Controlling false positive rates in mass-multivariate tests for electromagnetic responses

We address the problem of controlling false positive rates in mass-multivariate tests for electromagnetic responses in compact regions of source space. We show that mass-univariate thresholds based on sensor level multivariate thresholds (approximated using Roy's union-intersection principle) are unduly conservative. We then consider a Bonferroni correction for source level tests based on the number of unique lead-field extrema. For a given source space, the sensor indices corresponding to the maxima and minima (for each dipolar lead field) are listed, and the number of unique extrema is given by the number of unique pairs in this list. Using a multivariate beamformer formulation, we validate this heuristic against empirical permutation thresholds for mass-univariate and mass-multivariate tests (of induced and evoked responses) for a variety of source spaces, using simulated and real data. We also show that the same approximations hold when dealing with a cortical manifold (rather than a volume) and for mass-multivariate minimum norm solutions. We demonstrate that the mass-multivariate framework is not restricted to tests on a single contrast of effects (cf, Roy's maximum root) but also accommodates multivariate effects (cf, Wilk's lambda).