A Journal of Consulting and Clinical Psychology

Psretiototical.” A Journal of Consulting and Clinical Psychology I WO. Vol. 2. No. 2, 202-203

Copyright 1990 by the American Psychological Aaodatwn, Inc. 1040-3590/90/W0.75

BRIEF REPORTS

Guidelines for Interpreting W\IS-R Subtest Scores

Joel H. Kramer University of California, San Francisco Medical Center

Tables are provided that facilitate the clinical interpretation of individual Wechsler Adult Intelli- gence Scale-Revised (WAIS-R) subtest scores. Confidence intervals were computed for each possible

scaled score for each WAIS-R subtest The confidence intervals are centered around estimated true

scores and were calculated using the standard error terms for true scores. A system for converting

scores into descriptive terms is also provided.

Recognition of measurement error in psychological assess- ment has led to the publication of tables that convert an ob- tained score into a range of scores within which the examinee’s true score probably lies. Tables and formulas of this sort are currently available for use with the Wechsler Adult Intelligence Scale-Revised (WAIS-R) IQ scores (Brophy, 1986; Knight, 1983; Naglieri, 1982).

In addition to reporting IQs, clinicians also frequently use individual WAIS-R subtests as measures of specific cognitive abilities, such as short-term auditory memory, vocabulary, vi- suoconstruction. visual perception, and reasoning (Lezak, 1983). Responsible reporting of scores, however, requires awareness of the psychometric limitations of individual WAIS- R subtests as well as an understanding of the constructs the sub- tests purport to measure.

The purpose of this article is to provide guidelines for the interpretation of individual WAIS-R subtest scores. These guidelines rest on the premise that it is necessary to fully con- sider the effect a subtest’s reliability has on estimates of an ex- aminee’s true score and of the standard error of measurement around that score. It is known that for any given obtained score, there is a range of scores within which an examinee’s true score probably lies (Nunnally, 1980). The width of this range is in- versely related to the subtest’s reliability and directly related to the probability level the examiner wishes to use. The tables provided here are based on the view that this band of scores should be placed symmetrically around an examinee’s esti- mated true score rather than his or her obtained score (Brophy, 1986; Lord & Novik, 1968; Nunnally, 1980). The use of esti- mated true scores as the center point adjusts for measurement error by taking into consideration the reliability of the subtest.

It is also important for practitioners to have available a means for converting scores into descriptive terms. Wechsler (1981, p. 28) provided a scheme for classifying IQ scores into different

I thank Eileen Martin and Mark Zaslav for their valuable contribu-

tions.

Correspondence concerning this article should be addressed to Joel

H. Kramer, Memory Clinic and Alzheimer’s Center, University of Cali-

fornia, San Francisco Medical Center, 1350 Seventh Avenue, CSBS-228,

San Francisco, California 94143.

qualitative and diagnostic categories (e.g., high average or men- tally retarded). A second purpose of this article, therefore, is to adapt Wechsler’s (1981) system for use with subtest scores.

Table 1 provides the range of scores that fall one SEM below and above the estimated true score. Estimated true scores were calculated by the equation T = M + r(X – M), where T is the examinee’s estimated true score, X is the obtained score, M is the population mean score (10 in the case of WAIS-R subtests), and r is the subtest’s reliability coefficient (Nunnally, 1980). The appropriate formula for calculating the SEM around true scores

(SEMl) is SDJ[r(l – r)]” 2 where SDX is the subtest’s standard

deviation (Brophy, 1986;Dudek, 1979; Knight, 1983). This for- mula for SEM, referred to by Lord and Novik (1968) as the “standard error of estimation,” is the one recommended for es- tablishing confidence intervals; the more commonly used SEM term, SDJ.I – r)1/2, is a measure of error variance in a set of obtained scores and should not be used to estimate true score ranges (Knight, 1983). The estimated true scores and SEMs in Table 1 were calculated using the average reliability coefficients reported in the WAIS-R manual (Wechsler, 1981, p. 30).

The rows in Table 1 represent each possible obtained scaled score (1-19), and the columns represent individual subtests. Each coordinate contains the lower and upper ends of the band of scores contained within one SEMl of the estimated true score. Because the ranges are based on one SEMl, there is a 68.26% probability that the examinee’s true score fills within the range provided in Table 1 (Nunnally, 1980).

The classification scheme in Table 2 was adapted from the intelligence classifications presented by Wechsler (1981, p. 28) for IQ scores. The adaptation of the classification system was accomplished by converting the IQ ranges into standard scores (e.g., z = 0.67-1.27 = “High average”) and then by calculating the subtest scaled score equivalents of the standard scores. Wechsler’s terms for the lowest and highest scores have been replaced with less value-laden terms; Wechsler’s original terms are in parentheses. It must be emphasized that because the clas- sification scheme is typically used for comparing examinees to their age peers, only an examinee’s age-adjusted scaled scores should be used for interpretation.

As is evident in Table 1, the reliability of an individual subtest significantly affects the interpretation of a given obtained score. For example, an obtained score of 5 on Object Assembly indi-

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BRIEF REPORTS 203

Table 1

Confidence Intervals for WilS-R Subtest Scores

Scaled score

1

2

1

9

inlu

11

14

15

i ftlo

17

i slo

1 Q1?

In

1.1 2.9 1.9 3.8 2.8 4.7 3.7 5.6 4.6 6.5 5.5 7.4 6.4 8.3 7.3 9.2 8.2

10.0 9.1

10.9 100 11.8 10.8 12.7 11.7 13.6 12.6 14.5 13.5 15.4 14.4 16.3 15.3 17.2 16.2 18.1 17.1 18.9

DSp

1.4 3.7 2.2 4.5 3.1 5.3 3.9 6.1 4.7 7.0 5.6 7.8 6.4 8.6 7.2 9.5 8.0

10.3 8.9

11.1 9.7

12.0 10.5 12.8 11.4 13.6 12.2 14.4 13.0 15.3 13.9 16.1 14.7 16.9 15.5 17.8 16.3 18.6

Vo

.8 1.9 1.7 2.9 2.7 3.9 3.7 4.8 4.6 5.8 5.6 6.7 6.5 7.7 7.5 8.7 8.5 9,6 9.4

10.6 10.4 11.5 11.3 12.5 12.3 13.5 13.3 14.4 14.2 15.4 15.2 16.3 16.1 17.3 17.1 18.3 18.1 19.2

Ar

1.3 3.5 2.2 4.4 3.0 5.2 3.9 6.1 4.7 6.9 5.5 7.7 6.4 8.6 7.2 9.4 8.1

10.3 8.9

11.1 9.7

11.9 10.6 12.8 11.4 13.6 12.3 14.5 13.1 15.3 13.9 16.1 14.8 17.0 15.6 17.8 16.5 18.7

Co

1.3 3.5 2.2 4.4 3.0 5.2 3.9 6.1 4.7 6.9 5.5 7.7 6.4 8.6 7.2 9.4 8.1

10.3 8.9

11.1 9.7

11.9 10.6 12.8 11.4 13.6 12.3 14.5 13.1 15.3 13.9 16.1 14.8 17.0 15.6 17.8 16.5 18.7

Si

1.3 3.5 2.2 4.4 3.0 5.2 3.9 6.1 4.7 6.9 5.5 7.7 6.4 8.6 7.2 9.4 8.1

10.3 8.9

11.1 9.7

11.9 10.6 12.8 11.4 13.6 12.3 14.5 13.1 15.3 13.9 16.1 14.8 17.0 15.6 17.8 16.5 18.7

PC

1.5 3.9 2.3 4.7 3.2 5.5 4.0 6.3 4.8 7.1 5.6 7.9 6.4 8.7 7.2 9.6 8.0

10.4 8.8

11.2 9.6

12.0 10.4 12.8 11.3 13.6 12.1 14.4 12.9 15.2 13.7 16.0 14.5 16.8 15.3 17.7 16.1 18.5

PA

2.0 4.7 2.8 5.4 3.5 6.1 4.2 6.9 5.0 7.6 5.7 8.4 6.5 9.1 7.2 9.8 7.9

10.6 8.7

11.3 9.4

12.1 10.2 12.8 10.9 13.5 11.6 14.3 12.4 15.0 13.1 15.8 13.9 16.5 14.6 17.2 15.3 18.0

BD

1.2 3.2 2.0 4.0 2.9 4.9 3.8 5.8 4.6 6.7 5.5 7.5 6.4 8.4 7.3 9.3 8.1

10.1 9.0

11.0 9.9

11.9 10.7 12.7 11.6 13.6 12.5 14.5 13.3 15.4 14.2 16.2 15.1 17.1 16.0 18.0 16.8 18.8

OA

2.5 5.3 3.2 6.0 3.8 6.6 4.5 7.3 5.2 8.0 5.9 8.7 6.6 9.4 7.2

10.0 7.9

10.7 8.6

11.4 93

12.1 10.0 12.8 10.6 13.4 11.3 14.1 12.0 14.8 12.7 15.5 13.4 16.2 14.0 16.8 14.7 17.5

DSy

1.5 3.8 2.3 4.6 3.1 5.4 3.9 6.2 4.7 7.1 5.6 7.9 6.4 8.7 7.2 9.5 8.0

10.3 8.8

11.2 97

12.0 10.5 12.8 11.3 13.6 12.1 14.4 12.9 15.3 13.8 16.1 14.6 16.9 15.4 17.7 16.2 18.5

Note. WMS-R = Wechsler Adult Intelligence Scale-Revised; In = Information; DSp = Digit Span; Vo = Vocabulary; Ar = Arithmetic; Co = Comprehension; Si = Similarities; PC = Picture Completion; PA = Picture Arrangement; BD = Block Design; QA = Object Assembly; DSy = Digit Symbol.

cates a true score between 5.2 and 8.0. Considerable caution

must be exercised in interpreting such a score, because the esti-

mated true score falls within a rather broad range, from border-

line to average. In contrast, the meaning of more reliable sub-

tests such as Vocabulary can be reported with greater certainty;

Table 2

Classification of Ability Levels for Individual

WAIS-R Subtest Scores

Subtest score

16 and above 14.0-15.9 12.0-13.9 8.0-11.9 6.0-7.9 4.0-5.9 3.9 and below

Classification

Significantly above average (very superior) Above average (superior) High average (high average) Average (average) Low average (low average) Below average (borderline) Significantly below average (mentally retarded)

Note. WAIS-R = Wechsler Adult Intelligence Scale-Revised. Classifi- cations in parentheses are original terms used by Wechsler.

an obtained score of 5 on Vocabulary indicates a true score be-

tween 4.6 and 5.8 and is in the borderline range.

The bands of scores in Table 1 are based on the average reli-

ability coefficients for the entire WMS-R standardization sam-

ple. These scores provide reasonably accurate and conservative

confidence intervals for most of the subtests across most age

groups. The subtests of the WAIS-R are least reliable for youn-

ger subjects, however. Eight of the 11 reliability coefficients for

the 16-17-year-old group were lower than the average reliability

coefficient by a margin of .04 or greater. Three subtests (Com-

prehension, Picture Completion, and Picture Arrangement) for

the 18-19-year-olds and four subtests (Comprehension, Simi-

larities, Picture Completion, and Picture Arrangement) for the

20-24-year-old group also have reliability coefficients that are

at least .04 less than the average. Among the older age groups,

only Object Assembly in the 70-74-year-old group falls that far

below the average. To provide more accurate confidence inter-

vals for these age groups, Tables 3 and 4 present bands of scores

based on the reliability coefficients for the less reliable subtests.

Tables 1 through 4 offer the practitioner guidelines for more

accurate clinical interpretation of individual subtest scores.

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204 BRIEF REPORTS

Table 3

Confidence Intervals for the Least Reliable WAIS-R Subtests: 16-17- Year-Olds

Scaled score

ii

6

7

10

DSp

2.3 5.1 3.0 5.8 3.7 6.5 4.4 7.2 5.1 7.9 5.8 8.6 6.5 9.3 7.2

10.0 7.9

10.7 8.6

11.4

Ar

2.1 4.8 2.8 5.5 3.6 6.2 4.3 7.0 5.0 7.7 5.7 8.4 6.5 9.1 7.2 9.9 7.9

10.6 8.7

11.3

Co

1.7 4.2 2.5 5.0 3.3 5.8 4.1 6.6 4.9 7.3 5.6 8.1 6.4 8.9 7.2 9.7 8.0

10.5 8.8

11.2

Si

1.6 4.0 2.4 4.8 3.2 5.6 4.0 6.4 4.8 7.2 5.6 8.0 6.4 8.8 7.2 9.6 8.0

10.4 8.8

11.2

PC

2.2 5.0 3.0 5.7 3.7 6.4 4.4 7.1 5.1 7.8 5.8 8.5 6.5 9.2 7.2 9.9 7.9

10.7 8.6

11.4

PA

2.6 5.5 3.3 6.1 4.0 6.8 4.6 7.5 5.3 8.1 5.9 8.8 6.6 9.4 7.3

10.1 7.9

10.8 8.6

11.4

OA

3.8 6.8 4.3 7.3 4.9 7.9 5.4 8.4 5.9 8.9 6.4 9.4 6.9 9.9 7.5

10.5 8.0

11.0 8.5

11.5

DSy

2.1 4.8 2.8 5.5 3.6 6.2 4.3 7.0 5.0 7.7 5.7 8.4 6.5 9.1 7.2 9.9 7.9

10.6 8.7

11.3

Scaled score

11

12

13

14

15

16

17

18

19

DSp

9.3 12.1 10.0 12.8 10.7 13.5 11.4 14.2 12.1 14.9 12.8 15.6 13.5 16.3 14.2 17.0 14.9 17.7

Ar

9.4 12.1 10.1 12.8 10.9 13.5 11.6 14.3 12.3 15.0 13.0 15.7 13.8 16.4 14.5 17.2 15.2 17.9

Co

9.5 12.0 10.3 12.8 11.1 13.6 11.9 14.4 12.7 15.1 13.4 15.9 14.2 16.7 15.0 17.5 15.8 18.3

Si

9.6 12.0 10.4 12.8 11.2 13.6 12.0 14.4 12.8 15.2 13.6 16.0 14.4 16.8 15.2 17.6 16.0 18.4

PC

9.3 12.1 10.1 12.8 10.8 13.5 11.5 14.2 12.2 14.9 12.9 15.6 13.6 16.3 14.3 17.0 15.0 17.8

PA

9.2 12.1 9.9

12.7 10.6 13.4 11.2 14.1 11.9 14.7 12.5 15.4 13.2 16.0 13.9 16.7 14.5 17.4

OA

9.0 12.0 9.5

12.5 10.1 13.1 10.6 13.6 11.1 14.1 11.6 14.6 12.1 15.1 12.7 15.7 13.2 16.2

DSy

9.4 12.1 10.1 12.8 10.9 13.5 11.6 14.3 12.3 15.0 13.0 15.7 13.8 16.4 14.5 17.2 15.2 17.9

Note. WUS-R = Wechsler Adult Intelligence Scale-Revised; DSp = Digit Span; Ar = Arithmetic; Co = Comprehension; Si = Similarities; PC = Picture Completion; PA = Picture Arrangement; OA = Object Assembly; DSy = Digit Symbol.

Table 4

Confidence Intervals for the Least Reliable WIIS-R Subtests: 18-74-Year-Olds

Scaled score

ii

2

3

5

7

10

1 1

12

13

14

15

16

17

18

19

18-19-year-olds

Co

1.6 4.0 2.4 4.8 3.2 5.6 4.0 6.4 4.8 7.2 5.6 8.0 6.4 8.8 7.2 9.6 8.0

10.4 8.8

11.2 9.6

12.0 10.4 12.8 11.2 13.6 12.0 14.4 12.8 15.2 13.6 16.0 14.4 16.8 15.2 17.6 16.0 18.4

PC

2.0 4.7 2.8 5.4 3.5 6.1 4.2 6.9 5.0 7.6 5.7 8.4 6.5 9.1 7.2 9.8 7.9

10.6 8.7

11.3 9.4

12.1 10.2 12.8 10.9 13.5 11.6 14.3 12.4 15.0 13.1 15.8 13.9 16.5 14.6 17.2 15.3 18.0

PA

2.3 5.1 3.0 5.8 3.7 6.5 4.4 7.2 5.1 7.9 5.8 8.6 6.5 9.3 7.2

10.0 7.9

10.7 8.6

11.4 9.3

12.1 10.0 12.8 10.7 13.5 11.4 14.2 12.1 14.9 12.8 15.6 13.5 16.3 14.2 17.0 14.9 17.7

Co

1.8 4.3 2.6 5.1 3.3 5.9 4.1 6.6 4.9 7.4 5.7 8.2 6.4 9.0 7.2 9.7 8.0

10.5 8.7

11.3 9.5

12.0 10.3 12.8 11.0 13.6 11.8 14.3 12.6 15.1 13.4 15.9 14.1 16.7 14.9 17.4 15.7 18.2

20-24-year-olds

Si

1.7 4.2 2.5 5.0 3.3 5.8 4.1 6.6 4.9 7.3 5.6 8.1 6.4 8.9 7.2 9.7 8.0

10.5 8.8

11.2 9.5

12.0 10.3 12.8 11.1 13.6 11.9 14.4 12.7 15.1 13.4 15.9 14.2 16.7 15.0 17.5 15.8 18.3

PC

1.9 4.4 2.6 5.2 3.4 6.0 4.2 6.7 4.9 7.5 5.7 8.2 6.4 9.0 7.2 9.8 8.0

10.5 8.7

11.3 9.5

12.0 10.2 12.8 11.0 13.6 11.8 14.3 12.5 15.1 13.3 15.8 14.0 16.6 14.8 17.4 15.6 18.1

PA

2.5 5.3 3.2 6.0 3.8 6.6 4.5 7.3 5.2 8.0 5.9 8.7 6.6 9.4 7.2

10.0 7.9

10.7 8.6

11.4 9.3

12.1 10.0 12.8 10.6 13.4 11.3 14.1 12.0 14.8 12.7 15.5 13.4 16.2 14.0 16.8 14.7 17.5

70-74-year-olds

OA

3.0 5.9 3.6 6.5 4.2 7.1 4.8 7.7 5.4 8.4 6.1 9.0 6.7 9.6 7.3 10.2 7.9

10.8 8.5

11.5 9.2

12.1 9.8

12.7 10.4 13.3 11.0 13.9 11.6 14.6 12.3 15.2 12.9 15.8 13.5 16.4 14.1 17.0

Note. WAIS-R = Wechsler Adult Intelligence Scale-Revised; Co = Comprehension; PC = Picture Comple- tion; PA = Picture Arrangement; Si = Similarities; OA = Object Assembly.

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BRIEF REPORTS 205

Two cautionary notes concerning the use of these tables must

be emphasized, however. First, the ranges in Table 1 represent

a band of only one SEMi. This indicates that the probability of

the examinee’s true score falling within that band is 68%.

Greater degrees of confidence require broader ranges. Inter-

ested readers should use the formula T ± SEMl(z) to compute

broader ranges; z values of 1.15, 1.44, 1.64, 1.96, and 2.58 will

yield confidence intervals of 75%, 85%, 90%, 95%, and 99%,

respectively. For some of the less reliable subtests, however, use

of broader ranges will make meaningful interpretation of an in-

dividual score more difficult.

Second, even if an examinee’s estimated true score falls

within a sufficiently narrow range, interpretation is limited by

our understanding of what that particular subtest is measuring

in that particular person. Interpretation of any individual sulv

test is difficult when the specific variance of the subtest is less

than the variance shared by all of the subtests (Silverstein,

1976). Furthermore, most of the tasks represented on the

WAIS-R are heterogeneous; performance successes and failures

can be attributed to a number of different possible underlying

cognitive skills. Observation and quantification of such vari-

ables as the types of errors made and the problem-solving strate-

gies used often provide more clues about the status of an exam-

inee’s intellectual operations than does the final achievement

score (Kaplan, 1988).

The less-than-perfect reliability of Wechsler scale subtests

also has bearing on clinical assessment research. Many investi-

gators have examined the usefulness of subtest pattern analysis

for diagnosing organicity (Wechsler, 1958), Alzheimer’s disease

(Brinkman & Braun, 1984; Fuld, 1982), learning disabilities

(Hale & Saxe, 1983), emotional disturbance (Dean, 1977), and

other disorders. These efforts have met with minimal success,

however (Filley, Kobayashi, & Heaton, 1987; Matarazzo, 1972).

Considering the caution one must exercise in interpreting a sin-

gle subtest score, it is not surprising that the reliability, and

hence validity, of formulas based on multiple subtest scores will

be limited.

References

Brinkman, S. D., & Braun, P. (1984). Classification of dementia pa- tients by a WAIS profile related to central cholinergic deficiencies. Journal of Clinical Neuropsychdogy, 6, 393-400.

Bropny, A. L. (1986). Confidence intervals for true scores and retest

scores on clinical tests. Journal of Clinical Psychology, 42.989-991.

Dean, R. S. (1977). Patterns of emotional disturbance on the WISC-R.

Journal of Clinical Psychology, 33,4186-490.

Dudek, F. J. (1979). The continuing misinterpretation of the standard error of measurement. Psychological Bulletin, 86, 335-337.

Filley, C. M, Kobayashi, J., & Heaton, R. K. (1987). Wechsler intelli- gence scale profiles, the cholinergic system, and Alzheimer’s disease.

Journal of Clinical and Experimental Newopsychology, 9,180-186.

Fuld, P. A. (1982). Behavioral signs of cholinergic deficiency in Alzhei-

mer dementia. In S. Corkin, K. L. Davis, J. H. Growdon, E. Usdin,

& R. J. Wurtman (Eds.), Alzheimer’s disease: A report of progress in research (pp. 193-196). New \brk: Raven Press.

Hale, R. L., & Saxe, J. E. (1983). Profile analysis of the Wechsler Intelli- gence Scale for Children-Revised. Journal of Psychoeducalional As-

sessment, 1. 155-161.

Kaplan, E. (1988). A process approach to neuropsychological assess- ment. In T. Boll & B. K. Bryant (Eds.), Clinical neuropsyckotogy and

brainfunction: Research, measurement, and practice (pp. 129-167). Washington, DC: American Psychological Association.

Knight, R. G. (1983). On interpreting the several standard errors of

the WAIS-R: Some further tables. Journal of Consulting and Clinical Psychology, SI, 671-673.

Lezak, M. D. (1983). Neuropsychological assessment. New \ork: Ox- ford University Press.

Lord, F. M., & Novik, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

Matarazzo, J. D. (1972). Wechsler’s Measurement and Appraisal of

Adult Intelligence (5th ed.). New York: Oxford University Press.

Naglieri, J. A. (1982). TV«> types of tables for use with the WAIS-R.

Journal of Consulting and Clinical Psychology, SO. 319-321.

Nurmally. J. C. (1980). Introduction to psychological measurement. New -York: McGraw-Hill.

Silverstein, A. B. (1976). \feriance components in the subtests of the WISC-R. Psychological Reports, 39, 1109-1110.

Wechsler, D. (1958). The measurement and appraisal of adult intelli-

gence (4th ed.). Baltimore, MD: Williams & Wilkins.

Wechsler, D. (1981). WAIS-R manual. Cleveland, OH: The Psychologi- cal Corporation.

Received May 4,1989

Revision received August 31, 1989

Accepted October 2,1989

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