Sunday, March 27, 2011

IAP Applied Psychometrics 101 Report #10: "Just say no" to averaging IQ subtest scores

Should psychologists engage in the practice of calculating simple arithmetic averages of two or more scaled or standard scores from different subtests (pseudo-composites) within or across different IQ batteries? Dr. Joel Schneider and I, Dr. Kevin McGrew say "no."

Do psychologists who include simple pseudo-composite scores in their reports, or make interpretations and recommendations based on such scores, have a professional responsibility to alert recipients of psychological reports (e.g., lawyers, the courts, parents, special education staff, other mental health practitioners, etc.) of the potential amount of error in their statements when simple pseudo-composite scores are the foundation of some of their statements? We believe "yes."

Simple pseudo-composite scores, in contrast to norm-based scores (i.e., composite scores with norms provided by test publishers/authors--e.g., Wechsler Verbal Comprehension Index), contain significant sources of error. Although they have intuitive appeal, this appeal cloaks hidden sources of error in the scores---with the amount of error being a function of a combination of psychometric variables.

IAP Applied Psychometrics 101 Report #10 addresses the psychometric issues involved in pseudo-composite scores.

In the report we offer recommendations and resources that allow users to calculate psychometrically sound pseudo-composites when they are deemed important and relevant to the interpretation of a person's assessment results.

Finally, understanding the sources of error in simple pseudo-composite scores provides an opportunity for practitioners to understand the paradoxical phenomenon frequently observed in practice where norm-based or psychometrically sound pseudo-composite scores are often higher (or lower) than the subtest scores that comprise the composite. The "total does not equal the average of the parts" phenomenon is explained conceptually, statistically, and via an interesting visual explanation based on trigonometry.


The publishers and authors of intelligence test batteries provide norm-based composite scores based on two or more individual subtests. In practice, clinicians frequently form hypotheses based on combinations of tests for which norm-based composite scores are not available. In addition, with the emergence of Cattell-Horn-Carroll (CHC) theory as the consensus psychometric theory of intelligence, clinicians are now more frequently “crossing batteries” to form composites intended to represent broad or narrow CHC abilities. Beyond simple “eye-balling” of groups of subtests, clinicians at times compute the arithmetic average of subtest scaled or standard scores (pseudo-composites). This practice suffers from serious psychometric flaws and can lead to incorrect diagnoses and decisions. The problems with pseudo-composite scores are explained and recommendations made for the proper calculation of special composite scores.

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