Impact of Measurement Error on Statistical Power: Review of an Old Paradox

Abstract The relation between test reliability and statistical power has been a controversial issue, perhaps due in part to a 1975 publication in the Psychological Bulletin by Overall and Woodward, “Unreliability of Difference Scores: A Paradox for the Measurement of Change”, in which they demonstrated that a Student t test based on pretest-posttest differences can attain its greatest power when the difference score reliability is zero. In the present article, the authors attempt to explain this paradox by demonstrating in several ways that power is not a mathematical function of reliability unless either true score variance or error score variance is constant.