Exploring event-related brain dynamics with tests on complex valued time-frequency representations

A question subject to intense debate is whether scalp-recorded event-related brain potentials are due to phase resetting of the ongoing electroencephalogram (EEG) or rather to the superimposition of time-locked components on background activity. The two hypotheses are usually assessed by means of statistics in the time-frequency domain, for example, through wavelet transformation of multiple EEG trials that yield for each time and frequency a scatter plot of complex values coefficients. Currently, intertrial phase correlation (phase locking or phase coherence) is taken as evidence for phase resetting at a given frequency and latency. Here we present a formal analysis using a complex t-statistic to illustrate that such measures are, in effect, tests for the mean vector of the repeated trials, and as such on their own are inappropriate measures of phase resetting. We also propose simple t-like statistics for testing changes in (i) the mean (presence of an event-related potential), (ii) the amplitude variance (presence of (de)synchronization) and (iii) the concentration of phases (phase locking). The first two statistics are found to be proper measures of the presence of a non-zero mean activity and induced activity, respectively. In the third case, two different tests are introduced: one based on measuring the alignment of coefficients in the complex plane and another derived from the argument that phase locking persists when the mean of the coefficients is removed. Both statistics gave unambiguous evidence of the presence of phase locking suggesting that they constitute promising tools in the analysis of event-related brain dynamics.