The continuing misinterpretation of the standard error of measurement

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Monographs, texts, and guides designed to inform readers about the meanings and interpretations of test scores frequently misinform instead, because the standard error of measurement is misapplied. The standard error of measurement, σ-sub-1(1 - r-sub-1-sub(-iI-b)-super(½), is an estimate of the variability (i.e., the standard deviation) expected for observed scores when the true score is held constant. To set confidence intervals for true scores given an observed score, the appropriate standard error is that for true scores when observed scores are held constant and estimated by σ-sub-1[r-sub-1-sub(-iI-b(1 - r-sub-1-sub(-iI-b)]-super(½); and the interval is around the estimated true score rather than around the observed score. Except in the case of perfect reliability, the estimated true score is not the observed score, but is a value regressed toward the mean. (7 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved)

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