Exploring the Distribution for the Estimator of Rosenthal's 'Fail-Safe' Number of Unpublished Studies in Meta-analysis

TL;DR

This paper derives the probability distribution of Rosenthal's 'Fail-Safe' number estimator in meta-analysis, using the Central Limit Theorem and half-normal distribution assumptions, supported by simulations.

Contribution

It introduces a statistical distribution model for the estimator of Rosenthal's 'Fail-Safe' number, enhancing understanding of its behavior in meta-analyses.

Findings

Derived the distribution function of NR based on CLT

Supported the model with simulations and convergence analysis

Provides a theoretical foundation for assessing unpublished studies in meta-analysis

Abstract

The present paper discusses the statistical distribution for the estimator of Rosenthal's 'Fail-Safe' number NR, which is an estimator of unpublished studies in meta-analysis. We calculate the probability distribution function of NR. This is achieved based on the Central Limit Theorem and the proposition that certain components of the estimator NR follow a half normal distribution, derived from the standard normal distribution. Our proposed distributions are supported by simulations and investigation of convergence.