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

Background: 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. Findings: 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. Conclusions: 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.