The analysis of electrophysiological data often produces results that are continuous in one or more dimensions, e.g., time-frequency maps, peri-stimulus time histograms, and cross-correlation functions. Classical inferences made on the ensuing statistical maps must control family wise error (FWE) when searching across the map's dimensions. In this paper, we borrow multiple comparisons procedures, established in neuroimaging, and apply them to electrophysiological data. These procedures use random field theory (RFT) to adjust p-values from statistics that are functions of time and/or frequency. This RFT adjustment for continuous statistical processes plays the same role as a Bonnferonni adjustment in the context of discrete statistical tests. Here, by analysing the time-frequency decompositions of single channel EEG data we show that RFT adjustments can be used in the analysis of electrophysiological data and illustrate the advantages of this method over existing approaches.