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Four tables for the statistical interpretation of factor scores on the Wechsler intelligence scale for children—Revised (WISC-R)
Journal Pergamon
ofSchool Psychology, Journals
Ltd.
Printed
Vol. 24. pp. 395-404, in the USA.
1986 01986
The Journal
0022.4405/96/$3.00+ of School Psychology,
FOUR TABLES FOR THE STATISTICAL INTERPRETATION FACTOR SCORES ON THE WECHSLER INTELLIGENCE SCALE FOR CHILDREN-REVISED (WISC-R)
.@I Inc.
OF
M. K. CLAMPIT Family Service of Greater
STEPHEN
Boston
J. SILVER
Bentley College
Summary: When the Wechsler Intelligence Scale for Children-Revised (WISC-R) is analyzed into three factors (Verbal Comprehension, Perceptual Organization, and Freedom From Distractibility), the clinician has the choice of expressing each factor as either a deviation quotient (an IQ analog) or a factor score (the arithmetic mean of the constituent subtests). For the clinician who wishes to use factor scores instead of deviation quotients, four tables are presented that provide (1) the percentile equivalents of factor scores; (2) the significance of differences between factor scores; (3) the frequency with which specified discrepancies occur; and (4) the significance of differences between a factor score and the scaled score of a constituent subtest.
On the Wechsler Intelligence Scale for Children-Revised (WISC-R) (Wechsler, 1974) it is increasingly common for clinicians to interpret certain patterns of subtest scatter in terms of three factors rather than the two scales. This three-factor approach is supported by a series of factor analyses of the Wechsler tests, most of which have shown this Third Factor to load relatively high on Digit Span, Coding B (Digit Symbol), and Arithmetic. Although the factor loadings have varied in strength from test to test, being rather weak at some ages, the Third Factor has been found in at least moderate strength in the Wechsler-Bellevue (Balinsky, 1941; Cohen, 1952a, 1952b), the Wechsler Adult Intelligence Scale (Cohen, 1957a, 1957b), and the Wechsler Intelligence Scale for Children (Cohen, 1959); in the WISC, however, it was weak at younger ages, as it was for all ages of the Wechsler Preschool and Primary Scale of Intelligence (Hollenbeck & Kaufman, 1973). The Third Factor has emerged most strongly, however, on the WISC-R, where both Arithmetic and Digit Span had loadings averaging nearly .50 for all age levels, and Coding B had relatively high loadings for 8 of the 11 age levels. This led Kaufman (1975, p. 142) to declare that “each of the 12 WISC-R subtests is found to be an excellent measure of one and only one factor.” Though these factor analyses have verified the existence of this Third Factor, researchers have disagreed about exactly what cognitive or behavioral attribute it is measuring and hence what the factor should be called. Various names have been Requests for reprints should be sent to Stephen College, Waltham, MA 02154.
395
Silver,
Department
of Economics,
Bentley
396
Journal
of School
Psychology
5uggcsted for this factor (e.g., Memory, Sequencing, Numerical Ability, Freedom From Distractibility). Howe\cr, until additional research provides a clearer 5en5e of what is actually being measured, many researcher\ (Kaufman, 1979; Ownby & Mathc\+j, 1985; Stewart & Moely, 1983) advocate the LISC of a generic term: Third Factor. There is also disagreement regarding the best way to c/wn/ijj the Third Facto]- in an indiGdtral WISC-R profile. The most common techniqtte i$ to enter- the scaled \co~-es of the three subtests into a formula that twtttt\ in an IQ analog called the rlel~irrrio/l r/~otirnf, with the same mean (100) and standard deviation (15) as Verbal, Performance, and Full Scale IQs (Sattler, 1974; Tellegen & Briggs, 1967; Sobotka & Btach, 197X; Ciutkin, 197X, 1979). An alternative and easier technique is simply to a\eragc the scaled score5 of the constituent sttbtests in order to arrive at what has been called the ,ftrc./or .sw,.e (Cohen 1957a. 1959)-an equally weighted composite score that can be used to esti~~~trfe the factor that i5 common to the constituent subtests. One advantage of factor scows obcr deviation quotienta is the ease of computing them ~ql~ilr administering the WISC-R, thereby allowing the clinician the opportunity to ttse those data to decide whether to follow up with additional testing in the same wssion. In addition, Kaufman (1979) has suggested that in written testing reports, factor $corcs at-c preferable to deviation quotienta because they are less rnisleading and less likclq to bc misused by unsophisticated reader-s of case trepor-ts - readers for whom three extra IQ cqttivalcnts might well create confusion that could be better avoided by cxpre55ing the three factors as factor jcorcs rather than deviation qttotient5. For the clinician who wishes to avoid this possible confusion, or for those who Gmpty appreciate the ease of computing factor scores, there are no statistical tables of the sort that do exist for use with deviation quotients: corresponding percentiles (Sattler, 1982), significant discrepancies between quotients (Gutkin, 1979), the frequency of occttrrence of these discrepancies (Clampit, Adair, & Strenio, 1983), and significance of discrepancies between subtest scaled scores and the composite quotient (Sattler, 1982). The aim of this paper is to provide corresponding tables for factor- scores: In addition, these tables include three other composites: a Perceptual Organization composite, which includes Mazes along with the other four subtests; and two broader composites, FS, and FS,-composites that include the eight or nine subtesta of the WISC-R exclusive of the three “attentional” subtests (Arithmetic, Digit Span, and Coding). These broader composites are helpful in estimating intellectual strengths uput from the influence of the Third Factor. They are therefore clinically useful in the assessment of the significance and relative rarity of attention deficits in otherwise ttnimpaired children. METHOD
The WISC-R standardization sample includes 200 children (100 boys and 100 girls) from each of I1 age levels ranging from 6% to 16i/;_ years. The scores earned by these 2,200 children and the sumrnary statistics in the WI%-R manual (Wechsler, 1974), provide the data for this study.
Clampit
397
and Silver
Procedure Statistics are provided on six composites, each of which would be represented by its factor score (i.e., the sum of its constituent subtests). Of the six composites, three were the familiar triad of Verbal Comprehension (VC), Perceptual Organization (PO), and Freedom From Distractibility (FD); the other three were the larger composites discussed above. Tellegen and Briggs (1967) provided formulas for computing deviation quotients from the sum of the scaled scores that form each composite. We applied these formulas to compute deviation quotients for each of the six composites. From these deviation quotients (each of which has a mean of 100 and a standard deviation of 15) we used standard procedures to calculate the corresponding percentiles for each of the sum-of-scaled-scores between the 1st and 99th percentiles (Table 2). Next, we used the standard error of measurement for each subtest of the WISC-R (Wechsler, 1974, p. 30) and a formula found in Sattler (1982, p. 196) to compute the standard deviation for the difference between each pair of factor scores earned by an individual whose true scores would be the same on all subtests. From these values we produced Table 3, which lists (for various levels of significance) the differences between factor scores (in either direction) that could be expected to occur purely by chance. Next, we used the intercorrelation matrix (all ages) in the WISC-R manual (Wechsler, 1974, p. 47) to compute the standard deviation of the difference between each pair of factor scores earned by an individual. From these standard deviations, we calculated the observed differences (in one direction) at various levels of significance (Table 4). Finally, we used the intercorrelation matrix (all ages) and formulas found in Sattler (1982, p. 568) to calculate the standard deviation of the difference between the scaled score on any subtest and each of the factor scores of which that subtest is a part. From these standard deviations we calculated the observed differences in either direction scaled
(and score
at the .05 and
.Ol significance
on the constituent
subtests
Sample Profile for Computing
levels)
between
Subtest
Score
Information Similarities Vocabulary Comprehension
9 11 15 13
Pit. Compl Pit. Arrang Block Design Object Assm
I1 11 10 10
VC sum Factor score Percentile
48 12.0 78th
PO sum Factor score Percentile
42 10.5 58th
“Sum of all eight scaled scores in VC and PO.
score
and
the
Scaled Scores Freedom From Distractibility (FD)
Non-FD Composite
Score
a factor
5).
Table I Factor Scores From WISC-R
Perceptual Organization (PO)
Verbal Comprehension (VC) Subtest
(Table
Subtest
(FS,)
Arith Digit Span Coding
FS, sum Factor score Percentile
90”
FD sum
11.25 Factor score 71st
Percentile
Score 7 7 8
22 7.3 12th
28 _
29 _
30 _ _
27 _
28 _
29 _
33 _
32 _
31 _ _
30 _ _
26 27 _
20 _ 21 _ _
35 36 _
41 _ 42 _ 43
33 _ _
34
40 _ _
39 _
38 _
_
25 _
24 _ _
23 _ _ _
22 _ _
13 16 17 18 19 _
22 26 29 30 32 33 34 _
37 _
FD
75 76 _ 77 _
6X _
73 74 _
41 49 53 56 58 60 61 63 64 65 66 67 68 69 70 71 72
FS, 50th 5lst 52nd 53rd 54th 55th 56th 57th 58th 59th 60th 6lst 62nd 63rd 64th 65th 66th 67th 68th 69th 70th 71st 72nd 73rd 74th 75th
%ile
42 _ _ _ _
42 _ _ _
47
_
46
45 _ _
44 _ _ _
43 _ _
46
44 _ _ 45 _ _ _
43 _ _ _
41 _ _ _
41 _ _ _
57 _
56 _
55 _ _ _
54 _
53 _ _
52 _ _ _
51 _
50 _ _ _
40 _ _ _
40 _ _
VC
PO\
91 _
81 _
34 _ _
_
33 _ _
92
_ 8R _ 89 _ 90 _ 91 _
_ 87
_ _ _
103
99 100 101 102 _
98 _
97 _
96 _
95 _
_ 85 _ 86
94 _
93 _ _ 84
_ 83
82 _
92 _
90 _
80
_
FS,
FS,
32
_ _ _
31 _
30 _ _ _ _
FD
and Composites
PO
Table 2 Sums of Scaled Scores for Factors
66 67
35 42 46 48 50 52 54 55 56 57 58 59 60 61 _ 62 63 64 _ 65 -
FS,
for Corresponding
PO.
_
32
31 _
I6 20 22 24 2s _
I4 18 21 22 23 24 25 26 _
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th 15th 16th 17th 18th 19th 2Ot h 2lst 22nd 23rd 24th 25th 26th
PO
VC
%ile
Percentiles
_
48 _ _
49 _ _ _
39 _ _
39 _ _ _
47 _ _ _
46 _ _
45 _
44 _ _ -
_ _
38 _ -
37 _ _ _
36 _ _ -
35 _ _
_ _
38 _ _ _
37 _ _
36 _ -
35 _ _ _
34 _
_
_ _ _ _
29
28 _ _ _
27 _ _ _ _
26 _ _ _
88 _ 89 _
79 _
87 -
86 _
85 _
84 _
83 _
82 _
81 _
80 _
78 79 _
78 _
77 _
76 _
75 _
74 _
73 _
72 _
71
70 _
69 _
76th 77th 78th 79th 80th 81st 82nd 83rd 84th 85th 86th 87th 88th 89th 90th 91st 92nd 93rd 94th 95th 96th 97th 98th 99th 55 56 57 58 59 61 63
53 54 -
52 _
51 _
50 -
49 _ _
48 _ -
_
_
55 56 58 59 61
53 54 _
52 _
51 _
50 _
_
49
48 _
47 _ _
66 67 68 69 71 72 75
64 65 _
63 -
62 _
61 _
60 _
59 _ -
58 _ _
41 42 43 44 45
40 _
39 _
38 _ -
37 _ _
36 _ _ _ 99 100 101 102 103 104 105 106 107 109 111 113 115 119
96 97 98 _
95 _ 108 109 I10 Ill 112 113 114 115 116 117 118 120 121 123 125 128 132
106 107 _
_ 104 105 -
_ 93 94 _
_ 35 _ _ _
.No/e: Enter the column corresponding to the factor or composite being examined and locate the entry identical to the sum of the scaled scores. The corresponding percentile is shown in the left column on the same row. VC = Verbal Comprehension; PO = Perceptual Organization; PO, = PO plus Mazes; FD = Freedom From Distractibility; FSb = the composite of VC + PO; FS, = FS!, + Mazes. A dash indicates a percentile level that falls between adjacent sums of scaled scores and hence will not occur m normal scoring procedures. This table was constructed by using the intercorrelation matrix (for all ages) in Wechsler (1974, p, 47).
27th 28th 29th 30th 3lst 32nd 33rd 34th 35th 36th 37th 38th 39th 40th 41st 42nd 43rd 44th 45th 46th 47th 48th 49th
400
Journal
Probability Between
Probability of obtaining given or greater diwepanq by chance .5O .25 .I0 .05 .025 .Ol
of School
Table 3 of Obtaining DeGgnated Differences Individual Factor Score, on WISC-R
Factor score for Verbal Comprehenrion \t. factor wore for: PO
Psychology
PO,
Fact”r wore for breedom From Distractibilit) \s. factor score or composite for: VC
PO
PO,
.63
.6O
.59
I .(I7
I .02 I .46 I .74
I .oo
.67 I.15
I .43 1.71 I .95 2.25
I .6J
1.I0 I .57
1.95 2.23 2.57
1.87 2.14 2.46
I.53 1.83 2.09 2.40
I .Y8 2.28
.64
q .55 .93 1.34 I.59 I .x2 2.09
FS ‘) .54 .Y3 1.33 1.58 I .x0 2.08
:Vore: PO = Perceptual Organization (four subtert,); PO< = PO + Mazes; VC Verbal Comprehension; FS, = the eight subtests that make up VC and PO; FS, = FS, + Mazes. To use Table 3, enter the column pertaining to the pair of factor scores or composite scoxs that you wish to compare. Under that column. locate the entry that is just ICII than the discrepancy you are examining. In that same row, in the first column, you will find the probability of obtaining a giben or greater discrepancy by chance (i.e., the significance level). For example, the hypothesis that an examinee obtained a VC-PO discrepancy of 1.Y4 by chance can be rejected at the .05 level of significance. Table 3 is purposely two-tailed to minimize the clinical overinterpretation of mere statistical significance. This table uas constructed from rhe standard error of measurcmcnt for each subtest (Wechsler 1974, p. 30). by a formula found in Sattler (1982, p, 196) t” compute the standard deviation for the difference between t\\o factor wow\ earned by an individual (due to measurement c~-ror alone).
RESULTS AND DISCUSSION
The simplicity of using factor scores is illustrated by a sample profile (Table 1) in which the WISC-R subtests have been distributed among their corresponding factor5, the factor scores (i.e., means) have been computed, and percentiles have been obtained from Table 2. For this sample profile, the significant differences between factor scores, as determined from Table 3, are as follows: Freedom From Distractibility differs significantly from Verbal Comprehension (.Ol), Perceptual Organization (.Ol), and the nonattentional composite of these two, FS, (.Ol). Of these significant differences, two are relatively rare (Table 4): A 4.7-point difference in favor of Verbal Comprehension over Freedom From Distractibility occurs in fewer than 2.5% of the subjects in the standardization sample; and the corresponding superiority of FS, over FD (3.95 points) occurs in fewer than 540 of the subjects in the standardization sample. Finally, there are three significant differences between a constituent subtest and a corresponding factor score (Table 5), Information differing from Verbal Comprehension (.05), and Vocabulary differing from both Verbal Comprehension (.05) and FS, (.Ol).
Clampit
Interpretation
and Silver
401
and Use of Factor Scores
The use of factor scores (as well as the use of deviation quotients) has been both praised and condemned. While some researchers have found a demonstrated relationship between factor scores and academic achievement (Hale, 1981), Ysseldyke, Algozzine, and Epps (1983) and Ysseldyke, Algozzine, Shinn, & McCue (1982) have questioned the validity of scatter analysis in defining students as learning-disabled and have cautioned against overinterpreting patterns of subtest scatter. For those who do wish to use a three-factor approach, the tables facilitate a more complex analysis of the WISC-R, particularly in those cases where the Third Factor appears to be divergent. In some instances, a three-factor analysis changes a bland profile into a vivid one, either by bringing forth a significant verbal/nonverbal discrepancy previously disguised within a two-factor analysis, or by identifying a highly divergent Third Factor. Where the factor score for the Third Factor is quite low, a
Table 4 Percentage of Population Showing Discrepancies Between Various Factor Scores on the WISC-R Percentage showing discrepancy in specified direction (one-tailed) 25 12.5 5 2.5
1 0.5 0.2 0.1 0.05
Factor score for Freedom From Distractibility
Factor score for Verbal Comprehension vs. factor score for:
VS.
factor
score or composite
for:
PO
PO,
VC
PO
PO,
FS,
FS,
1.40 2.38 3.41 4.06 4.83 5.35 5.91 6.41 6.84
I .40 2.38 3.40 4.06 4.82 5.34 5.96 6.39 6.83
1.50 2.56 3.66 4.36 5.18 5.14 6.41 6.87 7.34
1.60 2.72 3.89 4.63 5.51 6.10 6.81 7.30 7.80
1.54 2.62 3.15 4.47 5.31 5.80 6.56 7.04 7.51
1.38 2.36 3.31 4.01 4.17 5.28 5.90 6.33 6.76
1.34 2.31 3.30 3.93 4.68 5.18 5.78 6.20 6.62
Note: PO = Perceptual Organization (four subtests); PO, = PO + Mazes; VC = Verbal Comprehension; FS, = the eight subtests that make up VC and PO; FS, = FS, + Mazes. To use Table 4, enter the column pertaining to the pair of factor scores or composites that are being compared. Under the column, locate the entry that is just less than the discrepancy obtained by the examinee. In that same row, but the first column, you will find the percentage of the standardization sample that obtained discrepancies as large as or larger than the discrepancies at hand (either factor score being higher, i.e., a one-tailed test). For a two-tailed test, double the percentage figure found in the first column. For example, a discrepancy of 5.5 points between the lower Freedom From Distractibility factor score and a higher Verbal Comprehension factor score is found in less than 1% of the population. The same discrepancy (either score being higher) is found to characterize 2% of the population. This table was created by using the subest intercorrelation matrix (all ages) in the WISC-R manual (Wechsler, 1974, p. 47) to compute the standard deviation of the difference between each pair of factor scores or composite scores, along with the percentage of the population expected to exhibit differences of various magnitudes.
E
_ _
3.19 3.45 3.12 3.78 _
_ _ _
2.64 2.85 2.58 3.15 _
_ _ _
.Ol
_ _
.05
_ _ _ 3.82 4.03 3.36 4.27
3.17 3.34 2.78 3.53 _
_
.Ol
_ _ _
_
.05
3 Perceptual Organization subtests (PO)
3.40 3.60 2.93 3.83 3.83
_ _ _
.OS
(or Composite)
4.06 4.31 3.51 4.59 4.59
_
_ _ _
_
.01
_ _ _ _
_
2.80 2.86 3.05 _
.05
_ _ _ _ _ _ _ _ _
3.43 3.50 3.73
.Ol
3 Freedom from Distractibility subtests (FD)
3.13 3.45 3.04 3.56 3.69 3.96 3.08 4.25 _
_ _
.05
3.65 4.03 3.55 4.16 4.31 4.62 3.60 4.96 _
_ _ _
.Ol
8 Subtests of FS, nonattentional composite
Scores on the WISC-R
of scaled score from the mean of:
5 Perceptual Organization subtests PO,)
Deviation
Table 5 Bet\veen Scaled Scores and Factor
3.19 3.52 3.10 3.64 3.78 4.05 3.15 4.36 4.36
_
.05
3.73 4.13 3.63 4.26 4.42 4.74 3.68 5.09 5.09
_
.Ol
9 Subtests of FS, nonattentional
.Yote: Table 5 5ho~s for any individual the minimum differences (between a subtest scaled score and a factor or composite score) that are significant at the .05 and .01 levels. Thi\ table \\as constructed by ustng the all-ages intercorrelation matrix in the WISC-R manual (Wechsler, 1974, p. 37) and formulas presented in Sattler (1982. p. 568), including the Bonferroni inequality described there.
Arithmetic Digit Span Coding Information Similarities Vocabular) Comprehension Picture Completion Picture Arrangement Bloch Design Object Assembly Mares
Differences
3 Verbal Comprehension subtests (VC)
Significant
Clampit
and Silver
403
three-factor analysis will produce values for the “nonattentional” composites of FS, or FS, that are correspondingly higher than the Full Scale IQ (and more in line with the vocabulary and verbal aptitude scores earned on group-administered tests). In short, removing the effect of the three “attentional” or Third-Factor subtests can help to clarify a confusing profile. Where there is a highly discrepant Third Factor, the clinician needs to avoid making a simplistic judgment that this low Freedom From Distractibility score necessarily implies an attentional weakness. While a low score on Coding may be caused by attentional weaknesses, it may also reflect undue concern about forming the shapes accurately, or simply poor pencil dexterity. Likewise, low scores on Arithmetic may be due to inadequate math education rather than attentional weaknesses. Therefore, when the Third Factor is computed and found to be divergent, the clinician should try to rule out alternative explanations and be cautious if the low factor score is caused by an extremely low value for only one of the three subtests (the other two being at or above the mean of all subtests). An accurate interpretation requires examination of the entire profile, as well as anecdotal observations of the testing behavior, and consideration of previous educational testing. Specific clinical advice regarding Third Factor interpretation can be found in Kaufman (1979, pp. 74-85), where minimal requirements for interpretation are presented, particular profiles examined in detail, and errors of overinterpretation discussed. For the clinician who uses them with caution, the tables presented here allow a threefactor analysis using factor scores rather than the more cumbersome (and possibly misleading) deviation quotients. The tables are somewhat less accurate for students under the age of 8.0, since this age group is administered Coding A rather than Coding B. The clinician may use these tables confidently, however, for all children 8.0 years old or older despite variable factor loadings at some of the older ages.
REFERENCES Balinsky, B. (1941). An analysis of the mental factors of various age groups from nine to sixty. Genetic Psychology
Monograph,
23, I91 -234.
Clampit, M., Adair, J., & Strenio, J. (1983). Frequency of discrepancies between deviation quotients on the WISC-R: A table for clinicians. Journal of Consulting and Clinical Psychology, 51, 195-796. Cohen, J. (1952a). A factor-analytically based rationale for the Wechsler-Bellevue. Journal of Consulting Psychology, 16, 272-271. Cohen, J. (1952b). Factors underlying Wechsler-Bellevue performance of three neurospsychiatric groups. Journal of Abnormal and Social Psychology, 47, 359-65. Cohen, J. (1957a). A factor-analytically based rationale for the Wechsler Adult Intelligence Scale. Journal of Consulting Psychology, 21, 451-457. Cohen, J. (1957b). The factorial structure of the WAlS between early adulthood and old age. Journal of Consulting Psychology, 21, 283-290. Cohen, J. (1959). The factorial structure of the WISC at ages 7-6, 10-6, and 13-6. Journal of Consulting Psychology, 23, 285-299. Gutkin, T. B. (1978). Some useful statistics for the interpretation of the WlSC-R. Journal of Consulting and Clinical Psychology, 46, 156 1- 1563. Gutkin, T. B. (1979). The WISC-R Verbal Comprehension, Perceptual Organization, and Freedom from Distractibility deviation quotients: Data for practitioners. Psychology in the Schools, 16, 359-360. Hale, R. L. (1981). Concurrent validity of the WISC-R factor scores. Journal of School Psycholog_v, 15, 172-175.
Journal
404
of School
Psychology
Hollenbeck, G., & Kaufman, (1973). Factor analysis of the Wechsler Preschool and Primary Scale of Intelligence (WPPSI). Journal of Clinical Psychology, 29, 41-45. Kaufman, A. (1975). Factor analysis of the WISC-R at eleven age levels between 6 and ‘% and 16 and ?Z Journal of Consulting und Clinical Psychology, 43, 135-147. Kaufman, A. (1979). Intelligenr testing with [he WISC-R. New York: Wiley. Ownby, R., & Matthews, C. (1985). On the meaning of the WISC-R Third Factor: Relations to selected neuropsychological measures. Journal of Consulting and Clinical Psychology, 53, 53 I-534. Sattler, J. M. (1974). Assessmeni of children’s intelligence. Philadelphia: W. B. Saunders. Sattler, J. M. (1982). Assessment of children’s infelligence und speciul abiliries. Boston: Allyn & Bacon. Sobotka, R., & Black, F. (1978). A procedure for the rapid computation of WISC-R factor scores. Journal of Clinical Psychology, 34, 117- 119. Stewart, K. J., & Moely, B. E. (1983). The WISC-R third factor: What does it mean? Journal of Consulting and Clinical Psychology, 51, 940-941. Tellegen, A., & Briggs, P. (1967). Old wine in new skins: Grouping Wechsler subtests into new scales. Journal of Consulting Psychology, 31, 499-506. Wechsler, D. (1974). Manual for the Wechsler Intelligence Scale for Children-Revised. New York: The Psychological Corporation. Ysseldyke, J. E., Algozzine, B., & Epps, S. (1983). A logical and empirical analysis of current practices in classifying students as handicapped. Excepfional Children, SO, 160-166. Ysseldyke, J. E., Algozrine, B., Shinn, M. R., & McCue, M. (1982). Similarities and differences between low achievers and students classified as learning disabled. The Journul of Special Educulion, 16, 73-85. M. K. Clampit 219 Kittredge Street Boston, MA 02131 Manuscript Manuscript
received: accepted:
November 7, 1984 March 1, 1986
ofSchool Psychology, Journals
Ltd.
Printed
Vol. 24. pp. 395-404, in the USA.
1986 01986
The Journal
0022.4405/96/$3.00+ of School Psychology,
FOUR TABLES FOR THE STATISTICAL INTERPRETATION FACTOR SCORES ON THE WECHSLER INTELLIGENCE SCALE FOR CHILDREN-REVISED (WISC-R)
.@I Inc.
OF
M. K. CLAMPIT Family Service of Greater
STEPHEN
Boston
J. SILVER
Bentley College
Summary: When the Wechsler Intelligence Scale for Children-Revised (WISC-R) is analyzed into three factors (Verbal Comprehension, Perceptual Organization, and Freedom From Distractibility), the clinician has the choice of expressing each factor as either a deviation quotient (an IQ analog) or a factor score (the arithmetic mean of the constituent subtests). For the clinician who wishes to use factor scores instead of deviation quotients, four tables are presented that provide (1) the percentile equivalents of factor scores; (2) the significance of differences between factor scores; (3) the frequency with which specified discrepancies occur; and (4) the significance of differences between a factor score and the scaled score of a constituent subtest.
On the Wechsler Intelligence Scale for Children-Revised (WISC-R) (Wechsler, 1974) it is increasingly common for clinicians to interpret certain patterns of subtest scatter in terms of three factors rather than the two scales. This three-factor approach is supported by a series of factor analyses of the Wechsler tests, most of which have shown this Third Factor to load relatively high on Digit Span, Coding B (Digit Symbol), and Arithmetic. Although the factor loadings have varied in strength from test to test, being rather weak at some ages, the Third Factor has been found in at least moderate strength in the Wechsler-Bellevue (Balinsky, 1941; Cohen, 1952a, 1952b), the Wechsler Adult Intelligence Scale (Cohen, 1957a, 1957b), and the Wechsler Intelligence Scale for Children (Cohen, 1959); in the WISC, however, it was weak at younger ages, as it was for all ages of the Wechsler Preschool and Primary Scale of Intelligence (Hollenbeck & Kaufman, 1973). The Third Factor has emerged most strongly, however, on the WISC-R, where both Arithmetic and Digit Span had loadings averaging nearly .50 for all age levels, and Coding B had relatively high loadings for 8 of the 11 age levels. This led Kaufman (1975, p. 142) to declare that “each of the 12 WISC-R subtests is found to be an excellent measure of one and only one factor.” Though these factor analyses have verified the existence of this Third Factor, researchers have disagreed about exactly what cognitive or behavioral attribute it is measuring and hence what the factor should be called. Various names have been Requests for reprints should be sent to Stephen College, Waltham, MA 02154.
395
Silver,
Department
of Economics,
Bentley
396
Journal
of School
Psychology
5uggcsted for this factor (e.g., Memory, Sequencing, Numerical Ability, Freedom From Distractibility). Howe\cr, until additional research provides a clearer 5en5e of what is actually being measured, many researcher\ (Kaufman, 1979; Ownby & Mathc\+j, 1985; Stewart & Moely, 1983) advocate the LISC of a generic term: Third Factor. There is also disagreement regarding the best way to c/wn/ijj the Third Facto]- in an indiGdtral WISC-R profile. The most common techniqtte i$ to enter- the scaled \co~-es of the three subtests into a formula that twtttt\ in an IQ analog called the rlel~irrrio/l r/~otirnf, with the same mean (100) and standard deviation (15) as Verbal, Performance, and Full Scale IQs (Sattler, 1974; Tellegen & Briggs, 1967; Sobotka & Btach, 197X; Ciutkin, 197X, 1979). An alternative and easier technique is simply to a\eragc the scaled score5 of the constituent sttbtests in order to arrive at what has been called the ,ftrc./or .sw,.e (Cohen 1957a. 1959)-an equally weighted composite score that can be used to esti~~~trfe the factor that i5 common to the constituent subtests. One advantage of factor scows obcr deviation quotienta is the ease of computing them ~ql~ilr administering the WISC-R, thereby allowing the clinician the opportunity to ttse those data to decide whether to follow up with additional testing in the same wssion. In addition, Kaufman (1979) has suggested that in written testing reports, factor $corcs at-c preferable to deviation quotienta because they are less rnisleading and less likclq to bc misused by unsophisticated reader-s of case trepor-ts - readers for whom three extra IQ cqttivalcnts might well create confusion that could be better avoided by cxpre55ing the three factors as factor jcorcs rather than deviation qttotient5. For the clinician who wishes to avoid this possible confusion, or for those who Gmpty appreciate the ease of computing factor scores, there are no statistical tables of the sort that do exist for use with deviation quotients: corresponding percentiles (Sattler, 1982), significant discrepancies between quotients (Gutkin, 1979), the frequency of occttrrence of these discrepancies (Clampit, Adair, & Strenio, 1983), and significance of discrepancies between subtest scaled scores and the composite quotient (Sattler, 1982). The aim of this paper is to provide corresponding tables for factor- scores: In addition, these tables include three other composites: a Perceptual Organization composite, which includes Mazes along with the other four subtests; and two broader composites, FS, and FS,-composites that include the eight or nine subtesta of the WISC-R exclusive of the three “attentional” subtests (Arithmetic, Digit Span, and Coding). These broader composites are helpful in estimating intellectual strengths uput from the influence of the Third Factor. They are therefore clinically useful in the assessment of the significance and relative rarity of attention deficits in otherwise ttnimpaired children. METHOD
The WISC-R standardization sample includes 200 children (100 boys and 100 girls) from each of I1 age levels ranging from 6% to 16i/;_ years. The scores earned by these 2,200 children and the sumrnary statistics in the WI%-R manual (Wechsler, 1974), provide the data for this study.
Clampit
397
and Silver
Procedure Statistics are provided on six composites, each of which would be represented by its factor score (i.e., the sum of its constituent subtests). Of the six composites, three were the familiar triad of Verbal Comprehension (VC), Perceptual Organization (PO), and Freedom From Distractibility (FD); the other three were the larger composites discussed above. Tellegen and Briggs (1967) provided formulas for computing deviation quotients from the sum of the scaled scores that form each composite. We applied these formulas to compute deviation quotients for each of the six composites. From these deviation quotients (each of which has a mean of 100 and a standard deviation of 15) we used standard procedures to calculate the corresponding percentiles for each of the sum-of-scaled-scores between the 1st and 99th percentiles (Table 2). Next, we used the standard error of measurement for each subtest of the WISC-R (Wechsler, 1974, p. 30) and a formula found in Sattler (1982, p. 196) to compute the standard deviation for the difference between each pair of factor scores earned by an individual whose true scores would be the same on all subtests. From these values we produced Table 3, which lists (for various levels of significance) the differences between factor scores (in either direction) that could be expected to occur purely by chance. Next, we used the intercorrelation matrix (all ages) in the WISC-R manual (Wechsler, 1974, p. 47) to compute the standard deviation of the difference between each pair of factor scores earned by an individual. From these standard deviations, we calculated the observed differences (in one direction) at various levels of significance (Table 4). Finally, we used the intercorrelation matrix (all ages) and formulas found in Sattler (1982, p. 568) to calculate the standard deviation of the difference between the scaled score on any subtest and each of the factor scores of which that subtest is a part. From these standard deviations we calculated the observed differences in either direction scaled
(and score
at the .05 and
.Ol significance
on the constituent
subtests
Sample Profile for Computing
levels)
between
Subtest
Score
Information Similarities Vocabulary Comprehension
9 11 15 13
Pit. Compl Pit. Arrang Block Design Object Assm
I1 11 10 10
VC sum Factor score Percentile
48 12.0 78th
PO sum Factor score Percentile
42 10.5 58th
“Sum of all eight scaled scores in VC and PO.
score
and
the
Scaled Scores Freedom From Distractibility (FD)
Non-FD Composite
Score
a factor
5).
Table I Factor Scores From WISC-R
Perceptual Organization (PO)
Verbal Comprehension (VC) Subtest
(Table
Subtest
(FS,)
Arith Digit Span Coding
FS, sum Factor score Percentile
90”
FD sum
11.25 Factor score 71st
Percentile
Score 7 7 8
22 7.3 12th
28 _
29 _
30 _ _
27 _
28 _
29 _
33 _
32 _
31 _ _
30 _ _
26 27 _
20 _ 21 _ _
35 36 _
41 _ 42 _ 43
33 _ _
34
40 _ _
39 _
38 _
_
25 _
24 _ _
23 _ _ _
22 _ _
13 16 17 18 19 _
22 26 29 30 32 33 34 _
37 _
FD
75 76 _ 77 _
6X _
73 74 _
41 49 53 56 58 60 61 63 64 65 66 67 68 69 70 71 72
FS, 50th 5lst 52nd 53rd 54th 55th 56th 57th 58th 59th 60th 6lst 62nd 63rd 64th 65th 66th 67th 68th 69th 70th 71st 72nd 73rd 74th 75th
%ile
42 _ _ _ _
42 _ _ _
47
_
46
45 _ _
44 _ _ _
43 _ _
46
44 _ _ 45 _ _ _
43 _ _ _
41 _ _ _
41 _ _ _
57 _
56 _
55 _ _ _
54 _
53 _ _
52 _ _ _
51 _
50 _ _ _
40 _ _ _
40 _ _
VC
PO\
91 _
81 _
34 _ _
_
33 _ _
92
_ 8R _ 89 _ 90 _ 91 _
_ 87
_ _ _
103
99 100 101 102 _
98 _
97 _
96 _
95 _
_ 85 _ 86
94 _
93 _ _ 84
_ 83
82 _
92 _
90 _
80
_
FS,
FS,
32
_ _ _
31 _
30 _ _ _ _
FD
and Composites
PO
Table 2 Sums of Scaled Scores for Factors
66 67
35 42 46 48 50 52 54 55 56 57 58 59 60 61 _ 62 63 64 _ 65 -
FS,
for Corresponding
PO.
_
32
31 _
I6 20 22 24 2s _
I4 18 21 22 23 24 25 26 _
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th 15th 16th 17th 18th 19th 2Ot h 2lst 22nd 23rd 24th 25th 26th
PO
VC
%ile
Percentiles
_
48 _ _
49 _ _ _
39 _ _
39 _ _ _
47 _ _ _
46 _ _
45 _
44 _ _ -
_ _
38 _ -
37 _ _ _
36 _ _ -
35 _ _
_ _
38 _ _ _
37 _ _
36 _ -
35 _ _ _
34 _
_
_ _ _ _
29
28 _ _ _
27 _ _ _ _
26 _ _ _
88 _ 89 _
79 _
87 -
86 _
85 _
84 _
83 _
82 _
81 _
80 _
78 79 _
78 _
77 _
76 _
75 _
74 _
73 _
72 _
71
70 _
69 _
76th 77th 78th 79th 80th 81st 82nd 83rd 84th 85th 86th 87th 88th 89th 90th 91st 92nd 93rd 94th 95th 96th 97th 98th 99th 55 56 57 58 59 61 63
53 54 -
52 _
51 _
50 -
49 _ _
48 _ -
_
_
55 56 58 59 61
53 54 _
52 _
51 _
50 _
_
49
48 _
47 _ _
66 67 68 69 71 72 75
64 65 _
63 -
62 _
61 _
60 _
59 _ -
58 _ _
41 42 43 44 45
40 _
39 _
38 _ -
37 _ _
36 _ _ _ 99 100 101 102 103 104 105 106 107 109 111 113 115 119
96 97 98 _
95 _ 108 109 I10 Ill 112 113 114 115 116 117 118 120 121 123 125 128 132
106 107 _
_ 104 105 -
_ 93 94 _
_ 35 _ _ _
.No/e: Enter the column corresponding to the factor or composite being examined and locate the entry identical to the sum of the scaled scores. The corresponding percentile is shown in the left column on the same row. VC = Verbal Comprehension; PO = Perceptual Organization; PO, = PO plus Mazes; FD = Freedom From Distractibility; FSb = the composite of VC + PO; FS, = FS!, + Mazes. A dash indicates a percentile level that falls between adjacent sums of scaled scores and hence will not occur m normal scoring procedures. This table was constructed by using the intercorrelation matrix (for all ages) in Wechsler (1974, p, 47).
27th 28th 29th 30th 3lst 32nd 33rd 34th 35th 36th 37th 38th 39th 40th 41st 42nd 43rd 44th 45th 46th 47th 48th 49th
400
Journal
Probability Between
Probability of obtaining given or greater diwepanq by chance .5O .25 .I0 .05 .025 .Ol
of School
Table 3 of Obtaining DeGgnated Differences Individual Factor Score, on WISC-R
Factor score for Verbal Comprehenrion \t. factor wore for: PO
Psychology
PO,
Fact”r wore for breedom From Distractibilit) \s. factor score or composite for: VC
PO
PO,
.63
.6O
.59
I .(I7
I .02 I .46 I .74
I .oo
.67 I.15
I .43 1.71 I .95 2.25
I .6J
1.I0 I .57
1.95 2.23 2.57
1.87 2.14 2.46
I.53 1.83 2.09 2.40
I .Y8 2.28
.64
q .55 .93 1.34 I.59 I .x2 2.09
FS ‘) .54 .Y3 1.33 1.58 I .x0 2.08
:Vore: PO = Perceptual Organization (four subtert,); PO< = PO + Mazes; VC Verbal Comprehension; FS, = the eight subtests that make up VC and PO; FS, = FS, + Mazes. To use Table 3, enter the column pertaining to the pair of factor scores or composite scoxs that you wish to compare. Under that column. locate the entry that is just ICII than the discrepancy you are examining. In that same row, in the first column, you will find the probability of obtaining a giben or greater discrepancy by chance (i.e., the significance level). For example, the hypothesis that an examinee obtained a VC-PO discrepancy of 1.Y4 by chance can be rejected at the .05 level of significance. Table 3 is purposely two-tailed to minimize the clinical overinterpretation of mere statistical significance. This table uas constructed from rhe standard error of measurcmcnt for each subtest (Wechsler 1974, p. 30). by a formula found in Sattler (1982, p, 196) t” compute the standard deviation for the difference between t\\o factor wow\ earned by an individual (due to measurement c~-ror alone).
RESULTS AND DISCUSSION
The simplicity of using factor scores is illustrated by a sample profile (Table 1) in which the WISC-R subtests have been distributed among their corresponding factor5, the factor scores (i.e., means) have been computed, and percentiles have been obtained from Table 2. For this sample profile, the significant differences between factor scores, as determined from Table 3, are as follows: Freedom From Distractibility differs significantly from Verbal Comprehension (.Ol), Perceptual Organization (.Ol), and the nonattentional composite of these two, FS, (.Ol). Of these significant differences, two are relatively rare (Table 4): A 4.7-point difference in favor of Verbal Comprehension over Freedom From Distractibility occurs in fewer than 2.5% of the subjects in the standardization sample; and the corresponding superiority of FS, over FD (3.95 points) occurs in fewer than 540 of the subjects in the standardization sample. Finally, there are three significant differences between a constituent subtest and a corresponding factor score (Table 5), Information differing from Verbal Comprehension (.05), and Vocabulary differing from both Verbal Comprehension (.05) and FS, (.Ol).
Clampit
Interpretation
and Silver
401
and Use of Factor Scores
The use of factor scores (as well as the use of deviation quotients) has been both praised and condemned. While some researchers have found a demonstrated relationship between factor scores and academic achievement (Hale, 1981), Ysseldyke, Algozzine, and Epps (1983) and Ysseldyke, Algozzine, Shinn, & McCue (1982) have questioned the validity of scatter analysis in defining students as learning-disabled and have cautioned against overinterpreting patterns of subtest scatter. For those who do wish to use a three-factor approach, the tables facilitate a more complex analysis of the WISC-R, particularly in those cases where the Third Factor appears to be divergent. In some instances, a three-factor analysis changes a bland profile into a vivid one, either by bringing forth a significant verbal/nonverbal discrepancy previously disguised within a two-factor analysis, or by identifying a highly divergent Third Factor. Where the factor score for the Third Factor is quite low, a
Table 4 Percentage of Population Showing Discrepancies Between Various Factor Scores on the WISC-R Percentage showing discrepancy in specified direction (one-tailed) 25 12.5 5 2.5
1 0.5 0.2 0.1 0.05
Factor score for Freedom From Distractibility
Factor score for Verbal Comprehension vs. factor score for:
VS.
factor
score or composite
for:
PO
PO,
VC
PO
PO,
FS,
FS,
1.40 2.38 3.41 4.06 4.83 5.35 5.91 6.41 6.84
I .40 2.38 3.40 4.06 4.82 5.34 5.96 6.39 6.83
1.50 2.56 3.66 4.36 5.18 5.14 6.41 6.87 7.34
1.60 2.72 3.89 4.63 5.51 6.10 6.81 7.30 7.80
1.54 2.62 3.15 4.47 5.31 5.80 6.56 7.04 7.51
1.38 2.36 3.31 4.01 4.17 5.28 5.90 6.33 6.76
1.34 2.31 3.30 3.93 4.68 5.18 5.78 6.20 6.62
Note: PO = Perceptual Organization (four subtests); PO, = PO + Mazes; VC = Verbal Comprehension; FS, = the eight subtests that make up VC and PO; FS, = FS, + Mazes. To use Table 4, enter the column pertaining to the pair of factor scores or composites that are being compared. Under the column, locate the entry that is just less than the discrepancy obtained by the examinee. In that same row, but the first column, you will find the percentage of the standardization sample that obtained discrepancies as large as or larger than the discrepancies at hand (either factor score being higher, i.e., a one-tailed test). For a two-tailed test, double the percentage figure found in the first column. For example, a discrepancy of 5.5 points between the lower Freedom From Distractibility factor score and a higher Verbal Comprehension factor score is found in less than 1% of the population. The same discrepancy (either score being higher) is found to characterize 2% of the population. This table was created by using the subest intercorrelation matrix (all ages) in the WISC-R manual (Wechsler, 1974, p. 47) to compute the standard deviation of the difference between each pair of factor scores or composite scores, along with the percentage of the population expected to exhibit differences of various magnitudes.
E
_ _
3.19 3.45 3.12 3.78 _
_ _ _
2.64 2.85 2.58 3.15 _
_ _ _
.Ol
_ _
.05
_ _ _ 3.82 4.03 3.36 4.27
3.17 3.34 2.78 3.53 _
_
.Ol
_ _ _
_
.05
3 Perceptual Organization subtests (PO)
3.40 3.60 2.93 3.83 3.83
_ _ _
.OS
(or Composite)
4.06 4.31 3.51 4.59 4.59
_
_ _ _
_
.01
_ _ _ _
_
2.80 2.86 3.05 _
.05
_ _ _ _ _ _ _ _ _
3.43 3.50 3.73
.Ol
3 Freedom from Distractibility subtests (FD)
3.13 3.45 3.04 3.56 3.69 3.96 3.08 4.25 _
_ _
.05
3.65 4.03 3.55 4.16 4.31 4.62 3.60 4.96 _
_ _ _
.Ol
8 Subtests of FS, nonattentional composite
Scores on the WISC-R
of scaled score from the mean of:
5 Perceptual Organization subtests PO,)
Deviation
Table 5 Bet\veen Scaled Scores and Factor
3.19 3.52 3.10 3.64 3.78 4.05 3.15 4.36 4.36
_
.05
3.73 4.13 3.63 4.26 4.42 4.74 3.68 5.09 5.09
_
.Ol
9 Subtests of FS, nonattentional
.Yote: Table 5 5ho~s for any individual the minimum differences (between a subtest scaled score and a factor or composite score) that are significant at the .05 and .01 levels. Thi\ table \\as constructed by ustng the all-ages intercorrelation matrix in the WISC-R manual (Wechsler, 1974, p. 37) and formulas presented in Sattler (1982. p. 568), including the Bonferroni inequality described there.
Arithmetic Digit Span Coding Information Similarities Vocabular) Comprehension Picture Completion Picture Arrangement Bloch Design Object Assembly Mares
Differences
3 Verbal Comprehension subtests (VC)
Significant
Clampit
and Silver
403
three-factor analysis will produce values for the “nonattentional” composites of FS, or FS, that are correspondingly higher than the Full Scale IQ (and more in line with the vocabulary and verbal aptitude scores earned on group-administered tests). In short, removing the effect of the three “attentional” or Third-Factor subtests can help to clarify a confusing profile. Where there is a highly discrepant Third Factor, the clinician needs to avoid making a simplistic judgment that this low Freedom From Distractibility score necessarily implies an attentional weakness. While a low score on Coding may be caused by attentional weaknesses, it may also reflect undue concern about forming the shapes accurately, or simply poor pencil dexterity. Likewise, low scores on Arithmetic may be due to inadequate math education rather than attentional weaknesses. Therefore, when the Third Factor is computed and found to be divergent, the clinician should try to rule out alternative explanations and be cautious if the low factor score is caused by an extremely low value for only one of the three subtests (the other two being at or above the mean of all subtests). An accurate interpretation requires examination of the entire profile, as well as anecdotal observations of the testing behavior, and consideration of previous educational testing. Specific clinical advice regarding Third Factor interpretation can be found in Kaufman (1979, pp. 74-85), where minimal requirements for interpretation are presented, particular profiles examined in detail, and errors of overinterpretation discussed. For the clinician who uses them with caution, the tables presented here allow a threefactor analysis using factor scores rather than the more cumbersome (and possibly misleading) deviation quotients. The tables are somewhat less accurate for students under the age of 8.0, since this age group is administered Coding A rather than Coding B. The clinician may use these tables confidently, however, for all children 8.0 years old or older despite variable factor loadings at some of the older ages.
REFERENCES Balinsky, B. (1941). An analysis of the mental factors of various age groups from nine to sixty. Genetic Psychology
Monograph,
23, I91 -234.
Clampit, M., Adair, J., & Strenio, J. (1983). Frequency of discrepancies between deviation quotients on the WISC-R: A table for clinicians. Journal of Consulting and Clinical Psychology, 51, 195-796. Cohen, J. (1952a). A factor-analytically based rationale for the Wechsler-Bellevue. Journal of Consulting Psychology, 16, 272-271. Cohen, J. (1952b). Factors underlying Wechsler-Bellevue performance of three neurospsychiatric groups. Journal of Abnormal and Social Psychology, 47, 359-65. Cohen, J. (1957a). A factor-analytically based rationale for the Wechsler Adult Intelligence Scale. Journal of Consulting Psychology, 21, 451-457. Cohen, J. (1957b). The factorial structure of the WAlS between early adulthood and old age. Journal of Consulting Psychology, 21, 283-290. Cohen, J. (1959). The factorial structure of the WISC at ages 7-6, 10-6, and 13-6. Journal of Consulting Psychology, 23, 285-299. Gutkin, T. B. (1978). Some useful statistics for the interpretation of the WlSC-R. Journal of Consulting and Clinical Psychology, 46, 156 1- 1563. Gutkin, T. B. (1979). The WISC-R Verbal Comprehension, Perceptual Organization, and Freedom from Distractibility deviation quotients: Data for practitioners. Psychology in the Schools, 16, 359-360. Hale, R. L. (1981). Concurrent validity of the WISC-R factor scores. Journal of School Psycholog_v, 15, 172-175.
Journal
404
of School
Psychology
Hollenbeck, G., & Kaufman, (1973). Factor analysis of the Wechsler Preschool and Primary Scale of Intelligence (WPPSI). Journal of Clinical Psychology, 29, 41-45. Kaufman, A. (1975). Factor analysis of the WISC-R at eleven age levels between 6 and ‘% and 16 and ?Z Journal of Consulting und Clinical Psychology, 43, 135-147. Kaufman, A. (1979). Intelligenr testing with [he WISC-R. New York: Wiley. Ownby, R., & Matthews, C. (1985). On the meaning of the WISC-R Third Factor: Relations to selected neuropsychological measures. Journal of Consulting and Clinical Psychology, 53, 53 I-534. Sattler, J. M. (1974). Assessmeni of children’s intelligence. Philadelphia: W. B. Saunders. Sattler, J. M. (1982). Assessment of children’s infelligence und speciul abiliries. Boston: Allyn & Bacon. Sobotka, R., & Black, F. (1978). A procedure for the rapid computation of WISC-R factor scores. Journal of Clinical Psychology, 34, 117- 119. Stewart, K. J., & Moely, B. E. (1983). The WISC-R third factor: What does it mean? Journal of Consulting and Clinical Psychology, 51, 940-941. Tellegen, A., & Briggs, P. (1967). Old wine in new skins: Grouping Wechsler subtests into new scales. Journal of Consulting Psychology, 31, 499-506. Wechsler, D. (1974). Manual for the Wechsler Intelligence Scale for Children-Revised. New York: The Psychological Corporation. Ysseldyke, J. E., Algozzine, B., & Epps, S. (1983). A logical and empirical analysis of current practices in classifying students as handicapped. Excepfional Children, SO, 160-166. Ysseldyke, J. E., Algozrine, B., Shinn, M. R., & McCue, M. (1982). Similarities and differences between low achievers and students classified as learning disabled. The Journul of Special Educulion, 16, 73-85. M. K. Clampit 219 Kittredge Street Boston, MA 02131 Manuscript Manuscript
received: accepted:
November 7, 1984 March 1, 1986