Monday, March 28, 2011

Cognitive ability domain cohesion-why composite scores comprised of significantly different subtest scores are still valid

Some excellent discussion has been occurring on the NASP and CHC listservs in response to the "Just say no to averaging IQ subtest scores" blog post and report.

An issue/question that has surfaced (not for the first time) is why markedly discrepant subtest scores that form a composite can still be considered valid indicators of the construct domain. Often clinicians believe that if there is a significant and large discrepancy between tests within a composite, the total score should be considered invalid.

The issue is complex and was touched on briefly in our report and in the NASP and CHC threads by Joel Schneider. Here I mention just ONE concept for consideration.

Below is a 2-D MDS analysis of the WJ III Cog/Ach tests for subjects aged 6-18 in the norm sample. MDS also finds structure as does factor analysis. This 2D model is based on the analysis of the tests correlation matrix. What I think is a major value of MDS, and other spatial statistics, is that one can "see" the numerical relations between tests. Although the metrics are not identical, the visual-spatial map of the WJ III tests does, more-or-less, mirror the intercorrelations between tests. [Double click on image to enlarge]

So....take a look at the Gc, Grw, or Gq tests in this MDS map. All of these tests cluster closely together. Inspection of their intercorrelations finds high correlations among all measures. Conversely, look at the large amount of spatial territory covered by the WJ III Gv tests. Also look at the Ga tests (note that a red line is not connecting Auditory Attention, AA, down in the right-hand quadrant with the other Ga tests). Furthermore, even though most of the Gsm tests are relatively cohesive or tight, Memory for Sentences is further away from the other Gsm tests.

IMHO, these visual-spatial maps, which mirror intercorrelations, tell us than in humans, not all cognitive/ach domains include narrow abilities that are highly interrcorrrelated. I call it "ability domain cohesion." Clearly the different Gv abilities measured by the WJ III Gv tests indicate that the Gv domain is less cohesive (less tight) than the Gc or Grw domain. This does not suggest the tests are flawed..instead it tells us about the varying degrees of cohesiveness present in different ability domains.

Thus, for ability domains that are very very broad (in terms of domain cohesion--e.g., Gv and Ga in this MDS figure), wildly different test scores (e.g., between WJ III Spatial Relations, SR, and Picture Recognition, PR) may be valid and simply reflect that inherent lower cohesiveness (tightness) of these ability domains in human intelligence. Thus, if a person is significantly different in his/her respective Gv SR or PR scores, and these scores are providing valid indications of their relative standing on these measured abilities, then combining them together is appropriate and reflects a valid estimate of the Gv domain....which by nature is broad...and people will often display significant within-domain variability.

Bottom line. Composite scores produced by subtests that are markedly different are likely valid estimates of is just the nature of human intelligence that some of these domains are more tight or cohesive than others.
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