An Alpha-Exhaustive Multiple Testing Procedure
- 1 Boston University, United States
- 2 Veristat, United States
Copyright: © 2021 Mark Chang, Xuan Deng and John Balser. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
A multiple testing procedure can be a single-step procedure such as Bonferroni's method or a stepwise procedure such as Hochberg's stepup method and Hommel's method. It can be an α-exhaustive or α-conservative approach. We develop a single α-exhaustive procedure that can improve power 2-5% over Hochberg's and Hommel's methods in common situations when the test statistics are mutually independent. The method can also be generalized to dependent test statistics. The idea behind our method is to construct the rejection rules using the product of marginal p-values and by controlling the upper bounds of the kth order terms so that α is controlled for any configuration of k null hypotheses. Such upper bounds or critical values are determined progressively from k = 1 towards k = K, the number of null hypotheses in the problem.
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- Multiple Testing
- Hypothesis Test