When many (m) null hypotheses are tested with a single dataset, the control
of the number of false rejections is often the principal consideration. Two
popular controlling rates are the probability of making at least one false
discovery (FWER) and the expected fraction of false discoveries among all
rejections (FDR). Scaled multiple comparison error rates form a new family that
bridges the gap between these two extremes. For example, the Scaled Expected
Value (SEV) limits the number of false positives relative to an arbitrary
increasing function of the number of rejections, that is, E(FP/s(R)). We
discuss the problem of how to choose in practice which procedure to use, with
elements of an optimality theory, by considering the number of false rejections
FP separately from the number of correct rejections TP. Using this framework we
will show how to choose an element in the new family mentioned above.Comment: arXiv admin note: text overlap with arXiv:1112.451