Hypothesis testing in distributed source models for the electro- or magnetoencephalogram is generally performed for each voxel separately. Derived from the analysis of functional magnetic resonance imaging data, such a statistical parametric map (SPM) ignores the spatial smoothing in hypothesis testing with distributed source models. For example, when intending to test a single voxel, actually an entire region of voxels is tested simultaneously. Because there are more parameters than observations, typically constraints are employed to arrive at a solution which spatially smooths the solution. If ignored, it can be concluded from the hypothesis test that there is activity at some location where there is none. In addition, an SPM on distributed source models gives the illusion of very high resolution. As an alternative, a multivariate approach is suggested in which a region of interest is tested that is spatially smooth. In simulations with MEG and EEG it is shown that clear hypothesis testing in distributed source models is possible, provided that there is high correspondence between what is intended to be tested and what is actually tested. The approach is also illustrated by an application to data from an experiment measuring visual evoked fields when presenting checkerboard patterns. Hum Brain Mapp, 2005. © 2005 Wiley-Liss, Inc.