Beyond Random Effects: When Small-Study Findings Are More Heterogeneous

New meta-regression methods are introduced that identify whether the magnitude of heterogeneity across study findings is correlated with their standard errors. Evidence from dozens of meta-analyses finds robust evidence of this correlation and that small-sample studies typically have higher heterogeneity. This correlated heterogeneity violates the random-effects (RE) model of additive and independent heterogeneity. When small studies not only have inadequate statistical power but also high heterogeneity, their scientific contribution is even more dubious. When the heterogeneity variance is correlated with the sampling-error variance to the degree we find, simulations show that RE is dominated by an alternative weighted average, the unrestricted weighted least squares (UWLS). Meta-research evidence combined with simulations establish that UWLS should replace RE as the conventional meta-analysis summary of psychological research.