Multiple Testing Procedures: Monotonicity and Some of Its Implications

Alexander Y. Gordon
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Alexander Y. Gordon: Professor Gordon wrote this chapter while at University of North Carolina at Charlotte

A chapter in Statistical Modeling for Biological Systems, 2020, pp 81-96 from Springer

Abstract: Abstract We review some results concerning the levels at which multiple testing procedures (MTPs) control certain type I error rates under a general and unknown dependence structure of the p-values on which the MTP is based. The type I error rates we deal with are (1) the classical family-wise error rate (FWER); (2) its immediate generalization: the probability of k or more false rejections (the generalized FWER); (3) the per-family error rate—the expected number of false rejections (PFER). The procedures considered are those satisfying the condition of monotonicity: reduction in some (or all) of the p-values used as input for the MTP can only increase the number of rejected hypotheses. It turns out that this natural condition, either by itself or combined with a property of being a step-down or step-up MTP (where the terms “step-down” and “step-up” are understood in their most general sense), has powerful consequences. Those include optimality results, inequalities, and identities involving different numerical characteristics of a procedure, and computational formulas.

Keywords: Multiple testing procedure; Monotone procedure; Step-down procedure; Step-up procedure; Family-wise error rate; Generalized family-wise error rate; Per-family error rate (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34675-1_5

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DOI: 10.1007/978-3-030-34675-1_5

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