Alpha-Investing: A Procedure for Sequential Control of Expected False Discoveries

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alpha spending
Bonferroni method
false discovery rate (FDR
mFDR)
family-wise error rate (FWER)
multiple comparisons
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Statistics and Probability
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Foster, Dean
Stine, Robert A
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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.

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2008-04-01
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Journal of the Royal Statistical Society: Series B: Statistical Methodology
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