Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same spatiotemporal data: topographic and tomographic. Until now, statistical tests for these two situations have developed separately. This work introduces statistical tests for assessing simultaneously the significance of spatiotemporal event-related potential/event-related field (ERP/ERF) components and that of their sources. The test for detecting a component at a given time instant is provided by a Hotelling's T-2 statistic. This statistic is constructed in such a manner to be invariant to any choice of reference and is based upon a generalized version of the average reference transform of the data. As a consequence, the proposed test is a generalization of the well-known Global Field Power statistic. Consideration of tests at all time instants leads to a multiple comparison problem addressed by the use of Random Field Theory (RFT). The Union-Intersection (UI) principle is the basis for testing hypotheses about the topographic and tomographic distributions of such ERP/ERF components. The performance of the method is illustrated with actual EEG recordings obtained from a visual experiment of pattern reversal stimuli. (C) 2004 Elsevier Inc. All rights reserved.