Post hoc power analysis

Abstract

The objective of a post hoc review of statistical power is to determine the average power of tests used in a particular field. Because most theories in psychology are not sufficiently advanced to provide an exact prediction of effect size, post hoc reviews invariably calculate the power of a test in terms of the test's ability to detect the expected effect size as estimated from the data. However, to achieve their stated objective, such reviews should instead compute the expected power of a test over the range of likely effect sizes. Current practice commits the statistical error of confusing a function of an expectation with the expectation of a function. In consequence, post hoc power reviews overestimate the average power of statistical tests, often by a substantial margin. (PsycInfo Database Record (c) 2025 APA, all rights reserved)