Multiple-hypothesis testing involves guarding against much more complicated errors than single-hypothesis testing. Whereas we typically control the type I error rate for a single-hypothesis test, a compound error rate is controlled for multiple-hypothesis tests. For example, controlling the false discovery rate FDR traditionally involves intricate sequential p-value rejection methods based on the observed data. Whereas a sequential p-value method fixes the error rate and estimates its corresponding rejection region, we propose the opposite approach-we fix the rejection region and then estimate its corresponding error rate. This new approach offers increased applicability, accuracy and power. We apply the methodology to both the positive false discovery rate pFDR and FDR, and provide evidence for its benefits. It is shown that pFDR is probably the quantity of interest over FDR. Also discussed is the calculation of the q-value, the pFDR analogue of the p-value, which eliminates the need to set the error rate beforehand as is traditionally done. Some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the Benjamini-Hochberg FDR method.
Series B (Statistical Methodology) of the Journal of the Royal Statistical Society started out simply as the Supplement to the Journal of the Royal Statistical Society in the Society's centenary year of 1934. The journal now publishes high quality papers on the methodological aspects of statistics. The objective of papers is to contribute to the understanding of statistical methodology and/or to develop and improve statistical methods. JSTOR provides a digital archive of the print version of Journal of the Royal Statistical Society, Series B: Statistical Methodology. The electronic version of Journal of the Royal Statistical Society, Series B: Statistical Methodology is available at http://www.interscience.wiley.com. Authorized users may be able to access the full text articles at this site.
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Journal of the Royal Statistical Society. Series B (Statistical Methodology)
© 2002 Royal Statistical Society
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