Power Approximations for Meta-Analysis of Dependent Effect Sizes

Meta-analytic models for dependent effect sizes have grown increasingly sophisticated over the last few decades, which has created challenges for a priori power calculations. We introduce power approximations for tests of average effect sizes based upon the most common models for handling dependent effect sizes. In a Monte Carlo simulation, we show that the new power formulas can accurately approximate the true power of common meta-analytic models for dependent effect sizes. Lastly, we investigate the Type I error rate and power for several common models, finding that tests using robust variance estimation provide better Type I error calibration than tests with model-based variance estimation. We consider implications for practice with respect to selecting a working model and an inferential approach.