False discovery rate and permutation test: an evaluation in ERP data analysis.

Current analysis of event-related potentials (ERP) data is usually based on the a priori selection of channels and time windows of interest for studying the differences between experimental conditions in the spatio-temporal domain. In this work we put forward a new strategy designed for situations when there is not a priori information about 'when' and 'where' these differences appear in the spatio-temporal domain, simultaneously testing numerous hypotheses, which increase the risk of false positives. This issue is known as the problem of multiple comparisons and has been managed with methods that control the false discovery rate (FDR), such as permutation test and FDR methods. Although the former has been previously applied, to our knowledge, the FDR methods have not been introduced in the ERP data analysis. Here we compare the performance (on simulated and real data) of permutation test and two FDR methods (Benjamini and Hochberg (BH) and local-fdr, by Efron). All these methods have been shown to be valid for dealing with the problem of multiple comparisons in the ERP analysis, avoiding the ad hoc selection of channels and/or time windows. FDR methods are a good alternative to the common and computationally more expensive permutation test. The BH method for independent tests gave the best overall performance regarding the balance between type I and type II errors. The local-fdr method is preferable for high dimensional (multichannel) problems where most of the tests conform to the empirical null hypothesis. Differences among the methods according to assumptions, null distributions and dimensionality of the problem are also discussed.