A correction on the Bradley and Brand method of estimating effect sizes from published literature

Abstract

Kühberger, Scherndl, and Fritz commented on an attempt by Bradley and Brand to adjust sets of exaggerated effect sizes reported in literatures associated with underpowered Null Hypothesis Statistical Tests (NHST). Their comment highlighted two important issues: (a) the senior author, Bradley, made an error in presenting the correction formula, and (b) there is an inherent incompatibility between inferential statistics and accurate measurement. The proper formula is presented here with evidence that the formula is relatively accurate in appropriately estimating effect sizes that have been exaggerated through NHST. The term relatively accurate is used since power cannot be 100%, and thus any attempt to estimate a true effect size will be out by some relationship between the alpha level, power, and of course statistical variability of the estimates.