Abstract: There is a growing literature on the large-scale multiple testing in which the Benjamini-Hochberg (BH) procedure and its variants play a key role. Almost all this work assumes that the underlying distribution is normal in calculating the p-values. Here we study the effect of non-normality on false discovery control in large-scale multiple testing. The normal approximation, bootstrap calibration and the skewness-corrected normal approximation methods of approximating the individual p-values used to rank the significance levels are investigated. As an illustration, we compare these procedures with the BH method in terms of the cutting threshold and the false discovery rate.

Key words and phrases: False discovery rate, multiple testing.