Archives of Clinical Neuropsychology
19 (2004) 227–243
A proposed method to estimate premorbid intelligence
utilizing group achievement measures
from school records夽
Lyle E. Baade a,∗ , Mike R. Schoenberg b,1
a
Department of Psychiatry and Behavioral Sciences, University of Kansas School of Medicine—Wichita,
1010 N. Kansas, Wichita, KS 67214-3199, USA
b
Department of Psychology, Wichita State University, Wichita, KS, USA
Accepted 20 January 2003
Abstract
Estimating premorbid cognitive functioning is an important part of any neuropsychological evaluation. This estimate is the benchmark against which current cognitive functioning is compared to
establish the existence, degree, and rate of cognitive decline. Typically methods used to estimate premorbid cognitive functioning are based on; (1) demographic information, (2) combined current test
performance with demographics, and (3) current reading (word recognition) ability. These approaches
each have drawbacks including difficulty estimating premorbid abilities of people close to the extremes
of intellectual functioning (i.e., estimating the premorbid ability of individuals in the gifted or borderline
intellectual ranges). The current study reviewed the existing data comparing commonly used group administered achievement and college board tests with the Wechsler IQ tests. It is proposed that clinicians
may predict premorbid cognitive functioning by applying the well-known predicted-difference method
to estimate IQ from group administered achievement test scores. The correlations between group administered achievement and college board tests with the Wechsler IQ tests are reviewed and the descriptive
statistics of selected group administered achievement and college board tests are presented.
© 2003 Academy of Neuropsychology. Published by Elsevier Ltd. All rights reserved.
Keywords: Premorbid intelligence; School records; Cognitive functioning; Predicting IQ
夽
This article is based, in part, upon a poster presented at the 20th Annual Conference of the National Academy
of Neuropsychology in Orlando, FL, November 15–18, 2000.
∗
Corresponding author. Tel.: +1-316-293-2647; fax: +1-316-293-1863.
E-mail address: [email protected] (L.E. Baade).
1
Present address: Department of Psychiatry and Behavioral Sciences, University of Oklahoma Health Sciences
Center, USA.
0887-6177/$ – see front matter © 2003 National Academy of Neuropsychology.
doi:10.1016/S0887-6177(03)00092-1
228
L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
Estimating premorbid cognitive functioning is crucial in establishing the presence of cognitive decline in any neuropsychological evaluation (e.g., Lezak, 1995). The estimate of an
individual’s cognitive functioning is the benchmark against which current neuropsychological
functioning is compared, in order to establish the existence, degree, and rate of cognitive decline. Established methods to estimate premorbid intelligence scores include: (a) demographically based regression equations (Barona, Reynolds, & Chastain, 1984; The Psychological
Corporation, 2001a), (b) best current performance of the Wechsler Adult Intelligence Scale—
Revised (WAIS-R; Wechsler, 1981) (e.g., Lezak, 1983, 1995), and (c) current reading ability (e.g., Blair & Spreen, 1989; Schwartz & Saffran, 1987; The Psychological Corporation,
2001a). Some authors have combined demographic and current ability measures (Crawford,
Stewart, Parker, Besson, & Cochrane, 1989; Krull, Scott, & Sherer, 1995; Schoenberg, Scott,
Duff, & Adams, 2002; The Psychological Corporation, 2001a; Vanderploeg & Schinka, 1995).
These approaches generally result in large standard errors of estimate (Graves, Carswell, &
Snow, 1999; Veiel & Koopman, 2001) and some, particularly the best performance and
demographically based methods, routinely overestimate premorbid intellectual functioning
(e.g., Mortensen, Gade, & Reinisch, 1991; Paolo, Ryan, Troster, & Hilmer, 1996). Thus,
large differences between estimated premorbid IQ and current test scores are necessary before a clinician can infer that an individual’s cognitive functioning has significantly changed
(Veiel & Koopman, 2001).
Another estimate of premorbid IQ is based on historical data (i.e., achievement tests) (e.g.,
Lezak, 1983, 1995; Putnam, Ricker, Ross, & Kurtz, 1999; Schinka & Vanderploeg, 2000).
Many American school systems routinely administer standardized group achievement tests that
include: California Achievement Test (CAT/5; CTB/McGaw-Hill, 1992), Comprehensive Test
of Basic Skills (CTBS; CTB/McGaw-Hill, 1991), Iowa Tests of Basic Skills (ITBS; Hoover,
Hieronymus, Frisbie, & Dunbar, 1996), Metropolitan Achievement Test (MAT; Balow et al.,
1992), or Stanford Achievement Test (Stanford/8; The Psychological Corporation, 1992a).
Most college bound students take either the Scholastic Aptitude Test (SAT; College Board
Tests Inc., 1995) or the American College Test (ACT; American College Testing Program,
1987) as a college entrance requirement. These measures are employed as predictors of future
academic success (e.g., American College Testing Program, 1987; College Board Tests Inc.,
1995; Wikoff, 1979) and they correlate highly with measures of intelligence (e.g., Wechsler,
1991). In fact, state laws defining learning disabilities in children rely on the strong relationship between achievement and intelligence (Education for All Handicapped Children Act,
1975; Shepard, 1980). Ability-achievement discrepancies are commonly determined by the
predicted-difference method in which achievement is predicted from performance on an intelligence test (e.g., Reynolds, 1985; The Psychological Corporation, 1992b, 1997, 2001b). The
obtained IQ score is used in a regression equation to predict the person’s performance on a
standardized measure of academic achievement. The discrepancy between the predicted and
actual achievement test scores is evaluated to determine the probability that the difference occurred by chance. The predicted-difference method is dependent upon the correlation between
achievement and IQ tests as well as the internal consistency and standard deviation (S.D.) of
the two measures (Shepard, 1980).
Despite the frequency with which standardized achievement scores are predicted from intelligence test scores, there has been little research or clinical attention given to estimating
L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
229
intelligence from achievement tests (Crano, Kenny, & Campbell, 1972; Graves et al., 1999;
Murrey, 2000; Putnam et al., 1999). Further, although it is common practice to use academic
performance (grades) and/or achievement test scores as an index of premorbid cognitive functioning, the literature is devoid of guidelines for predicting an individual’s IQ score from a
group administered achievement test score (e.g., Graves et al., 1999; Lezak, 1995; Lynch &
McCaffrey, 1997; Murrey, 2000; Putnam et al., 1999; Schinka & Vanderploeg, 2000). The
exception is an unpublished dissertation by Collins (2000) that developed a regression equation to estimate Wechsler Adult Intelligence Scale—Third Edition (WAIS-III; Wechsler, 1997)
FSIQ from ACT Composite scores and age. Derived from a sample of 65 university students
without a history of neurological insult, the regression formula accounted for 65.7% of the
variance in WAIS-III FSIQ scores while ACT scores alone correlated .757 with WAIS-III
FSIQ. The generalizability of this study is limited by the sample characteristics (i.e., small
homogeneous sample of college students) and because IQ estimates can only be derived
from the ACT. Another method that may be employed broadly is to predict premorbid intellectual functioning using the predicted-difference methodology. It is proposed that the
same algorithms used for learning disability determinations be applied to estimate premoribid
IQ functioning.
1. Methodology
A literature search from 1972 to January 2002 was conducted utilizing the Psychlit and
ERIC electronic databases entering the following search words separately and in combination: (a) predict, (b) intelligence, (c) IQ, (d) achievement, (e) Wechsler, (f) estimate, (g)
relationship, (h) correlation, (i) association, (j) standardized achievement test, (k) ACT, (l)
SAT, (m) WAIS, (n) WAIS-R, (o) WAIS-III, (p) WISC, (q) WISC-R, (r) WISC-III, (s) ITBS,
(t) CTBS, (u) MAT, (v) SAT, (w) Metropolitan, (x) Stanford, (y) Iowa Test of Basic Skills,
and (z) Comprehensive Test of Basic Skills. In addition, we examined all articles referenced
by the Thirteenth Mental Measurements Yearbook (Impara & Plake, 1998) that reviewed
the: Wechsler Adult Intelligence Scale (WAIS; Wechsler, 1955), WAIS-R, WAIS-III, Wechsler Intelligence Scale for Children (WISC; Wechsler, 1949), Wechsler Intelligence Scale for
Children—Revised (WISC-R; Wechsler, 1974), or Wechsler Intelligence Scale for Children—
Third Edition (Wechsler, 1991) and inspected the abstract of each article to determine if the
study assessed the relationship between the Wechsler tests and a group administered achievement test. The references of each article were reviewed for additional relevant studies. All articles that reported a relationship between a Wechsler test and a group administered achievement
test were reviewed in terms of study design and achievement measure(s) employed. Studies using single subject designs and those that did not use a standardized group achievement test were
removed from further analyses. Finally, all studies that did not report a correlation between a
group administered achievement test index score and at least one Wechsler IQ score were excluded. When available, we report the correlations of the standardized group achievement test
Composite, Reading, and Arithmetic scores with the Wechsler Verbal, Performance, and Full
Scale IQ scores. Whenever possible, standardized scores adjusted for age and education are
reported.
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L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
Table 1
Pearson correlation coefficients between Wechsler intelligence tests and group achievement tests
Author
Karnes et al. (1986)
CAT (Reading)
CAT (Math)
CAT (Spelling)
CAT (Composite)
N
27
Oakland (1983)
CAT (Reading)
CAT (Math)
343
Poteat, Wuensch, and
Gregg (1988)
CAT (Composite)
CAT (Composite)
162
Population
IQ test
Gifted students
WISC-R
Nonreferred children
(stratified sample)
WISC-R
Special edition referrals
WISC-R
79
83
African–American
Caucasian
Hartlage and Boone (1977)
CTBS (Reading)
CTBS (Arithmetic)
CTBS (Spelling)
37
Fourth and fifth grade
children
WISC
Hartlage and Boone (1977)
CTBS (Reading)
CTBS (Arithmetic)
CTBS (Spelling)
37
Fourth and fifth grade
children
WISC-R
Dean (1979)
ITBS (Reading)
ITBS (Arithmetic)
ITBS (Vocabulary)
ITBS (Composite)
46
Mexican–American
children
WISC-R
Johnson and McGowan (1984)
ITBS (Reading)
ITBS (Arithmetic)
ITBS (Vocabulary)
ITBS (Composite)
56
Elementary school children
WISC-R
Stroud and Blommers (1957)
ITBS (Reading)
ITBS (Arithmetic)
ITBS (Spelling)
Egeland, DiNello,
and Carr (1970)
MAT (Reading)
MAT (Spelling)
Reschly and Sabers (1979)a
MAT (Reading)
MAT (Mathematics)
MAT (Reading)
MAT (Mathematics)
621
82
910
Special edition referrals
Third grade children (WISC
administered in first grade)
Nonreferred children
Grade 1 (N = 181)
Grade 3 (N = 181)
Grade 3 (N = 187)
VIQ
PIQ
FSIQ
.33
.11
.04
.18
.41
.53
−.07
.49
.44
.40
−.03
.42
–
–
–
–
.70
.66
–
–
–
–
.50
.65
.72
.68
.52
.56
.58
.51
.70
.69
.56
.70
.62
.46
.51
.59
.57
.68
.67
.56
.41
.57
.61
.63
.35
.36
.49
.41
.44
.53
.59
.55
.33
.43
.20
.33
.26
.20
.15
.19
.37
.41
.23
.33
.58
.67
.62
.63
.52
.60
.66
.66
.67
–
–
–
–
.35
.43
–
–
–
–
–
–
–
–
.55
.59
.68
.55
WISC
WISC
WISC-R
L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
231
Table 1 (Continued )
Author
N
MAT (Reading)
MAT (Mathematics)
MAT (Reading)
MAT (Mathematics)
MAT (Reading)
MAT (Mathematics)
Wechsler (1991)
Achievement (Reading)b
Achievement (Math)b
Achievement (Total)b
Population
IQ test
Grade 5 (N = 189)
Grade 9 (N = 159)
358
6–16-year-old nonreferred
WISC-III
.70
VIQ
PIQ
–
–
–
–
–
–
–
–
–
–
–
–
.73
.71
.71
.65
.72
.69
.66
.58
.57
.68
.74
.43
.63
.74
FSIQ
a
Please see Reschly and Sabers (1979) for correlations between WISC-R FSIQ and MAT Reading and Mathematics scaled scores separately for Caucasians, African–Americans, Chicanos, Papago, and the combined sample
for Grades 1, 3, 5, 7, and 9.
b
WISC-III manual indicates that students took one of the following Achievement tests: CAT, CTBS, ITBS,
MAT, or Stanford; CAT: California Achievement Test, CTBS: Comprehensive Tests of Basic Skills, ITBS: Iowa
Tests of Basic Skills, MAT: Metropolitan Achievement Test, Stanford: Stanford Achievement Test.
2. Results
A total of 198 studies were located. Of these, 183 failed to meet inclusion criteria and were
eliminated from the study. Table 1 displays the correlations between Wechsler intelligence tests
Full Scale (FSIQ), Verbal (VIQ), and Performance (PIQ) index scores and group administered
achievement test index scores. The correlations between Wechsler FSIQ, VIQ, and PIQ with
the group administered achievement test scores2 varied from a high of r = .74 (Wechsler,
1991) between WISC-III FSIQ and Achievement test (Total) index score to a low of r = −.03
(Karnes, Edwards, & McCallum, 1986) between WISC-R FSIQ and CAT (Spelling). Sample
characteristics ranged from gifted students to educational referrals.
The number of participants in the studies ranged from 27 to 910. In general, the studies that
used small samples reported moderate correlations while those with larger samples yielded
strong relationships between the achievement test scores and Wechsler Intelligence test scores.
Review of Table 1 indicates that Spelling Composite scores correlated less with Wechsler FSIQ
than did Reading or Mathematic Composite scores. Finally, with the exception of Wechsler
(1991), there is a dearth of data on the relationship between group administered achievement
tests and the WAIS-III or WISC-III.
Table 2 provides the correlations between Wechsler intelligence tests FSIQ, VIQ, and PIQ
and college board tests. Review of Table 2 reveals that correlations between the ACT scores and
Wechsler index scores ranged from a low of r = .39 to a high of r = .87 with the ACT Composite demonstrating the strongest relationship with the WAIS-R FSIQ (Carvajal, McKnab,
Gerber, Hewes, & Smith, 1989). Only one study documented the correlation between the SAT
2
Wechsler (1991) combined the achievement tests when reporting the correlation between the WISC-III and
group administered achievement tests and did not provide the correlations for individual group administered achievement tests.
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L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
Table 2
Pearson correlation coefficients between Wechsler intelligence tests and college board tests
Author
N
Population
IQ test
Collins (2000)
ACT (Composite)
ACT (English)
ACT (Mathematics)
65
College students
WAIS-III
Carvajal et al. (1989)
ACT (Composite)
ACT (English)
ACT (Mathematics)
30
Lewis and Johnson (1985)
ACT (Composite)
ACT (English)
ACT (Mathematics)
35
Lewis and Johnson (1985)
ACT (Composite)
ACT (English)
ACT (Mathematics)
39
Steinberg, Segel, and
Levine (1967)
ACT (Composite)
ACT (English)
ACT (Mathematics)
84
Bailey et al. (1979)
SAT (Verbal)
SAT (Quantitative)
45
College students
College students
College students
College students
College students
VIQ
PIQ
FSIQ
.75
–
–
–
–
–
.75
–
–
.76
.56
.65
.62
.55
.65
.87
.70
.81
.85
.73
.62
.56
.51
.41
.77
.67
.56
.58
.46
.37
.45
.32
.35
.56
.43
.37
.71
.65
.61
–
–
–
.75
.73
.72
.73a
.39a
–
–
–
–
WAIS-R
WAIS-R
WAIS
WAIS
WAIS
a
Correlation coefficient computed between SAT and WAIS Vocabulary subtest only; ACT: American College
Test; SAT: Scholastic Aptitude Test.
and a Wechsler IQ test (Bailey & Gederman, 1979), and the data was limited to the relationship between the WAIS Vocabulary and Similarities subtest scaled scores with the SAT Verbal
and Quantitative index scores. The correlation observed between the SAT Verbal and WAIS
Vocabulary subtest scores was substantial (r = .73), while the relationship between the SAT
Quantitative score and Vocabulary subtest was small (r = .39). The WAIS Similarities score
correlated r = .40 with the SAT Verbal score and only r = .10 with the SAT Quantitative score.
Because of the difficulty in obtaining descriptive data for group administered achievement
tests, Table 3 displays descriptive statistics for the CAT/5, CTBS/5 (Fall), ITBS (Fall 1992),
MAT/7 (Fall), and Stanford/8 (Fall) for each grade.3 The slight variation in descriptive statistics
3
The data provided here is selected. For more extensive normative information, please refer to the test publisher: CAT/5 and CTBS, CTB/McGraw Hill (www.ctb.com); ITBS, Hoover et al. (1996) and Riverside Publishing
Company (www.riverpub.com); MAT, Balow et al. and The Psychological Corporation/Harcourt Brace & Company (www.hbem.com/trophy/achvtest/mat8info.htm); Stanford Achievement Test, The Psychological Corporation/Harcourt Brace & Company (www.hbem.com/trophy/achvtest/techinf.htm); SAT, College Board Tests Inc.
(www.collegeboard.com); ACT, American College Testing Program (www.act.org).
L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
233
Table 3
Means and standard deviation for group administered achievement tests
Test
Mean
S.D.
rxx
S.E.M.
CAT/5 (1991–1992 norms)
Grade 7, Level 17 (Fall)
Grade 7, Level 17 (Spring)
Grade 9, Level 19 (Fall)
Grade 9, Level 19 (Spring)
Grade 10, Level 20 (Fall)
Grade 10, Level 20 (Spring)
Grade 11, Level 21/22 (Fall)
Grade 11, Level 21/22 (Spring)
Grade 12, Level 21/22 (Fall)
Grade 12, Level 21/22 (Spring)
734
745
756
761
766
769
774
784
779
790
37.7
38.8
39.2
41.1
39.5
39.7
40.4
39.7
40.2
41.9
.98
.98
.98
.98
.98
.98
.98
.98
.98
.98
6.95
6.80
6.96
6.85
6.95
6.88
6.98
6.85
6.87
6.74
28.03
25.75
25.37
24.56
.97
.97
.97
.96
4.85
4.82
4.75
4.66
CTBS/5 (Fall)
Grade 4, Level 14
Grade 8, Level 18
Grade 10, Level 20
Grade 12, Level 21/22
88.46
85.39
74.71
76.32
ITBS (Fall 1992)
Grade 3, Level 9
Grade 7, Level 12
Grade 8, Level 13
175.8
233.4
243.9
16.48
31.56
33.90
.98
.98
.98
2.60
4.50
4.80
MAT/7 (Fall)
Grade 4, Elementary 2S
Grade 6, Intermediate 2S
Grade 7, Intermediate 3S
Grade 8, Intermediate 4S
Grade 9, Secondary 1S
Grade 10, Secondary 2S
Grade 11, Secondary 3S
Grade 12, Secondary 4S
589.5
624.8
635.1
645.3
659.1
671.1
675.6
682.3
32.7
30.3
29.8
29.9
31.5
32.1
31.4
34.0
.98
.98
.98
.98
.97
.97
.97
.98
7.06
7.31
7.43
7.45
7.15
7.01
7.18
7.11
Stanford/8 (Fall)
Grade 4, Primary 3
Grade 6, Intermediate 2
Grade 7, Intermediate 3
Grade 8, Advanced 1
Grade 9, Advanced 2
Grade 9, TASK 1
Grade 10, TASK 2
Grade 11, TASK 3
Grade 12, TASK 3
606.0
643.4
649.6
663.1
671.6
675.1
682.7
688.0
690.9
34.5
29.7
29.5
30.6
30.8
27.6
29.7
27.2
30.9
.99
.99
.99
.99
.99
.97
.98
.98
.98
9.7
9.6
9.7
9.6
9.7
8.5
8.5
8.5
8.5
S.D. = standard deviation; S.E.M. = standard error of measurement; CAT = California Achievement Test;
CTBS = Comprehensive Tests of Basic Skills; ITBS = Iowa Tests of Basic Skills; MAT = Metropolitan
Achievement Test; Stanford/8 = Stanford Achievement Test—Eighth Edition.
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L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
Table 4
Means and standard deviation for college board tests
Test
Index
ACT
National 1995
National 1988
Composite
Composite
SATa
National 2000
Composite
Verbal
Math
Mean
17.58
17.45
1019
505
514
S.D.
rxx
S.E.M.
.97
.96
0.90
0.92
208.0
111.0
113.0
.96
.90–.93
.91–.94
42.50
29–32
29–32
4.83
4.54
National 1999
Verbal
Math
505
511
110
110
.90–.93
.91–.94
29–32
29–32
National 1998
Verbal
Math
505
512
110
110
.90–.93
.91–.94
29–32
29–32
National 1997
Verbal
Math
505
511
110
110
.90–.93
.91–.94
29–32
29–32
National 1996
Verbal
Math
505
508
110
110
.90–.93
.91–.94
29–32
29–32
National 1995
Verbal
Math
504
506
110
110
.90–.93
.91–.94
29–32
29–32
National 1994
Verbal
Math
499
504
110
110
.90–.93
.91–.94
29–32
29–32
National 1993
Verbal
Math
500
503
110
123
.91
.90
31
35
National 1992
Verbal
Math
500
501
110
123
.91
.90
31
35
National 1991
Verbal
Math
499
500
110
123
.91
.90
31
35
National 1990
Verbal
Math
500
501
110
123
.91
.90
31
35
National 1989
Verbal
Math
504
502
110
120
.91
.90
31
35
National 1988
Verbal
Math
505
501
110
120
.91
.90
31
35
National 1987
Verbal
Math
507
501
110
120
.91
.90
31
35
National 1986
Verbal
Math
509
500
110
120
.91
.90
31
35
National 1985
Verbal
Math
509
500
110
120
.91
.90
31
35
L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
235
Table 4 (Continued )
Test
Index
Mean
S.D.
rxx
S.E.M.
National 1984
Verbal
Math
504
497
110
120
.91
.90
31
35
National 1983
Verbal
Math
503
494
110
120
.91
.90
31
35
National 1982
Verbal
Math
504
493
110
120
.91
.90
31
35
National 1981
Verbal
Math
502
492
110
120
.91
.90
31
35
National 1980
Verbal
Math
502
492
110
120
.91
.90
31
35
National 1979
Verbal
Math
505
493
110
120
.91
.90
31
35
National 1978
Verbal
Math
507
494
110
120
.91
.90
31
35
National 1977
Verbal
Math
507
496
110
120
.91
.90
31
35
National 1976
Verbal
Math
509
497
110
120
.91
.90
31
35
National 1975
Verbal
Math
512
498
110
120
.91
.90
31
35
National 1974
Verbal
Math
521
505
110
115
.91
.90
31
35
National 1973
Verbal
Math
523
506
110
115
.91
.90
31
35
National 1972
Verbal
Math
530
509
110
115
.91
.90
31
35
Note: ACT = American College Test; SAT = Scholastic Aptitude Test; S.D. = standard deviation.
a
Standard deviation (S.D.), reliability coefficients, and standard errors of measure (S.E.M.) for the SAT provided by College Board Tests Inc. (Gonzalez, K., personal communication, April 30, 2002). The S.D. values are
approximate and the ranges in reliability coefficients and S.E.M. represent minimum and maximum values for
administrations of the test given during that academic year.
reflects alterations in the population sample that takes the test each year and the altered item
content of group administered achievement tests on each test administration date. Despite the
variation in population samples, the internal consistency of the CAT/5, CTBS/5, ITBS, MAT/7,
and Stanford/8 range from .96 to .99. The normative data provided for each group administered
achievement tests (CAT/5, CTBS/5, ITBS, and MAT/7, Stanford/8) were derived from each
test’s national normative study. The distributions of test scores closely approximated a normal
distribution and the samples were generally representative of the U.S. student population in
terms of ethnicity, social and economic status, and region of the country.
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L.E. Baade, M.R. Schoenberg / Archives of Clinical Neuropsychology 19 (2004) 227–243
Table 4 displays the descriptive statistics for the college board exams (ACT and SAT).
Overall, these tests are well normed and, while the statistical properties of the college board tests
vary depending on the year of administration, the mean, S.D., and standard error of measure
(S.E.M.) has remained relatively stable across editions. For example, American College Testing
Program (2001) reported that the mean ACT Composite score obtained by National Normative
samples has been roughly 18 with a S.D. of 4.5 since 1988. The national normative data for the
ACT was comprised of a cross section of the U.S. high school students and was not limited to
students electing to take the exam as a college entrance requirement. Similarly, the statistical
properties of the SAT have remained relatively stable since 1972. The mean, S.D., and S.E.M.
of the SAT were derived from all the students that elected to take the SAT.
3. Discussion
Employing achievement tests is frequently cited as a means to estimate premorbid intellectual functioning in neuropsychological assessment (e.g., Lynch & McCaffrey, 1997; Putnam
et al., 1999; Schinka & Vanderploeg, 2000), but, there has been no objective methodology
proposed to derive IQ estimates from group administered achievement tests. It is proposed
that the predicted-difference method (e.g., Shepard, 1980) be used to estimate premorbid IQ
from historical standardized group achievement tests data. The predicted-difference algorithm
is a commonly used method (The Psychological Corporation, 1992b) to predict achievement
from IQ scores and determine the significance of ability-achievement discrepancies in learning disability evaluations (Reynolds, 1985). Better prediction is obtained when the correlation
between tests approaches (r = 1.0) and the S.D. of the predictor test is small. Despite the
extensive literature documenting the relationship between individually administered achievement tests, for example, Wechsler Individual Achievement Test (WIAT; The Psychological
Corporation, 1992b) and the Wechsler IQ tests (Wechsler, 1991, 1997), there is limited data
regarding the correlations between group administered achievement or college board tests and
the Wechsler IQ tests. The extensive cross-norming data of the WIAT or Wechsler Individual
Achievement Test—Second Edition (WIAT-II; The Psychological Corporation, 2001b) and
the WISC-III/WAIS-III was not included because individual achievement tests are administered in the U.S. educational system only when the student is thought to have an exceptionality,
and then the evaluation generally includes administration of a Wechsler IQ test as well (please
see the WIAT/WIAT-II or WAIS-III manuals to predict WIAT/WIAT-II scores from WAIS-III
FSIQ).
Table 5 displays the procedure for predicting WAIS-R FSIQ using a group administered
aptitude test (procedure is identical with an achievement test). The individual obtained an ACT
Composite score of 25 in 1990. Using the National Normative data for 1989, the ACT mean
score was 17.45 (college and noncollege bound students combined), with a S.D. of 4.5 unit
points. The correlation between the ACT Composite score and WAIS-R is .87 (Carvajal et al.,
1989). An ACT Composite score of 25 yielded a Z score of 1.68. The next step is using the ACT
Composite Z score to predict the WAIS-R FSIQ in Z score units (1.46) and than converting the
predicted WAIS-R FSIQ Z score to Wechsler IQ units. Finally, the standard error of estimate
(S.E.est ) was found using the correlation of the WAIS-R with the ACT (r = .87) and the
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237
Table 5
Example of estimating IQ from a college board test
ACT Composite score
ACT Composite score mean
ACT standard deviation
ACT standard error of measure
ACT reliability
WAIS-R reliability
WAIS-R correlation with ACT
X = 25.00
Mean = 17.45
S.D. = 4.5
S.E.M. = 0.92
rxx = .96
ryy = .97
rxy = .87
Converting ACT score to Z score
Z = (X − mean)/S.D. = (25 − 17.45)/4.5 = 1.68
Z = 1.68
Regression equation
Predicted Zability = rxy (Zachievement ) = .87(1.68) = 1.46
Predicted Zability = 1.46
Converting predicted ability Z to standard score units
Predicted IQ = 1.46(15) + 100 = 122
Predicted IQ = 122
Standard error of estimate
2 1/2
S.E.est = S.D.ability (1 − rxy
) = 15(1 − .757)1/2 = 15(.243)
S.E.est = 7.39
S.D. of the WAIS-R. Examination of the equation used to derive the S.E.est indicates that as
the correlation between the Wechsler IQ test and the achievement test increases, the S.E.est
decreases. Conversely, as the covariation between tests decreases, the S.E.est increases to equal
the S.D. of the Wechsler tests. The S.E.est is 7.4 FSIQ points, yielding a 95% confidence interval
of 14.5 points [1.96(7.4)]. Stated another way, we are 95% certain that the person’s WAIS-R
FSIQ was at least 107.5.
The correlations between group administered and college board achievement tests with
Wechsler FSIQ were moderate to large (Cohen, 1988), and the reliability and S.E.M. of the
group administered achievement tests were high, and rivaled those of the Wechsler IQ tests.
Indeed, the relationship between college board tests with various editions of the WAIS was
similar to the correlations reported between estimated IQ from demographic, current reading,
and other “hold” methods and obtained Wechsler IQ scores. For example, Blair and Spreen
(1989) reported that the FSIQ estimate derived from the North American Adult Reading Test
(NAART), an irregular word reading test, correlated r = .75 with actual WAIS-R FSIQ
scores, r = .83 with WAIS-R VIQ scores, but only r = .40 with actual WAIS-R PIQ scores.
Similarly, Raguet, Campbell, Berry, Schmitt, and Smith (1996) report that the Barona FSIQ
estimate correlated r = .61 with actual WAIS-R FSIQ scores while the NAART FSIQ estimate
correlated r = .73 with actual FSIQ.
When IQ scores and group achievement scores strongly covary, the S.E.est of the predicteddifference method will be minimized. For example, the S.E.est derived from the above example
was smaller than that yielded by demographic methods (e.g., Barona et al., 1984), and was similar to the S.E.est reported for reading (Blair & Spreen, 1989; The Psychological Corporation,
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2001a), and combined current performance with demographic methods (Krull et al., 1995;
Schoenberg et al., 2002; Vanderploeg, Schinka, & Axelrod, 1996). Using the ACT example, and
assuming normal distributions, a difference between estimated and obtained IQ scores greater
than 14.5 points suggests that cognitive decline has occurred in 95% of cases. This discrepancy is similar to that reported for the North American Adult Reading Test (NAART) (Blair &
Spreen, 1989), Oklahoma Premorbid Intelligence Estimate (OPIE) (Krull et al., 1995), OPIE-3
(Schoenberg et al., 2002), BEST-3 (Vanderploeg et al., 1996), or WTAR (The Psychological
Corporation, 2001a). In addition, the predicted-difference method may also compare favorably
to other methods in yielding a less restricted range of estimated IQ scores, as the demographically based and reading procedures systematically under- and over-estimate IQ scores in the
lower and upper extremes of ability (Schinka & Vanderploeg, 2000). These data indicate that
the predicted-difference method holds promise in estimating premorbid IQ and has several
advantages over other current methods.
One advantage of using historical group achievement test data to predict premorbid IQ is
that reading ability and other methods based on “hold” measures (e.g., the BEST-3 and OPIE
which use WAIS-R verbal and performance subtests and demographic data) can be adversely
affected by brain injury or dementia (e.g., Axelrod, Vanderploeg, & Rawlings, 1999; Cockburn,
Keen, Hope, & Smith, 2000; Hawkins, 1998; Larrabee, Largen, & Levin, 1985; O’Carroll,
Prentice, Murray, Van Beck, & Goodwin, 1995). Indeed, Axelrod et al. (1999) found that the
BEST-3 estimate of premorbid intellectual functioning was “not useful for head injured patients that had been in a coma for more than seven days” (p. 373). Another advantage involves
contextual demands. The motivational variables present in the school setting are likely to be
very different from those during a neuropsychological evaluation, particularly if the evaluation is part of litigation. Current reading (or WAIS-R subtest) test scores may be decreased by
dissimulation as well as brain injury. A third advantage is obtaining trends in the individual’s
premorbid functioning. It is common for a student in the U.S. public education system to take
the CTBS, ITBS, MAT, or Stanford/8 several times during elementary, middle, and high school,
followed by a college board test in high school. For example, the American College Testing
Program (2001) reported that more than one million high school students (36.4 percent of
graduating high school students) took the ACT in 1999 and the College Board Tests Inc.
(1999) reported that 1.3 million high school students (46% of graduating high school students) took the SAT. Using standardized achievement test scores from several school years
offers multiple assessments of the individual’s cognitive skills prior to suspected brain insult
and minimizes the effect of dissimulation in estimating cognitive functioning from current
performances.
A limitation to the proposed methodology is the small number of studies examining the
relationship between Wechsler intelligence tests and group administered or College Board
achievement tests. The quality of the studies varied from research using a small homogenous
sample (Dean, 1979), to data derived from a large sample of nonreferred children ranging
in age from 6 to 16 (Wechsler, 1991). Frequently, however, the correlations between IQ and
group achievement tests were derived from small homogenous samples of clinically referred
children, which decreases the variance in scores and lowers the correlation between tests. For
example, Johnson and McGowan (1984) reported a r = .36 between the ITBS Composite
and WISC-R FSIQ in a sample of 56 Mexican–American children in a parent–child education
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239
program. Despite the limitations in study samples, the relationship between IQ and group
achievement scores was generally large (see also Follman, 1984 for the generally excepted
relationship between achievement and IQ).
A statistical limitation of the proposed methodology is that the score distributions for the
group administered achievement tests vary on each administration of the test. The source for
variation in scores is that, unlike the Wechsler intelligence tests, group administered achievement tests are continually being updated with new test items (e.g., American College Testing
Program, 1987; College Board Tests Inc., 1995; The Psychological Corporation, 1992a). The
minor impact of these variations in test operating characteristics is highlighted by the small
variations in the SAT mean, S.D., and reliability from 1972 to the present. Close inspection of
the fluctuation in Verbal SAT scores, however, revealed that the variability in the mean, S.D.,
and S.E.M. has been small. For example, since 1972 the Verbal SAT S.D. has been about 110,
and the S.E.M. has only varied three points. Additionally, the correlations between the ACT
and SAT with Wechsler IQ have remained relatively stable.
A unique disadvantage to college board tests is that the sample of students taking the test is biased such that students aspiring to enter college elect to take the ACT or SAT. Clearly, the skewness of the normative groups can be a concern as prediction errors increase as the distribution
becomes less normal (Anastasi & Urbina, 1997). To address this concern, an effort was made
to obtain national standardizing data for the ACT, as this represents a large, demographically
diverse student sample, consisting of college bound and noncollege bound students (American
College Testing Program, 1987, 2001). The SAT did not provide normative data of noncollege
bound students. However, the demographic composition of the SAT sample was broad, and
the variance in scores was large and normally distributed (College Board Tests Inc., 1995,
2002; Dorans, 2002). Nevertheless, a SAT score corresponding to the mean of the SAT national norms should not be interpreted as the average performance for the U.S. high school
population.
An additional caveat to using the predicted-difference method is that while the correlations
of group achievement tests and Wechsler IQ tests were obtained from administering tests in
close temporal order, the correlation between group administered achievement scores obtained
in adolescence (e.g., 11th grade) and IQ scores in adulthood is less established. However,
Crano et al. (1972) found a strong correlation (r = .727) between students’ fourth grade ITBS
Composite scores and their sixth grade Lorge–Thorndike IQ scores (1957 version) two years
later in a large sample (N = 5,495) of nonreferred school children. The findings suggest that,
within neurologically intact individuals, the correlation between achievement in adolescence
and IQ in adulthood is likely to be large.4
The available literature supports the use of the predicted-difference method to estimate premorbid IQ in adults and adolescents. Estimates will likely be better in younger adults as the
temporal relationship between achievement and IQ scores is decreased. Estimates for children
(6–16) may be possible, although other validated methods are available (e.g., Vanderploeg,
4
Additional data in support of the hypothetisized high correlation between a group achievement test score
obtained in adolescent and a Wechsler FSIQ score during adulthood stems from research indicating that, within a
neurologically intact sample, WISC-III and WAIS-III FSIQ scores strongly covaried (r = .88; The Psychological
Corporation, 1997, p. 81).
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Schinka, Baum, Tremont, & Mittenberg, 1998). The application of this approach requires
selection of a correlation between IQ and the achievement test given. Verbal and Composite scores are better correlated with IQ scores than are math scores. It is recommended
that estimates not be based from Spelling achievement test scores, as correlations between
Spelling test scores and IQ scores ranged from r = −.03 (Karnes et al., 1986) to r = .67
(Stroud & Blommers, 1957). School records normally provide the individual’s standardized
achievement test standard and raw scores as well as national percentile rank. Often, the test
publisher can provide appropriate descriptive statistics, or clinicians may find Tables 1–4
helpful. An alternative is to compute a standard score using the age referenced percentile
score (Braden, Wollack, & Allen, 1995). Finally, it is recommended that clinicians use national norms rather than local percentile data to compute an individual’s achievement test
Z-score.
While the applicability of the predicted-difference method offers neuropsychologists a supplemental method to predict premorbid intellectual functioning that has advantages over current
hold measures, empirical validation of this approach is needed. Additional data that investigates the relationship between group administered achievement tests (e.g., ACT, SAT, and
CAT/5) and the WISC-III or WAIS-III, is needed (but see Collins, 2000). The correlation
between previously administered group achievement test scores and IQ scores obtained 5–20
years later should also be assessed. Future research could also investigate if estimates of specific cognitive abilities may be obtained from group administered achievement subtest scores
(e.g., math quantitative may correlate highly with WMS-III Working Memory Index). The
differential estimate of specific cognitive abilities (e.g., problem solving, memory, divided
attention) has far reaching implications, as it is recognized that predictions of FSIQ is a crude
estimate of discrete cognitive functions (e.g., Lezak, 1995; Schinka & Vanderploeg, 2000;
The Psychological Corporation, 2001a).
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