Addressing the estimation of standard errors in fixed effects meta‐analysis

Standard methods for fixed effects meta‐analysis assume that standard errors for study‐specific estimates are known, not estimated. While the impact of this simplifying assumption has been shown in a few special cases, its general impact is not well understood, nor are general‐purpose tools available for inference under more realistic assumptions. In this paper, we aim to elucidate the impact of using estimated standard errors in fixed effects meta‐analysis, showing why it does not go away in large samples and quantifying how badly miscalibrated standard inference will be if it is ignored. We also show the important role of a particular measure of heterogeneity in this miscalibration. These developments lead to confidence intervals for fixed effects meta‐analysis with improved performance for both location and scale parameters.