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2020 | OriginalPaper | Chapter

Multiple Testing Procedures: Monotonicity and Some of Its Implications

Author : Alexander Y. Gordon

Published in: Statistical Modeling for Biological Systems

Publisher: Springer International Publishing

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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.

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previous chapter Correlation Between the True and False Discoveries in a Positively Dependent Multiple Comparison Problem
next chapter Applications of Sequential Methods in Multiple Hypothesis Testing
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Metadata
Title
Multiple Testing Procedures: Monotonicity and Some of Its Implications
Author
Alexander Y. Gordon
Copyright Year
2020
Book
Statistical Modeling for Biological Systems

Print ISBN: 978-3-030-34674-4

Electronic ISBN: 978-3-030-34675-1

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-34675-1_5

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