In this paper several multivariate tests are presented, in particular permutation tests, which can be used in multiple endpoint problems as for example in comparisons of high-dimensional vectors of EEG data. We have investigated the power of these tests using artificial data in simulations and real EEG data. It is obvious that no one multivariate test is uniformly most powerful. The power of the different methods depends in different ways on the correlation between the endpoints, on the number

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... f endpoints for which differences exist and on other factors. Based on our findings, we have derived rules of thumb regarding under which configurations a particular test should be used. In order to demonstrate the properties of different multivariate tests we applied them to EEG coherence data. As an example for the paired samples case, we compared the 171-dimensional coherence vectors observed for the alpha1-band while processing either concrete or abstract nouns and obtained significant global differences for some sections of time. As an example for the unpaired samples case, we compared the coherence vectors observed for language students and non-language students who processed an English text and found a significant global difference.