analysis wais twenty reference tests

505

Factor Analysis of the WAIS and Twenty French-KitReference Tests

Philip H. RamseyHofstra University

Over a 3-year period, 20 reference tests weregiven to 114 undergraduate students ranging in agefrom 18 to 46. The WAIS was given to 107 of thestudents. Maximum likelihood factor analysis wasperformed on the 31-variable correlation matrixformed by the 11 WAIS subscales and 20 referencetests. A maximum likelihood test of significancesupported the hypothesis of 10 factors. Significantsplit-sample factor reliabilities and WAIS subscaleloadings were found on all 10 factors. The rotatedfactors in order of explained variance were VerbalComprehension, Visualization, Memory Span,Syllogistic Reasoning, General Reasoning, Induc-tion, Mechanical Knowledge, Number Facility, Spa-tial Orientation, and Associative Memory. Theapparent contradictions between many previousanalyses of the WAIS are discussed and a unifiedinterpretation is presented.

Previous factor analyses of the WechslerAdult Intelligence Scale (WAIS) seem to havepresented widely differing underlying factor

structures. The number of factors has rangedfrom 2 (Silverstein, 1969) to 10 or 11 (Saunders,1959). Many of the previous factor analyses ofthe WAIS have been reviewed by Matarazzo(1972), who argued for three factors and severelycriticized factor analytic research as highly sub-jective. All previous researchers seemed to have

APPLIED PSYCHOLOGICAL MEASUREMENTVol. 2, No. 4 Fall 1978 pp. 505-517@ Copyright 1978 West Publishing Co.

been able to produce factor analytic resultswhich appeared to confirm their own theories ofintelligence. Many of these theories seem to dif-fer drastically. Wallbrown, Blaha, and Wherry(1974) have produced a three-factor solution in-cluding a g factor, while Saunders (1959) seemsalmost to have produced a separate factor foreach of the 11 subscales of the WAIS. Such

apparent discrepancies, coupled with &dquo;interpre-tations&dquo; of randomly generated data (Horn,1967; Humphreys, Ilgen, McGrath, & Mon-

tanelli, 1969), seem to provide strong support forcharges of subjectivity. It will be suggested laterin the present work that the contradictions aremore apparent than real.

Few of the previous factor analytic studies ofthe Wechsler tests have included reference teststo confirm or refute independently the manyinterpretations given to the various factors. Anearly study by Davis (1956) of the Wechsler-Bellevue was an exception, but it included only alimited number of reference tests. Cronbach

(1970, p. 330) has suggested that at least 10 fac-tors are measured to some degree by the Wechs-ler tests. The major purpose of the present inves-tigation was to evaluate the contribution of eachof the 10 specific factors mentioned by Cron-bach by direct assessment, using reference testsproduced by French, Ekstrom, and Price (1969).

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506

Method

SubjectsOver a period of three years, data were col-

lected on students in an undergraduate course inpsychological testing at Hofstra University. In afive-semester period the number of students ineach class was 22, 7, 41, 19, and 25, respectively.There were 44 men and 70 women, ranging inage from 18 to 46. Only 3 students were Black (2males and 1 female). All 114 students were

tested with 20 tests from the French Kit (Frenchet al., 1969) for purposes of the course. All but 7of the students also participated as subjects forfurther research by being tested with the WAIS.For the purpose of split-sample factor reliabilityestimation (Armstrong & Soelberg, 1968), thetotal sample was divided into two subsamples.Classes 1, 2, and 5 were combined to form Sub-

sample A with 54 students; and Classes 3 and 4were combined to form Subsample B, with 60students. Marked differences in the classes

should lead to systematic differences betweenSubsamples A and B, so comparable resultsfrom the two subsamples should be strongersupport for factor reliability than results fromtwo randomly divided subsamples.

Reference Tests

Twenty reference tests were used to establish10 reference factors with 2 tests for each factor.

They are as follows: Induction (1-1, 1-2), Asso-ciative (Rote) Memory (Ma-2, Ma-3), Mechani-cal Knowledge (Mk-2, Mk-3), Memory Span(Ms-1, Ms-2), Number Facility (N-2, N-3), Gen-eral Reasoning (R-2, R-4), Syllogistic Reasoning(Rs-1, Rs-3), Spatial Orientation (S-1, S-2), Ver-bal Comprehension (V-3, V-5), and Visualiza-tion (Vz-2, Vz-3). (For a more detailed descrip-tion of the factors and tests see French et al.,1969.)

Procedure

The 20 reference tests were administered as

group tests in six 1-hour sessions. All tests were

administered according to the instructions andtime limits specified in the test manual. The 107students participating as subjects for WAIS test-ing were tested individually by graduate stu-dents who had just completed an intensive one-semester course in Wechsler testing. The 11WAIS subscales were used in raw score form.Verbal IQ (VIQ), Performance IQ (PIQ), andFull Scale IQ (FIQ) were used in standard IQunits. The Arithmetic subscale was inadvertent-

ly omitted from the testing of the 19 students inClass 4. The VIQ and FIQ scores for those 19students were calculated from the remainingsubscales. All 19 students were in Subsample B,and the implications of these missing scores forthe factor results are discussed. Subscale scoreson one additional student were lost; but VIQ,PIQ, and FIQ scores for that student were basedon all 11 subscales.Three 31-variable correlation matrices were

constructed, using the 20 reference tests and the11 WAIS subscales. The matrices were for thetotal sample, Subsample A, and Subsample B.The number of factors was determined by

three conventional factor analytic procedures:(1) Kaiser’s (1960) unit eigenvalue rule (based onthe work of Guttman, 1954); (2) Joreskog’s(1963) maximum likelihood test of significance;and (3) Cattell’s (1966) &dquo;scree&dquo; test of residual

eigenvalues. The 10-factor unrestricted maxi-mum likelihood solution from Joreskog’s pro-gram (UFABY3; Joreskog & van Thillo, 1971)was rotated to fit a target matrix by the leastsquares procedure of Schonemann (1966). Thisprocedure orthogonally rotates a given solutionto any prespecified target solution. The targetmatrix was determined by placing 1’s in thecolumn corresponding to the appropriate factorfor each reference test and O’s in the other 9columns. Tests 3 and 4 were targeted for 1’s onthe second factor, Tests 5 and 6 for the third fac-tor, and so forth. Tests 1 and 2, the Inductiontests, had a very low correlation (.254) which, al-though statistically significant, was not con-

sidered to be of large enough magnitude to ade-quately establish a common Induction factor.



507

Therefore, Tests 1 and 2 were treated as nonref-erence tests and not used to define a referencefactor in the target matrix. On the other hand,two WAIS subscales-Digit Span and

Vocabulary-were used as reference tests for

Memory Span and Verbal Comprehension, re-spectively, since they were considered to repre-sent adequate reference tests for those factors intheir own right. The remaining 9 WAIS sub-scales, as well as Tests 1 and 2, were not targetedfor any specific factor. Each of those 11 tests wastargeted for the same loading on all 10 factors.Since orthogonal rotation leaves the communali-ties unchanged, the actual size of the equal tar-get loadings makes little difference. Loadings of.30 were used, since that value gives a sum ofsquared loadings over the 10 factors of justunder 1.0.The two subsamples, A and B, were used to

determine reliability of the factors. Due to therelatively small number of subjects, both sub-sample correlation matrices were singular; andmaximum likelihood analyses could not be used.Each subsample was analyzed by principal fac-tor analysis, using the largest off-diagonal corre-lation as the initial communality; and an itera-tive procedure was used to improve the com-munality estimate. Solutions were then rotatedto least squares fits to the total sample solution,and corresponding factors from the two subsam-ples were compared, using both the salientvariable similarity index (Cattell, Balcar, Horn,& Nesselroade, 1969) and the coefficient of con-gruence (Burt, 1948; Tucker, 1951).A version of Dwyer’s (1937) extension was

used to estimate the loadings of five additionalvariables: VIQ, PIQ, FIQ, sex, and age. Theexact procedure was the one described byGorsuch (1974, pp. 129, 233).

In most factor analytic studies, the factors areidentified by examining those variables with

loadings above some minimum absolute value(usually .30) on a particular factor. That processwas used in the present investigation but wassupplemented by a more objective procedure.Joreskog’s (1970) confirmatory maximum likeli-

hood analysis was used to test the fit of the finalsolution when &dquo;small&dquo; loadings were set to zero.

Results

Summary statistics for the 114 students on the20 reference tests are presented in Table 1.

Reliabilities agree with values reported in pre-vious research (French, 1957; Fleishman &

Dusek, 1971). The variance-covariance matrix ofthe 20-factor tests was compared for Subsam-ples A and B using the Box (1950) test, X2 (210) =205.53, p > .20. The nonsignificance of the Boxtest indicates the absence of any marked dif-ference between the two subsamples in the do-main measured by these 20 tests, at least with re-gard to covariation. Of course, there could bedifferences on the WAIS measures not related tothe reference tests.

Summary statistics on the WAIS measures,sex, and age are presented in Table 2. The rangeof WAIS FIQ scores was 101 to 137. As would beexpected from a restricted range group, all relia-bilities and standard deviations were somewhatlower than the values reported for the generalpopulation in the test manual (Wechsler, 1955).All reliabilities were statistically significant. Ex-cluding the dichotomous sex variable, the re-maining 35 variables were tested for skewnessand kurtosis by testing the 3rd and 4thmoments. The only variable to show significancein the departure from normality was age. Ageshowed both positive skewness and leptokurtickurtosis.

The unit eigenvalue rule indicated 9 factors,while Cattell’s scree test indicated 13 factors.

Joreskog’s statistical test produced a significantchi square for 9 factors, x2(222) = 259.25, p =.044. However, a nonsignificant chi-square wasfound for 10 factors, X2(200) = 226.02, p = .100.The total sample rotated maximum likelihood

solution is presented in Table 3. All 10factors were found to have significant split-sam-ple reliability as indicated by the salient variablesimilarity index. Values of the coefficient of con-gruence were also quite high.



508

Table 1

Summary Statistics on All 20 Reference Tests forTotal Sample (N = 114)

Note. Tests Ms-1 and Ms-2 have no subtests so

split-half reliabilities were omittedo Alpha wasomitted from the three highly speeded tests N-2,N-3, and S-1. All split-half reliabilities werefrom separately timed subtests.

The 10 factors presented in Table 3 can beeasily identified, with the possible exception ofFactor 1. The use of reference tests seems tohave clearly established at least 9 of the 10

hypothesized factors. The use of Schonemann’sleast squares (or &dquo;Procrustes&dquo;) rotation raisesthe question of how the present results comparewith those of randomly generated data as re-ported by Horn (1967) and Humphreys et al.

(1969). Interpolation from the randomly gen-

erated data of Humphreys et al. (1969) indicatesthat for 31 variables fitted to 10 factors with 2tests per factor and an orthogonal rotation, themean target loading from random data would be.397 with a standard deviation of .151. The

present 20 target variables (Reference Tests 3 to20 plus Digit Span and Vocabulary) had a

mean loading of .677 with a standard deviationof .176. Comparing these mean loadings pro-duced a significant difference, t(38) = 5.26, p <



509

Table 2

Summary Statistics for WAIS and Subject Variables

Note. Raw scores were used on all WAIS subscales.areliabilities for all WAIS subscales except Digit Symbolwere calculated from Flanagan’s (Kelley, 1942) formula

for split-half reliability with unequal halves.bDigit Symbol reliability was estimated using therestricted range formula employed by Wechsler (1955,p. 12) for the standardization sample.cReliabilities for all IQ scores were estimated byNunnally’s (1967, p. 229) formula 7-10 for the

reliability of a composite score.

.001. Clearly, the present results showed muchhigher loadings than those produced by randomdata.Most factor analytic studies, as mentioned

earlier, set some minimum absolute loading size,usually .30, as the smallest absolute loading avariable may have and still be of use in the inter-

pretation of the factor. Only variables with

absolute loadings above the minimum are usedto identify each factor. In the present study, 9 ofthe 10 predicted factors were easily identified bythis traditional method. Factor 1 was identified

as Induction on the basis of the Test 2 (1-2) load-

ing of .34, but the near zero loading of .05 forTest 1 (1-1) suggests that the identification mustbe considered tentative.Once the factors are identified, the process is

generally reversed and the &dquo;factorial content&dquo; ofeach variable is evaluated by examining all fac-tors on which a particular variable has absoluteloadings above the minimum .30. The computerprogram ACOVS (J6reskog, Gruvaeus, & van

Thillo, 1971) was used to provide a more objec-tive minimum value for the contribution of a



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512

variable to a factor (or vice-versa). As expected,the full solution in Table 3-after all loadingsbelow .10 were set to 0-produced a good fit ofthe factor solution to the original correlationmatrix, X2(379) = 354.69, p = .810. However, ifall loadings less than .13 were set to 0, the depar-ture of the fit just missed significance at the .05level, X2 = 422.48, p = .061. Setting all loadingsless than .15 to 0 produced a highly significantdeparture, X2(379) = 463.72, p = .002. To avoid astatistically significant departure, loadings of.13 or greater cannot be ignored.This seems to indicate that consideration only

of loadings of .30 or greater ignores a great dealof important information in the factor solution.It should be noted that these small loadings (.13to .30) are not of much importance in the iden-tification of factors, since they represent so littleof the variance of the factor. On the other hand,they may be very important in identifying thefactorial content of a variable. The shared vari-ance of a variable might be spread thinly overmany factors. To adequately reproduce that

variable, one would need to include informationfrom factors with loadings even as low as .13.Unfortunately, none of the specific loadings (inthe range from .13 to .30) can be accepted withmuch confidence. Although the aggregate effectof all these loadings may be crucial, any specificloading could be a chance value.

The large number of loadings in Table 3 withabsolute values of .13 and above suggests con-siderable complexity in the factor structure formost of the WAIS subscales. Most of the sub-scale communalities are reasonable except forBlock Design (.994), which is clearly inflated.Some of the other communalities, such as DigitSymbol (.314) and Picture Arrangement (.223),seem too low; and these subscales would

probably load on factors other than the present10. Estimated loadings for VIQ, PIQ, FIQ, sex,and age from Dwyer’s extension are also pre-sented in Table 3. A number of these exceed .30,and quite a few more exceed .13 in absolutevalue.

Discussion

Although the 3 empirical procedures rangedfrom 9 to 13 in their indication of the number of

factors, they seem to give general support to theuse of 10 factors. In particular, the maximumlikelihood solution showed a nonsignificantresidual matrix after the extraction of 10 factors.Additional reference tests could probably befound to establish 2 or 3 more factors. However,the present set of 31 variables seemed to be quiteadequately represented by a 10-factor solution.

Factor 9, Verbal Comprehension, is the

strongest single factor in the rotated solutionpresented in Table 4 and explained 11.07% ofthe variance of the 11 WAIS subscales. Verbal

Comprehension was also identified by Davis(1956) in his analysis of the Wechsler-Bellevue.He reported similar loadings on several sub-scales-Vocabulary (.601), Information (.423),and Similarities (.310).

Factor 10, Visualization, was the second

strongest factor, explaining 9.15% of the WAISsubscale variance. Davis (1956) also identified aVisualization factor with high loadings on BlockDesign (.439), Picture Completion (.384), andObject Assembly (.338). Even Saunders’s (1959)analysis showed Block Design and ObjectAssembly to appear on the same factor, as theydo on Factor 10 in the present case. An interest-ing feature of the present Visualization factor isthat the original targeted reference tests, Vz-2and Vz-3, overlapped in factor structure withSpatial Orientation (Factor 8), while Block De-sign and Object Assembly did not. These WAISsubscales may be better discriminators of theVisualization and Spatial Orientation factorsthan are the reference tests.The third strongest factor was Factor 4,

Memory Span, explaining 7.18% of the subscalevariance. Berger, Bernstein, Klein, Cohen, andLucas (1964) and Cohen (1957) have reported asimilar factor. None of the previous analysesseem to have shown quite as distinct a MemorySpan factor as the present results. On the otherhand, none of the previous analyses (not even



513

Davis, 1956) included reference tests for

Memory Span. It would appear that the factorcan be established if it is specified as in a targetmatrix. Some writers, such as Matarazzo (1972,pp. 273-274), have argued for the inclusion ofsuch a factor in factor analytic results but do notidentify it as Memory Span.

Factor 7, Syllogistic Reasoning, was thefourth strongest factor, explaining 7.05% of theWAIS subscale variance. This factor and the re-

maining ones have not been widely reported inprevious analyses of the WAIS. Davis (1956) didnot include reference tests for this factor; theclosest factor he reported was a Similarities fac-tor which had large loadings only from twosimilarities tests. In other analyses (Cohen,1957; Berger et al., 1964) this factor seems tohave been combined with Verbal Comprehen-sion to form a single verbal factor. The identifi-cation of Syllogistic Reasoning as the dominantfactor in Similarities and Comprehension doesnot seem to have been determined previously.

_

Factor 6, General Reasoning, was the fifthstrongest factor, explaining 5.51% of the WAISsubscale variance. It resembles the fourth factor

reported by Berger et al. (1964) in some of theanalyses they reported, but in others it seemsto have been combined with Memory Span.Davis (1956) identified the same factor in hisWechsler-Bellevue analysis, finding a high load-ing for Arithmetic (.571). However, Davis alsoreported a moderately high loading for Compre-hension (.331), which had a slightly negativeloading here of -.26.

Factor 1, Induction, was the sixth strongestfactor, explaining 5.16% of the WAIS subscalevariance. Its identification as Induction may be

questionable, since the two reference tests-I-1 Iand I-2-failed to establish a clear factor. The

heavy loading for Block Design (.42) is question-able because of its clearly inflated communalityof .994. To identify Factor 1, five tests with

moderately high loadings (.28 or higher) can beexamined, as shown in Table 3-I-2 (.34), Infor-mation (.30), Arithmetic (.28), Similarities (.34),

and Block Design (.42). Davis (1956) reported asimilar factor with loadings on three subscales:Information (.560), Arithmetic (.318), and BlockDesign (.305). Davis identified his factor as In-formation after the highest subscale loading.For lack of a better name, Induction was re-tained on the basis of the 1-2 loading.

Factor 3, Mechanical Knowledge, explained4.23% of the WAIS subscale variance. Davis

(1956) again identified the same factor, althoughhe found high loadings only for Block Design(.411), Arithmetic (.340), and Digit Span (.336)among the Wechsler-Bellevue subscales.

Factor 5, Number Facility, explained 3.24% ofthe WAIS subscale variance. Davis (1956) iden-tified the same factor with high loadings forDigit Symbol (.524) and Arithmetic (.359). Davisalso found a high loading for age (.320). The ex-tension analysis would appear to agree, with anage loading of .15; but Davis reversed his scor-ing of age to give younger subjects the higherscore. The disagreement in loadings betweenDavis and the present results is probably due todifferences in the age groups examined. Davisused 12- to 16-year-old junior high school stu-dents. The students in the present sampleranged in age from 18 to 46, with the majority ofthem in their 20’s.

Factor 8, Spatial Orientation, was the ninthfactor in size and explained only 2.95% of theWAIS subscale variance. Davis (1956) did not

report such a factor, but he acknowledged theabsence of any reference tests for memory or

spatial relations. None of the WAIS subscalesshowed loadings above .30 in Table 3. However,a number of them exceeded .13: Information

(.24), Comprehension (.14), Arithmetic (.28),Similarities (.20), Picture Completion (.19), andPicture Arrangement (.19). Spatial Orientationseems to play a statistically significant, althoughrelatively minor, role in a number of the WAISsubscales.

Factor 2, Associative (Rote) Memory, was theweakest of the 10 factors, explaining only 2.50%of the WAIS subscale variance. It was not iden-



514

tified by Davis (1956) nor by any other previousfactor analytic study which has been reviewedhere. Digit Symbol (.35) has the most prominentloading.The only factor reported by Davis (1956)

which represents a likely candidate for an

eleventh factor is his Perceptual Speed. He re-ports high loadings for Object Assembly (.415),Block Design (.385), and Digit Symbol (.366).Object Assembly and Digit Symbol both havelow communalities in the present results, withvalues of .389 and .314, respectively. Inclusion ofa perceptual speed reference test might have es-tablished such a factor.

Five of the present factors-Verbal Compre-hension, Visualization, General Reasoning,Number Facility, and Mechanical Knowl-

edge-seem to represent clear replication of theresults of Davis (1956). Replication is particular-ly important because of the many differences be-tween the present work and that of Davis. Threemore factors-Memory Span, Syllogistic Rea-soning, and Induction-are similar to factorsfound by Davis or others (Cohen, 1957; Berger etal., 1964). The two remaining factors, SpatialOrientation and Associative Memory, have notpreviously been shown to contribute to WAISmeasures. There seems to be good support forCronbach’s specification of the 10 factors whichwere investigated. One or two additional factorsmay be justified, with Perceptual Speed beingthe most likely candidate.The extension analysis provided some

important additional information about theWAIS factor structure. For example, age had amajor factor loading only on Verbal Compre-hension (.34). This loading seems reasonable,since this ability is likely to increase with educa-tion and experience.

Present correlations of sex with VIQ, PIQ,and FIQ were all non-significant with respectivevalues of .082, .114, and .116. This is the ex-

pected result, since the WAIS was constructedin such a manner as to eliminate sex differencesfrom IQ scores (Matarazzo, 1972, p. 352). How-

ever, sex differences have been noted in the sub-

scales. The combined 1955 standardization dataon 850 males and 850 females aged 16 to 64showed small, but statistically significant, dif-ferences on 8 of the 11 subscales (Matarazzo,1972, p. 355). Converting those mean differencecritical ratios to correlations, in order to facili-tate comparison to present results, producesquite small correlations. Males were better onInformation (.090), Arithmetic (.174), Compre-hension (.053), Picture Completion (.119), andBlock Design (.067). Females were better onSimilarities (-.054), Vocabulary (-.059), and

Digit Symbol (-.177). None of these correlationswould have exceeded the .05 critical value, .189,required for significance in the much smallertotal sample size of 106 in the present study. The.189 critical value was exceeded by only 4 of thepresent 11 correlations between sex and subscalescores. As in the standardization data, maleswere higher on Information (.311), Arithmetic(.192), Picture Completion (.250), and Block De-sign (.194). Females did not score significantlyhigher on any of the subscales.Higher male scores on Arithmetic were re-

flected in the moderately high loading of sex onGeneral Reasoning (.26). Males also scoredabove females in Mechanical Knowledge, as

shown by the loading of .47. Smaller differenceswere present in the memory factors, with higherfemale scores on Associative Memory (-.20) andhigher male scores on Memory Span (.16).The various IQ measures in Table 3 showed

surprisingly equal loadings on all factors. Theheavy loading of PIQ on Visualization (.60) is tobe expected, since so many performance sub-scales load on that factor. The most unexpectedloading is probably the low value of FIQ on Gen-eral Reasoning (.10), which occurred despite therather high loading of Arithmetic on GeneralReasoning (.54). This low loading cannot beeasily explained as attributable to the 19 stu-dents with missing Arithmetic scores. An exten-sion analysis based on the 87 students with nomissing scores produces almost identical results,



515

with FIQ loading .11 on General Reasoning.However, a few such unexpected results could bedue to chance and require replication.The present investigation has attempted to

detect substantial loadings for WAIS measureson the 10 relatively independent factors. Theattempt has been generally successful; however,in reviewing previous factor analytic results, itwas noted that most investigators have beenequally able to produce results in agreementwith their own theories. The most likely explana-tion for the success of so many different theoriesmust be that all of the theories are compatiblewith the data. This would suggest that from thepoint of view of reproducing the original correla-tion matrix, any of the factor solutions would beadequate. The accuracy of the reproduction isprobably determined primarily by the number offactors.An unrotated principal components solution

for the present data offers some useful informa-tion about the number of factors. The first unro-tated component had an FIQ loading of .883and was a good estimate of the g factor. It ex-plained 24% of the variance of the 11 WAIS sub-scales. Any investigator whose interests can beserved by a single measure of general intelli-

gence could use a one-factor solution with FIQas the measure of that factor.

Investigators who desire a two-factor solutionwith a verbal and performance factor could usethe results of Silverstein (1969) and measure thetwo factors by VIQ and PIQ. The present unro-tated components solution showed 31% of theWAIS subscale variance being explained by thefirst two components.

Three- and four-factor solutions have alsobeen presented (Berger et al., 1964; Cohen,1957; Wallbrown et al., 1974). The present unro-tated third and fourth components showcumulative explained variances of 42% and50%. It is not immediately obvious how to bestmeasure those factors, but empirical estimatescould be constructed.At least three 10-factor solutions are avail-

able, the present solution and those of Davis

(1956) and Saunders (1959). The 10 unrotated

components of the present analysis explained76% of the WAIS subscale variance, with no lessthan 3% of the variance being explained by anyone component. One argument for the use of 10or more factors is that the reliability of the sub-scales seems to be sufficiently large to justify ex-plaining more than 70% of the variance. How-ever, it must be kept in mind that both the num-ber and structure of factor solutions are in-

fluenced by the number and type of tests

analyzed. Additional or different reference testsmight change many of the present observations.Despite these limitations, there seems to be goodjustification for a 10-factor solution.The present results have already been shown

to agree closely with those of Davis (1956). For a10-factor solution of the WAIS, an investigatorcould choose either the Saunders (1959) type fac-tor solution or the reference test solution usedhere and by Davis. The advantage of the ref-erence test solution is that the WAIS factors canthen be related to a larger body of factor analyticresearch (French, 1957; Fleishman & Dusek,1971).It is not clear from the present analysis how

many, if any, of the 10 factors can be adequatelymeasured by WAIS subscales. Vocabulary andDigit Span must be good candidates for measur-ing Verbal Comprehension and Memory Span.Visualization and General Reasoning also seemlikely as abilities measurable by WAIS sub-scales. The reliabilities of any such measureswould need to be determined. Perhaps an evenmore important consideration is the one raisedby Silverstein (1969) regarding the predictiveutility of any such factor measure.

Several important issues must be consideredin the final evaluation of the present investiga-tion. Many previous researchers (Cohen, 1957;Silverstein, 1969; Wallbrown et al., 1974) havemanaged to maintain 18 or more subjects pervariable by restricting their analyses to the

standardization data for the WAIS. Others

(Davis, 1956; Saunders, 1959) have typically had8 to 12 subjects per variable. Unfortunately, no



516

reference tests have been included in any pre-vious factor analyses of the WAIS (Davis only in-cluded a few reference tests, and he analyzed theWechsler-Bellevue). All previous analyses werealso highly subjective both in the rotation andidentification of the factors. The present studyhad only 3.5 subjects per variable; but most ofthe variables were reference tests, the factorswere defined before the data were collected, andthe rotations were completely objective. Ac-

tually, the domain being analyzed was only the11 subscales of the WAIS for which there werefrom 8 to 11 subjects for every variable.There are some difficulties due to missing

data in the present study. However, previousstudies (e.g., Davis, 1956) have had the sameproblem when a large number of variables werebeing used; and in spite of these difficulties, thepresent results agree well with previous results,where comparisons are possible. In fact, the suc-cess of the present analysis in producing reason-able results provides some limited support to thepractice of calculating WAIS IQs when the scoreon a single subscale is missing.The use of graduate students as examiners

might also be challenged, even though these stu-dents were carefully trained and closely super-vised. Again, previous work suggests thereshould be no problem, since Saunders (1959) re-ported that half his data were collected by aninitially inexperienced examiner; and when thehalves were analyzed separately, Saunders foundno important difference.The present results should be of considerable

use to applied psychologists, despite the outdat-ing of the WAIS by the soon-to-be-published re-vision. The present version of the WAIS will al-most certai1tly be used for many years, since thathas happened with previous tests. Any dif-ferences or agreements between the old and newWAIS in factor structure will be most clearlyshown by factor analyses based on referencetests.

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Acknowledgments

The author thanks Dr. Howard Kassinove and Dr.Marie Meier for assisting in the supervision of theWAIS testing.

Author’s Address

Philip H. Ramsey, Psychology Department, HofstraUniversity, Hempstead, NY 11550 (After September1978: Psychology Department, Queens College of theCity University of New York, Flushing, NY 11367).



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