Power and sample size comparisons of stepwise FWE and FDR controlling test procedures in the normal many-one case

Abstract

Our paper compares the any-pair power, all-pairs power and per-pair power of several test procedures that control either the familywise error rate (FWE) or the false discovery rate (FDR). Our investigations are restricted to one-sided many-one comparisons of normal distributions. Some of the investigated procedures make use of this known special structure and some do not. The numbers $k$ of hypotheses we considered were 5, 10 and 100. The statements with small and large $k$ were quite similar. We found that all methods except one do not essentially differ in their any-pair powers. The most remarkable differences between the test procedures can be observed concerning their all-pairs powers.

We also compared the sample sizes that are necessary for the different procedures to ensure a specified power and investigated their dependency on the number $k$ of hypotheses. With specified per-pair or any-pair power, the FWE controlling methods need similar sample sizes as the FDR controlling methods. With specified all-pairs power, the sample sizes for four of the six FDR controlling procedures studied increase with $k$ at noticeably lower rates than for the FWE controlling procedures.