The effect of screening for publication bias on the outcomes of meta-analyses

Conducting a meta-analysis on a body of studies subject to publication bias is a type of post-selection inference that may invalidate findings. Therefore, analysts often run a hypothesis test to check for publication bias prior to conducting a meta-analysis. However, conducting meta-analyses conditional on the outcome of such preliminary tests is itself a form of post-selection inference. We investigate the effect on the outcome of a meta-analysis of a null finding at the preliminary stage. We find that in many situations there is no or little bias in the findings at the main stage.