Using the DWI or GAI
Since Ron and I are allergic to
the blind application of numerical discrepancy formulae to determine whether a
student has a specific learning disability [9, 10], it was not our intent when
Ron generated the DWI-1 and DWI-2 tables to generate new numbers to plug into
such formulae. Rather, we hoped, following the lead of Kaufman, Prifitera,
Soklofske, Tulsky, Wilkins, Weiss, and others [4, 5, 6, 7, 8] to assist
evaluators in communicating their analyses of examinees' WISC-IV scores.
The concern with the inclusion
of low-g "processing" scores in the FSIQ long predates the revisions made in the
WISC-IV . Even with the earliest Wechsler scales, some of us simply prorated
scores for groups of tests  to avoid the "Mark Penalty" [9, p. 174; 12].
Weighting the contributions of (sub)tests by their g loading or correlation with
the total score (the WJ III model, cited by one recent poster) does not
eliminate the contribution of low-g, so-called "processing" (sub)tests. That
procedure merely diminishes their contribution in proportion to their lack of
relationship to the total score or g. Colin Elliott's approach , rather
than weighting subtests on the basis of g loadings, was to include in the total
score for the DAS only subtests with relatively high g loadings and only three
CHC factors: Gc, Gv, and Gf. However, even that approach does not eliminate the
potential for the Mark Penalty [9, p.174; 12]. A student might, for example,
have visual perception weaknesses that make an occupational therapist weep and
depress scores on Gv tests dramatically and scores on some Gf tests
moderately. For such a student, the total score would disguise both strengths
As noted below in the excerpt
from Ron's discussion of the DWI tables at
http://alpha.fdu.edu/psychology/WISCIV_DWI.htm, one would not routinely look
up such scores for examinees. However, there are some cases in which there are
(a) no significant differences within VCI, (b) no significant differences within
PRI, (c) no significant differences within WMI, (d) no significant differences
within PSI, (e) no significant difference between VCI and PRI, and (f) no
significant difference between WMI and PSI, but there are (g) significant
differences between VCI and FDI , between PRI and PSI, or both. In that case,
as Colin Elliott [13, p. 88] says with regard to the Differential Ability
Scales, "If its contributing cluster scores are significantly diverse, we would
conclude that the [total score] alone provides an incomplete description of the
child's cognitive abilities as measured by the subtests."
Under the circumstances outlined
above, a more detailed understanding of the child's cognitive functioning that
day on that test might be obtained by considering the VCI and PRI subtests as
one group (DWI-1, GAI) and the WMI and PSI subtests as another group (DWI-2,
SCAD). Children with very low FSIQ scores are likely to have DWI-1 < DWI-2, and
children with very high FSIQ scores are likely to have DWI-1 > DWI-2, because of
the higher g loadings of DWI-1 than DWI-2 subtests, but that is not always the
case, and an unexpected outcome should trigger further investigation. As with
all test scores, DWI (GAI and SCAD) scores would simply serve to generate
hypotheses that one would pursue through review of records, classroom
observations, questionnaires, interviews, and additional assessment.
Flanagan and Kaufman 
provide a cogent and detailed discussion (pp. 125 - 132), with specific
numerical guidelines, of when and how to use their GAI tables (pp. 331 – 334) as
part of their overall approach to WISC-IV interpretation (pp. 121 – 170). As
Cecil Reynolds and others have explained, there are differences between tables
based on Tellegen and Briggs procedures, depending, for example on whether the
scores are derived from sums of scaled scores on the subtests or from sums of
standard scores on the indices, and those tables would differ from tables
derived directly from original normative data [5, 6].
We think that there are clearly
circumstances, as outlined above, in which it makes sense to use the DWI-1 (GAI)
and DWI-2 scores to help understand a child's current intellectual performance
on the WISC-IV. As Cathy Fiorello and others have commented, it would not make
sense to use the DWI-2 or SCAD score as an estimate of higher-level cognitive
Guy McBride raised the question
of whether it would make sense to use the DWI-1 or GAI score as a measure of
cognitive ability in determining whether there were a severe discrepancy between
levels of ability and achievement. We would consider this an instance of Willis
and Dumont's Mark Penalty [9, p. 174; 12]. If a student has weaknesses in basic
sensory, motor, or psychological processes (e.g., visual impairment, hearing
loss, cerebral palsy, oral language disorder, word-finding impairment, auditory
perception, visual perception, processing speed, working memory, etc.), we think
it is only reasonable to seek a measure of intelligence that is not contaminated
by weaknesses that have been documented by testing (other than the cognitive
ability test itself), observation, classroom performance, and other sources of
information. In fact, Ron Dumont has said that the intelligence test for a
child should not be selected until other assessment is completed. If you are
trying to assess thinking, reasoning, and problem-solving ability, you do not
want to use intelligence tests that require a blind child to copy block designs
or a child with an oral language disorder to define words. You want an
intelligence measure that is not contaminated by the documented weaknesses, even
– or especially – if those weaknesses are in abilities important to intellectual
Regulations regarding evaluation of children are also helpful in this
regard: “Tests are selected and administered so as best to ensure that if a test
is administered to a child with impaired sensory, manual, or speaking skills,
the test results accurately reflect the child's aptitude or achievement level
or whatever other factors the test purports to measure, rather than reflecting
the child's impaired sensory, manual, or speaking skills...” [§300.541 (c) (2)
(e)]. (bold, italic added)
The independent documentation of
the excluded weaknesses is, we think, very important. It is not reasonable to
follow the above guidelines or the very explicit ones developed by Flanagan and
Kaufman [14, pp. 125 – 132] merely as a post-hoc effort to find a higher score.
The logic must, we think, include independent confirmation that we are excluding
a documented motor, sensory, or basic-process weakness. In that case, use of
the DWI-1 or GAI instead of the FSIQ or use of a different test (e.g., DAS
rather than WISC or WJ) or use of a highly specialized test (e.g., LIPS-R) or
use of only verbal or only visual or only motor-free portions of a test seems to
me to be entirely justified.
. . . . Examiners may wish to
report DWIs when the Verbal (VCI) and Perceptual (PRI) abilities are found to
be close to one another yet significantly different from those of the Working
Memory (WMI) or Processing Speed (PSI) abilities. . . . These tables were
developed using the WISC-IV subtest intercorrelations (Table 5.1, page 51,
WISC-IV Technical and Interpretive Manual)
and the Tellegen and Briggs procedure.
Conceptually, the Dumont-Willis DWI-1 Index parallels the General Ability
Index (GAI) developed by Prifitera, Weiss, and Saklofske
and by Tulsky, Saklofske, Wilkins, & Weiss
for the sum of scaled scores for the VCI and POI subtests of the WISC-III and
WAIS-III. Unlike the DWI tables, the GAI tables are based directly on the WISC-III
and WAIS-III normative data. Similarly, the Dumont-Willis DWI-2 Index is based
on the sum of scaled scores for the Digit Span and Letter-Number Sequencing (WMI)
and Coding and Symbol Search (PSI) subtests. This score is very similar to
Alan Kaufman's "third factor"
scores. It should be computed and considered only when the four WMI and PSI
subtest scores are close to one another and substantially separate from the
VCI and PRI subtests. In those cases, the DWI-1 and DWI-2 scores may be an
efficient alternative means of summarizing the 10 WISC-IV core subtests, but
they must never be confused with normative WISC-IV factor and IQ scores. . . .
Estimates of overall abilities calculated in this way should always be clearly
identified as DWI scores in both text and tables of reports. These scores must
not be confused with the Full Scale IQ, although they may be more useful
estimates of intellectual ability in some cases, for example, for some gifted
children and for some children with relative weaknesses in working memory
and/or processing speed. For the latter group, the DWIs may help avoid Dumont
and Willis's Mark Penalty,
the depression of a measure of intelligence by a low score on a measure of a
student's specific weakness. Other children may score significantly higher on
the WMI and PSI indices than on the VCI and PSI indices, which may mask
important difficulties with conceptual thinking if the FSIQ is used without
We hope these tables prove
useful until Prifitera, Tulsky, Saklofske, Weiss, and/or Wilkins provide us
with normative data.
Comment from Dr Larry Weiss regarding the differences
between the DWI, Flanagan and Kaufman'd tables, and the GAI provided by the
PsychCorp (personal communication, Dr. Larry Weiss, November 11, 2004):
The Psych Corp tables are developed directly from the standardization
data, rather then the Tellegan & Briggs forumula used by others. While
similar to the tables found on your website, and in Kaufman & Flanagan
(2004), there are differences in the tails. Scores on the Psych Corp GAI
will be slightly higher in the upper portion of the distribution, and
slightly lower in the lower portion of the distribution. Thus, high
functioning children will obtain higher GAI scores, and low functioning
children will obtain lower GAI scores, using the Psych Corp GAI tables as
compared to the Dumont and Willis Index, or the GAI tables provided by
Kaufman & Flanagan.
On average, these differences are about 2 to 3 points in the tails, but
can be as high as 6 points in isolated cases. Near the middle of the
distribution, the Psych Corp GAI tables yield scores identical to the other
 Wechsler, D. (2003). Wechsler
Intelligence Scale for Children (4th ed.) (WISC-IV). San Antonio,
TX: The Psychological Corporation.
 Wechsler, D. (1991). Wechsler
Intelligence Scale for Children (3rd ed.) (WISC-III). San
Antonio, TX: The Psychological Corporation.
 Wechsler, D. (2003). WISC-IV
Technical and Interpretive Manual. San Antonio, TX: The Psychological
 Tellegen, A., & Briggs, P. (1967). Old
wine in new skins: Grouping Wechsler subtests into new scales. Journal of
Consulting Psychology, 31, 499-506.
 Prifitera, A., Weiss, L. G., &
Saklofske, D. H. (1998). WISC-III in context. In A. Prifitera & D. H. Saklofske
(Eds.) WISC-III clinical use and interpretation: Scientist-practitioner
perspectives (pp. 1-38). San Diego: Academic Press.
 Tulsky, D. S., Saklofske, D. H.,
Wilkins, C., & Weiss, L. G. (2001). Development of a General Ability Index for
the Wechsler Adult Intelligence Scale–Third Edition. Psychological
Assessment, 13, 566-571.
 Kaufman, A. S. (1979). Intelligent
testing with the WISC-R. New York: Wiley Interscience.
 Kaufman, A. S. (1994). Intelligent
testing with the WISC-III. New York: Wiley Interscience.
 Willis, J. O. & Dumont, R. P. (2002,
pp. 131-132). Guide to identification of learning disabilities (3rd
ed.). Peterborough, NH: authors. [http://alpha.fdu.edu/psychology]
Dumont, R., Willis, J., & McBride, G. (2001). Yes, Virginia, there is a
severe discrepancy clause, but is it too much ado about something? The
School Psychologist, APA Division of School Psychology, 55 (1), 1,
 Sobotka, K. R., & Black, F.
W. (1978). A procedure for the rapid computation of WISC-R factor scores.
Journal of Clinical Psychology. 34, 117-119.
 Elliott, C. D. (1990).
Differential Ability Scales: Introductory and technical handbook. San Antonio,
TX: The Psychological Corporation.
 Flanagan, D. P., & Kaufman, A. S. (2004).
Essentials of WISC-IV assessment. New York: Wiley.