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Open Access Open Badges Technical Note

Controlling false discovery rates in factorial experiments with between-subjects and within-subjects tests

Eric D Schoen12*, Carina M Rubingh1, Suzan Wopereis1 and Marjan van Erk1

Author Affiliations

1 TNO Earth, Environmental and Life Sciences, PO Box 360, 3700 AJ Zeist, Netherlands

2 Department of Environment, Technology and Technology Management, University of Antwerp, Prinsstraat 13, 2000 Antwerp, Belgium

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BMC Research Notes 2013, 6:204  doi:10.1186/1756-0500-6-204

Published: 21 May 2013



The False Discovery Rate (FDR) controls the expected number of false positives among the positive test results. It is not straightforward how to conduct a FDR controlling procedure in experiments with a factorial structure, while at the same time there are between-subjects and within-subjects factors. This is because there are P-values for different tests in one and the same response along with P-values for the same test and different responses.


We propose a procedure resulting in a single P-value per response, calculated over the tests of all the factorial effects. FDR control can then be based on the set of single P-values.


The proposed procedure is very easy to apply and is recommended for all designs with factors applied at different levels of the randomization, such as cross-over designs with added between-subjects factors.

Trial registration


Analysis of variance; Between-subjects effects; Factorial experiment; False discovery rate; Within-subjects effects