Correction for bias in meta-analysis of little-replicated studies

1. Meta-analyses conventionally weight study estimates on the inverse of their error variance, in order to maximize precision. Unbiased variability in the estimates of these study-level error variances increases with the inverse of study-level replication. Here we demonstrate how this variability accumulates asymmetrically across studies in precision-weighted meta-analysis, to cause undervaluation of the meta-level effect size or its error variance (the meta-effect and meta-variance). 2. Small samples, typical of the ecological literature, induce big sampling errors in variance estimation, which substantially bias precision-weighted meta-analysis. Simulations revealed that biases differed little between random- and fixed-effects tests. Meta-estimation of a one-sample mean from 20 studies, with sample sizes of 3 to 20 observations, undervalued the meta-variance by ~20%. Meta-analysis of two-sample designs from 20 studies, with sample sizes of 3 to 10 observations, undervalued the meta-v...