Hamm v. Smith · ¶156

Second—and most critically—the Eleventh Circuit's sole reliance on the lower bound of Smith's lowest score refects a basic misunderstanding of statistics. When clinicians construct a confidence interval using the standard error of measurement, their calculations rely on the assumption that a defendant's test scores are normally distributed around his “true” IQ—i. e., if a defendant took a large number of IQ tests, the scores would form a bell curve centered on his “true” IQ. Cohen 176; K. Widaman, Concepts of Measurement, in The Death Penalty and Intellectual Disability 68 (E. Polloway ed. 2015). Under that assumption, an individual's score on any given test is more likely to be close to his “true” IQ than far away from it. This fact, in turn, means that the values near the center of a confidence interval are more likely estimates of the defendant's “true” IQ than the values at the…

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