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Calculation of the statistical power of statistical tests is important in planning and interpreting the results of research studies, including meta-analyses. It is particularly important in moderator analyses in meta-analysis, which are often used as sensitivity analyses to rule out moderator effects but also may have low statistical power. This article describes how to compute statistical power of both fixed- and mixed-effects moderator tests in meta-analysis that are analogous to the analysis of variance and multiple regression analysis for effect sizes. It also shows how to compute power of tests for goodness of fit associated with these models. Examples from a published meta-analysis demonstrate that power of moderator tests and goodness-of-fit tests is not always high.
Hedges et al. (2004) studied this question.