been made on the WISC-IV in US. As a result, the average FSIQ of gifted children was significantly lower than that of the WISC-III (Wechsler, 2003). Based on these findings plus the fact that an alteration of the cognitive factor weighting does diversify IQ score construct (Saklofske, Gorsuch, Weiss, Zhu, & Patterson, 2005), a caveat should be taken with care to use our tetrads in those individuals with remarkable strength or weakness on the third and fourth factors.

In conclusion, potential applications for these short forms remain numerous if the aforementioned limitations are recognized. When brief intellectual assessment for screening purposes is the main concern, or when group FSIQ averages, rather than individual FSIQ scores, in researches are desired, our evidence suggests the practical utility of SMADs, SPADs, IPADs, SBADs, and IBADs tetrads.

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本研究使用台灣版魏氏成人智力量表第三版之標準化樣本，共_{888位16至84歲之正常成年人，來檢視以魏} 氏成人智力量表第三版四因素為基礎的簡短式測驗組型。以各種心理計量特質、時間限制、以及比例與線性方程式的質性估計程序來比較_{54組測驗組型，結果支持使用線性方程式的程序。「類同-矩陣推理-算數-數字符} 號」組型在效度、內容代表性、以及節省時間的考量上，都比其他組型為優。_{Kaufman（1990）的「類同-圖} 畫補充_{-算數-數字符號」組型，以及「常識-圖畫補充-算數-數字符號」組型兩者也都是整體而言相對較佳的估} 計組型。對於認為圖形設計分測驗可提供高度臨床資訊的臨床工作者，另外兩個組型，「類同 -圖形設計-算數-數字符號」與「常識_{-圖形設計-算數-數字符號」，亦可以提供很好的估計品質。然而，目前的發現顯示即使是} 最好的組型還是有相當程度的錯誤分類比率，而且這些以四因素為基礎的測驗組型傾向會低估能力很高的正常成年人。使用者必須注意到這些簡短版的測驗組型，主要目的僅作為篩檢的用途。本研究結果提供相對的心理計量特質，來幫助我們選擇不同的魏氏成人智力量表第三版的簡短式測驗組型。關鍵詞：魏氏成人智力量表第三版、簡短版、台灣常模