Methods are described for non-parametric significance testing from event-related encephalographic data, using randomization tests. These methods may be applied in both signal space and source space. The methods include within-subject between-condition comparisons, paired and unpaired comparisons, and within-group and between-group comparisons. Test statistics are also derived for comparing the spatial or temporal response patterns, independent of specific changes at individual locations. Novel methods for testing peak-height significance, and also for making map-wide comparisons, are described. These methods have been validated using simulated data.