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Statistical Applications in Genetics and Molecular Biology

Editor-in-Chief: Stumpf, Michael P.H.

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1544-6115
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Volume 10, Issue 1

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The Joint Null Criterion for Multiple Hypothesis Tests

Jeffrey T Leek / John D. Storey
Published Online: 2011-06-01 | DOI: https://doi.org/10.2202/1544-6115.1673

Simultaneously performing many hypothesis tests is a problem commonly encountered in high-dimensional biology. In this setting, a large set of p-values is calculated from many related features measured simultaneously. Classical statistics provides a criterion for defining what a “correct” p-value is when performing a single hypothesis test. We show here that even when each p-value is marginally correct under this single hypothesis criterion, it may be the case that the joint behavior of the entire set of p-values is problematic. On the other hand, there are cases where each p-value is marginally incorrect, yet the joint distribution of the set of p-values is satisfactory. Here, we propose a criterion defining a well behaved set of simultaneously calculated p-values that provides precise control of common error rates and we introduce diagnostic procedures for assessing whether the criterion is satisfied with simulations. Multiple testing p-values that satisfy our new criterion avoid potentially large study specific errors, but also satisfy the usual assumptions for strong control of false discovery rates and family-wise error rates. We utilize the new criterion and proposed diagnostics to investigate two common issues in high-dimensional multiple testing for genomics: dependent multiple hypothesis tests and pooled versus test-specific null distributions.

This article offers supplementary material which is provided at the end of the article.

Keywords: false discovery rate; multiple testing dependence; pooled null statistics

About the article

Published Online: 2011-06-01


Citation Information: Statistical Applications in Genetics and Molecular Biology, Volume 10, Issue 1, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.2202/1544-6115.1673.

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©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston. Copyright Clearance Center

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Citing Articles

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[1]
Jeffrey T. Leek
Nucleic Acids Research, 2014, Volume 42, Number 21, Page e161
[2]
Guillem Rigaill, Sandrine Balzergue, Véronique Brunaud, Eddy Blondet, Andrea Rau, Odile Rogier, José Caius, Cathy Maugis-Rabusseau, Ludivine Soubigou-Taconnat, Sébastien Aubourg, Claire Lurin, Marie-Laure Martin-Magniette, and Etienne Delannoy
Briefings in Bioinformatics, 2016, Page bbw092
[3]
Richard J. Wang, Melissa M. Gray, Michelle D. Parmenter, Karl W. Broman, and Bret A. Payseur
Molecular Ecology, 2017, Volume 26, Number 2, Page 457

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