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