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The purpose of the present paper is to assess the efficacy of confidenceintervals for Rosenthal's fail-safe number. Although Rosenthal's estimator ishighly used by researchers, its statistical properties are largely unexplored.First of all, we developed statistical theory which allowed us to produceconfidence intervals for Rosenthal's fail-safe number.This was produced bydiscerning whether the number of studies analysed in a meta-analysis is fixedor random. Each case produces different variance estimators. For a given numberof studies and a given distribution, we provided five variance estimators.Confidence intervals are examined with a normal approximation and anonparametric bootstrap. The accuracy of the different confidence intervalestimates was then tested by methods of simulation under differentdistributional assumptions. The half normal distribution variance estimator hasthe best probability coverage. Finally, we provide a table of lower confidenceintervals for Rosenthal's estimator.

Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number