Abstract
In Gou et al. (Biometrika 101(4), 899–911 2014), we proposed an improved hybrid Hochberg-Hommel (HH0) step-up multiple test procedure. The procedure used a fixed, specified set of critical constants. In this follow-up note, we show that an entire class of critical constants can be derived by relaxing one of the assumptions in that paper. This allows a choice of more powerful critical constants. These critical constants do not control the type I error under positive dependence among the test statistics as shown by simulations. Therefore, they should be used only under independence and negative dependence when not only they control the type I error but also yield higher power. If positive dependence is expected, as is common in practice, then the HH0 procedure should be used since it is robust with respect to type I error control under dependence.
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