Abstract
Many primary research studies in ecology are underpowered, providing very imprecise estimates of effect size. Meta-analyses partially mitigate this imprecision by combining data from different studies. But meta-analytic estimates of mean effect size may still remain imprecise, particularly if the meta-analysis includes a small number of studies. Imprecise, large-magnitude estimates of mean effect size from small meta-analyses likely would shrink if additional studies were conducted (regression towards the mean). Here, I propose a way to estimate and correct this regression to the mean, using meta-meta-analysis (meta-analysis of meta-analyses). Hierarchical random effects meta-meta-analysis shrinks estimated mean effect sizes from different meta-analyses towards the grand mean, bringing those estimated means closer on average to their unknown true values. The intuition is that, if a meta-analysis reports a mean effect size much larger in magnitude than that reported by other meta-analyses, that large mean effect size likely is an overestimate. This intuition holds even if different meta-analyses of different topics have different true mean effect sizes. Drawing on a compilation of data from hundreds of ecological meta-analyses, I find that the typical (median) ecological meta-analysis overestimates the absolute magnitude of the true mean effect size by ~10%. Some small ecological meta-analyses overestimate the magnitude of the true mean effect size by >50%. Meta-meta-analysis is a promising tool for improving the accuracy of meta-analytic estimates of mean effect size, particularly estimates based on just a few studies.