Abstract
In this paper, it is put forward that the task of designing a procedure for a set of multiple comparisons should be considered as a decision-making under uncertainty. Due to this motivation, for the problem of multiple comparisons, we considered another error rate to be controlled, called PFER (per-family error rate), which requests that the expected number of false rejections of a test procedure should be bounded no more than a prespecified level k. Although PFER was proposed by Tukey in 1953, there is not much studying about it so far. We first present Bonferroni procedure (single-step) and then build two step-up procedures with one having generic critical values and another using critical values in BH (Benjamini and Hochberg) type. These procedures are compared through simulations.
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