Improving the Meta-Analytic Assessment of Effect Size Variance With an Informed Bayesian Prior

Abstract

Meta-analytic estimation of effect size variance is critical for determining the degree to which a relationship or finding generalizes across contexts. In most meta-analyses, population effect size variability is estimated by subtracting expected sampling error variance from observed variance, using only information from a limited set of available studies. We propose an improved Bayesian variance estimation technique that incorporates findings from previous meta-analytic research through an informed prior distribution of likely levels of effect size variance. The logic of exchangeability as a conceptual foundation for using an informed prior is explicated. On the basis of Monte Carlo simulations, we find the traditional method of meta-analytic variance estimation the most biased and least accurate technique across all sizes of meta-analyses considered. The Bayesian methodology incorporating an informed prior proved to be the most accurate and overall least biased of all estimation methods. Conceptual advantages and limitations that must be taken into account when incorporating an informed prior to estimate variability of effect sizes in a meta-analysis are also discussed.