Statistics Papers

Document Type

Journal Article

Date of this Version

4-2008

Publication Source

Journal of the Royal Statistical Society: Series B: Statistical Methodology

Volume

70

Issue

2

Start Page

429

Last Page

444

DOI

10.1111/j.1467-9868.2007.00643.x

Abstract

Alpha-investing is an adaptive, sequential methodology that encompasses a large family of procedures for testing multiple hypotheses. All control mFDR, which is the ratio of the expected number of false rejections to the expected number of rejections. mFDR is a weaker criterion than FDR, which is the expected value of the ratio. We compensate for this weakness by showing that alpha-investing controls mFDR at every rejected hypothesis. Alpha-investing resembles alpha-spending used in sequential trials, but possesses a key difference. When a test rejects a null hypothesis, alpha-investing earns additional probability toward subsequent tests. Alpha-investing hence allows one to incorporate domain knowledge into the testing procedure and improve the power of the tests. In this way, alpha-investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mFDR.

Keywords

alpha spending, Bonferroni method, false discovery rate (FDR, mFDR), family-wise error rate (FWER), multiple comparisons

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Date Posted: 27 November 2017

This document has been peer reviewed.