Equivalencies Between Ad Hoc Strategies and Multivariate Models for Meta-Analysis of Dependent Effect Sizes

Meta-analyses of educational research findings frequently involve statistically dependent effect size estimates. Meta-analysts have often addressed dependence issues using ad hoc approaches that involve modifying the data to conform to the assumptions of models for independent effect size estimates, such as by aggregating estimates to obtain one summary estimate per study, conducting separate analyses of distinct subgroups of estimates, or combinations thereof. We show that these ad hoc approaches correspond exactly to certain multivariate models for dependent effect sizes. Specifically, we describe classes of multivariate random effects models that have likelihoods equivalent to those of models for effect sizes that have been averaged by study, classified into subgroups, or both. The equivalencies also apply to robust variance estimation methods.