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

Abstract

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.

Trial registration: NCT00959790.

Figure 1

P-values for 21 oxylipids. Each circle represents an overal P-value for a particular oxylipid, summarizing the results of 7 statistical tests.

Figure 2

Rejections for two FDR procedures.P-values below lower line: rejected by the Benjamini-Hochberg procedure [2]; P-values below upper line: rejected by the Storey-Tibshirani procedure [3].