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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 the false discovery rate, which is the expected value of the ratio. We compensate for this weakness by showing that \u03b1-investing controls mFDR at every rejected hypothesis. \u03b1-investing resembles \u03b1-spending that is used in sequential trials, but it has a key difference. When a test rejects a null hypothesis, \u03b1-investing earns additional probability towards subsequent tests. \u03b1-investing hence allows us to incorporate domain knowledge into the testing procedure and to improve the power of the tests. In this way, \u03b1-investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mFDR.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2007.00643.x","type":"journal-article","created":{"date-parts":[[2008,2,6]],"date-time":"2008-02-06T08:05:39Z","timestamp":1202285139000},"page":"429-444","source":"Crossref","is-referenced-by-count":86,"title":["<i>\u03b1<\/i>-Investing: a Procedure for Sequential Control of Expected False Discoveries"],"prefix":"10.1093","volume":"70","author":[{"given":"Dean P.","family":"Foster","sequence":"first","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert A.","family":"Stine","sequence":"additional","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2008,2,6]]},"reference":[{"key":"2023040707175673200_","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing","volume":"57","author":"Benjamini","year":"1995","journal-title":"J. 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