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The cluster mass test has been widely used for massively univariate tests inM/EEG, fMRI and, recently, pupillometry analysis. It is a powerful method fordetecting effects while controlling weakly the family-wise error rate (FWER),although its correct interpretation can only be performed at the cluster levelwithout any point-wise conclusion. It implies that the discoveries of a clustermass test cannot be precisely localized in time or in space. We propose a newmultiple comparison procedure, the cluster depth tests, that both controls theFWER while allowing an interpretation at the time point level. The simulationstudy shows that the cluster depth tests achieve large power and guarantee theFWER even in the presence of physiologically plausible effects. By having aninterpretation at the time point/voxel level, the cluster depth tests make itpossible to take full advantage of the high temporal resolution of EEGrecording to precisely time the appearance of an effect.

The Cluster Depth Tests: Toward Point-Wise Strong Control of the Family-Wise Error Rate in Massively Univariate Tests with Application to M/EEG