Statistical Properties of Rosenthal’s Fail-Safe Number in Meta-Analysis

Rosenthal’s fail-safe number is widely used to assess the robustness of meta-analysis results against publication bias; however, its statistical properties remain insufficiently understood. This paper re-evaluates the coverage performance of confidence intervals for the Rosenthal’s fail-safe number using an updated simulation framework that incorporates zero truncation, an epsilon correction to the expected value, and a restriction to statistically significant meta-analyses. In addition to the standard normal bootstrap approximation, bias-corrected and accelerated bootstrap confidence intervals are considered. Simulation results show that standard bootstrap intervals tend to be conservative under symmetric settings and exhibit substantial deviations under asymmetric distributions. The bias-corrected and accelerated bootstrap method improves coverage accuracy, particularly under asymmetry and moderate sample sizes, although both methods exhibit conservative behavior in several scenarios. Overall, reliable inference for the fail-safe number depends on both appropriate parameter specification and bootstrap procedures that account for bias and asymmetry.