Relevant Observations for Averaging Stimulus Evoked Magnetic Fields across Trials and across Subjects

Abstract

The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) data commonly involves arithmetic averaging of the evoked magnetic fields across trials, but also across subjects (“grand average”), with subsequent comparisons of grand averages across stimuli or conditions. The classical, and most frequently used, model in the analysis of stimulus evoked brain responses in EEG and MEG is based on the assumptions that the arithmetic mean is a good estimator of the evoked responses, that the evoked responses are independent of background activity, and that the latter averages out. The comparison of evoked responses ideally requires homogeneity of the variance (homoscedasticity). Here, we explore the issue of homoscedasticity in a typical MEG experiment. Fifteen subjects were stimulated with tones of different onset intervals, while magnetic fields were measured with a whole-head MEG device. Our analyses revealed an approximately homogeneous standard deviation (SD) of the responses across repeated trials of the same stimulus, SD_trials, i.e. SD_trials was independent of the corresponding mean response amplitude. In contrast, the SD_subjects derived from averaging the trial-averaged responses across subjects increased approximately linearly with the corresponding mean amplitude. This result shows that the evoked responses, including the M100, from different subjects and stimulus conditions differed largely by scaling factors. The latter findings question the usefulness of the common practice of comparing arithmetic averages of trial-averaged responses across subjects to different stimuli or conditions, e.g. by subtraction of responses to different conditions, and thus have widespread implications.