TESTING FOR HETEROGENEITY OF EVOKED-POTENTIAL SIGNALS USING AN APPROXIMATION TO AN EXACT PERMUTATION TEST

In brain evoked potential research and various other fields, a signal embedded in noise is observed in each of many repeated trials. We propose a new test of the null hypothesis that the signal is the same in every trial. The test has power against the alternative hypothesis that the signal is changing slowly from trial to trial. The test statistic is the distance between the average of the trials and a parametric or nonparametric estimate of a slowly changing signal. We derive the exact mean and variance of the test statistic under permutation of the trials and use these moments to approximate the exact permutation test. We use simulated evoked potential data to evaluate the proposed test and to compare it to three previous tests.