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TECHNICAL REPORT #4Updated December 2008: Alternate formula usedin Table 2 to calculate the required differencesbetween the FSIQ and the GAI requiredfor statistical significanceG e n e ra l A b i l i t y I n d exJanuary 2005Susan E. Raiford, Ph.D. Lawrence G.Weiss, Ph.D. Eric Rolfhus, Ph.D. Diane Coalson, Ph.D.OVERVIEWThis technical report is the fourth in a series intended tointroduce the Wechsler Intelligence Scale for Children–FourthEdition (WISC–IV; Wechsler, 2003). Technical Report #1(Williams, Weiss, & Rolfhus, 2003a) presented the theoreticalstructure and test blueprint for the WISC–IV, as well as subtestchanges from the Wechsler Intelligence Scale for Children—Third Edition (WISC–III; Wechsler, 1991). Technical Report #2(Williams, Weiss, & Rolfhus, 2003b) presented the psychometricproperties of the WISC–IV. Technical Report #3 (Williams, Weiss,& Rolfhus, 2003c) addressed the instrument’s clinical validity.This report provides information about the derivation anduses of the General Ability Index (GAI). The GAI is a compositescore that is based on 3 Verbal Comprehension and 3Perceptual Reasoning subtests, and does not include theWorking Memory or Processing Speed subtests included in theFull Scale IQ (FSIQ). Detailed information about the GAI,beyond what is covered in this technical report, is available in achapter by Saklofske, Prifitera, Weiss, Rolfhus, and Zhu inWISC–IV Clinical Use and Interpretation: Scientist-PractitionerPerspectives (Prifitera, Saklofske, & Weiss, 2005).Background and History of the Wechsler Composites and the GAIThe original Wechsler Intelligence Scale for Children (WISC;Wechsler, 1949), the Wechsler Intelligence Scale for Children—Revised (WISC–R; Wechsler, 1974), and the WISC–III included anFSIQ as well as a Verbal IQ (VIQ) and Performance IQ (PIQ). TheWISC–III introduced four index scores to represent more narrowdomains of cognitive function: the Verbal Comprehension Index(VCI), the Perceptual Organization Index (POI), the Freedomfrom Distractibility Index (FDI), and the Processing Speed Index(PSI). With the introduction of these index scores, a total ofseven composite scores could be derived with the WISC–III: theFSIQ, VIQ, PIQ, VCI, POI, FDI, and PSI.The introduction of the index scores gave practitioners theability to select the composite scores that best described verbaland perceptual ability, based on the outcome of theassessment. When necessary to aid in interpretation, thepractitioner could describe verbal abilities using the VCI inplace of the VIQ, and describe perceptual abilities using the POIin place of the PIQ. This flexibility was particularly useful whenscores for certain subtests contributing to the VIQ or PIQ werediscrepant at a significant and unusual level. In particular, theindex scores were preferable for cases in which the VIQ wasconsidered less descriptive of verbal ability than the VCIbecause Arithmetic—a subtest from the working memorydomain—was discrepant from the verbal comprehensionsubtests at a level that was unusual in the standardizationsample and for cases in which the PIQ was considered lessdescriptive of perceptual ability than the POI because Coding—a subtest drawn from the processing speed domain—wasdiscrepant from the perceptual organization subtests at a levelthat was unusual in the standardization sample.The GAI was first developed for use with the WISC–III byPrifitera, Weiss, and Saklofske (1998) to offer additionalflexibility in describing broad intellectual ability. The WISC–IIIGAI provided a measure of general cognitive ability that did notinclude the influence of Arithmetic or Coding on FSIQ. TheWISC–III GAI was based on the sum of scaled scores for allsubtests that contributed to the traditional ten-subtest FSIQ,with the exception of Arithmetic and Coding. The eightcontributing subtests were all drawn from the verbalcomprehension and perceptual organization domains, andincluded Picture Completion, Information, Similarities, PictureArrangement, Block Design, Vocabulary, Object Assembly, andComprehension. The WISC–III GAI was recommended as auseful composite to estimate overall ability if a great deal ofvariability existed within VIQ and/or PIQ due to low scores onArithmetic and/or Coding (Prifitera et al., 1998). The GAI wassubsequently applied for use with the WISC–III using Canadiannorms (Weiss, Saklofske, Prifitera, Chen, & Hildebrand, 1999),the WAIS–III (Tulsky, Saklofske, Wilkins, & Weiss, 2001), and theWAIS–III using Canadian norms (Saklofske, Gorsuch, Weiss,Zhu, & Patterson, 2005).The WISC–IV provides an FSIQ and a four-index frameworksimilar to that of the WISC–III. The framework is based ontheory and supported by clinical research and factor-analyticresults. As noted in the WISC–IV Technical and InterpretiveManual (Wechsler, 2003) and in Technical Report #1 (Williamset al., 2003a), the POI was renamed the Perceptual ReasoningIndex (PRI) to reflect more accurately the increased emphasison fluid reasoning abilities in this index, and the FDI wasrenamed the Working Memory Index (WMI), which more

The FSIQ is used most frequently to describe an underlying,global aspect of general intelligence, or g. The FSIQ is utilizedfor a number of purposes in clinical practice. The FSIQ canserve as a summary of performance across a number of specificcognitive ability domains (i.e., verbal comprehension,perceptual reasoning, working memory, and processing speed).It is used most often in conjunction with other information aspart of a diagnostic evaluation in clinics and hospital settings,to determine eligibility to receive special education services inpublic school settings, or to make decisions about level of careand placement in residential settings.accurately describes the abilities measured. In addition, thedual IQ and Index score structure was no longer utilized. Theelimination of the dual structure reduced concerns about theinfluence of working memory and processing speed whensummarizing verbal comprehension and perceptual reasoningabilities, respectively. The WISC–IV FSIQ, however, includes(to a greater extent than the WISC–III FSIQ) the influence ofworking memory and processing speed, to reflect research thatsuggests both working memory and processing speed areimportant factors that contribute to overall intellectualfunctioning (Engle, Laughlin, Tuholski, & Conway, 1999; Fry &Hale, 1996, 2000; Heinz-Martin, Oberauer, Wittmann, Wilhelm,& Schulze, 2002; Miller & Vernon, 1996; Vigil-Colet & CodorniuRaga, 2002). Recent research continues to confirm theimportance of working memory and processing speed tocognitive ability and to refine knowledge about the nature ofthese relations (Colom, Rebollo, Palacios, Juan-Espinosa, &Kyllonen, 2004; Mackintosh & Bennett, 2003; Schweizer &Moosbrugger, 2004).The FSIQ is an aggregate score that summarizesperformance across multiple cognitive abilities in a singlenumber. When unusual variability is observed within the set ofsubtests that comprise the FSIQ, clinical interpretation shouldcharacterize this diversity of abilities in order to be most usefulfor parents, teachers, and other professionals.Introduction to the WISC–IV GAItables supported by Harcourt Assessment, Inc. (formerly knownas The Psychological Corporation). These tables were createdusing the actual WISC–IV standardization sample (n 2200),whereas the GAI tables provided in other sources were createdusing statistical approximation. The calculations in Flanaganand Kaufman (2004), and Dumont and Willis (2004) were basedon a statistical technique for linear equating that wasdeveloped by Tellegen and Briggs (1967, Formula 4), whichallowed the GAI to be calculated based on intercorrelationsamong the VCI and the PRI. In contrast, tables in this technicalreport provide values for the GAI based on the standardizationsample, and the sum of subtest scaled scores that contribute tothe index. The Tellegen and Briggs formula underestimatesscores in the upper portion of the distribution andoverestimates scores in the lower portion of the distribution.On average, this difference is approximately 2–3 points, but canbe as much as 6 points for some children with mentalretardation or some gifted children. The Tellegen and Briggsformula is appropriate for use if the actual standardization dataare not available: The tables provided by Flanagan andKaufman (2004) and by Dumont and Willis (2004) weregenerated while practitioners were waiting for the tables basedon the standardization sample to be created. As the tablesbased on the standardization sample are now available, thoseGAI tables should be considered out of date. Thus, practitionersare advised to use the GAI tables in this technical report, whichare the same (within rounding variance) as the tables inPrifitera et al. (2005).As with the WISC–III GAI and WAIS-III GAI, the WISC–IV GAIprovides the practitioner a summary score that is less sensitiveto the influence of working memory and processing speed. Forchildren with neuropsychological issues such as learningdisorders, Attention-Deficit/Hyperactivity Disorder, and othersimilar issues, difficulties with working memory and processingspeed may result in lower FSIQ scores (Wechsler, 2003). Inchildren with intact neuropsychological functioning, the GAImay provide a comparable approximation of overall intellectualability as represented by the FSIQ (Prifitera et al., 2005; Weisset al., 1999).The GAI can be used as a substitute for the FSIQ todetermine eligibility for special education services andplacement classification. The GAI increases flexibility in thisrespect, because it is sensitive to cases in which workingmemory performance is discrepant from verbalcomprehension performance and/or processing speedperformance is discrepant from perceptual reasoningperformance at an unusual level. It can also be compared to theFSIQ to assess the effects of working memory and processingspeed on the expression of cognitive ability.Various sources for GAI tables are available; however, thosesources differ according to the method by which they werecreated. Four such sources are (a) this technical report, (b)Prifitera et al. (2005); (c) Flanagan and Kaufman (2004); and (d)Dumont and Willis (2004). The GAI tables provided in thistechnical report and in Prifitera et al. (2005) are the only GAIThe Role of Ability in Determining Eligibility forSpecial Education Services as Learning Disabledability–achievement discrepancies as general screeners fornonspecific learning problems. The general finding of such adiscrepancy should be followed with additional assessmentbefore a formal diagnosis is rendered. A determination that alearning disability is present requires evidence of impairmentin the core cognitive processes underlying the specificacademic skill of concern, but an AAD alone is often sufficientThe WISC–IV Integrated Technical and Interpretive Manual(Wechsler et al., 2004) outlines a number of concerns with theisolated use of the ability–achievement discrepancy model foridentifying learning disabilities. An ability–achievementdiscrepancy (AAD) indicates that some problem exists, asachievement is not at a level commensurate with cognitiveability. Established practice currently includes the use of2Copyright 2008 Pearson Education, Inc. or its affiliate(s). All rights reserved. Normative data copyright 2005 NCS Pearson. All rights reserved.

general, a local educational agency is not required to take intoconsideration whether a child has a severe AAD in determiningwhether a child has a specific learning disability. Localeducation agencies may continue to use the AAD method ifdesired, or they may incorporate or transition to a process thatdetermines if the child responds to intervention as a part of theevaluation (Individuals with Disabilities EducationImprovement Act of 2004; Public Law 108–446). Proponents ofthe response-to-intervention model advocate that eligibility forspecial education services be determined solely on the basis ofthe student’s low achievement and failure to respond toempirically supported educational instruction, regardless of theresults of cognitive evaluations (Fletcher & Reschly, 2004).Others have defended the role of cognitive assessment in theevaluation of individuals with brain-based learning disorders,while not necessarily advocating strict adherence to AAD as theonly method for classification (Hale, Naglieri, Kaufman, &Kavale, 2004; Scruggs & Mastropieri, 2002).evidence to obtain special education services in most publicschool settings. Although several new models for evaluatinglearning disorders and learning disabilities have beenproposed recently (Berninger, Dunn, & Alper, 2005; Berninger& O’Donnell, 2005), diagnostic markers generally have yet tobe established clearly in the literature. Some progress has beenmade in this area, however. For example, pseudoworddecoding and rapid automatized naming appear to predictearly reading disorders.The progression toward utilizing a number of approaches toassess learning disabilities is evident in federal legislation. Thenew Individuals with Disabilities Education Improvement Actof 2004 indicates that local education agencies should ensurethat a variety of assessment tools and strategies are used togather relevant functional, developmental, and academicinformation that may assist in determining whether or not thechild has a learning disability. The Individuals with DisabilitiesEducation Improvement Act of 2004 further states that, inWhen to Use the GAIThe practitioner may wish to consider using the GAI in anumber of clinical situations, not limited to, but including thefollowing:Presently, most school district policies continue to requireevidence of an AAD in order to obtain special educationservices, and it was largely for this reason that the GAI was firstdeveloped. For some children with learning disabilities,attentional problems, or other neuropsychological issues,concomitant working memory and processing speeddeficienci