Averaging auditory evoked magnetoencephalographic and electroencephalographic responses: a critical discussion

Abstract

In the analysis of data from magnetoencephalography (MEG) and electroencephalography (EEG), it is common practice to arithmetically average event-related magnetic fields (ERFs) or event-related electric potentials (ERPs) across single trials and subsequently across subjects to obtain the so-called grand mean. Comparisons of grand means, e.g. between conditions, are then often performed by subtraction. These operations, and their statistical evaluation with parametric tests such as ANOVA, tacitly rely on the assumption that the data follow the additive model, have a normal distribution, and have a homogeneous variance. This may be true for single trials, but these conditions are rarely met when ERFs/ERPs are compared between subjects, meaning that the additive model is seldom the correct model for computing grand mean waveforms. Here, we summarize some of our recent work and present new evidence, from auditory-evoked MEG and EEG results, that the non-normal distributions and the heteroscedasticity observed instead result because ERFs/ERPs follow a mixed model with additive and multiplicative components. For peak amplitudes, such as the auditory M100 and N100, the multiplicative component dominates. These findings emphasize that the common practice of simply subtracting arithmetic means of auditory-evoked ERFs or ERPs is problematic without prior adequate transformation of the data. Application of the area sinus hyperbolicus (asinh) transform to data following the mixed model transforms them into the requested additive model with its normal distribution and homogeneous variance. We therefore advise checking the data for compliance with the additive model and using the asinh transform if required.

Persistent neural activity in auditory cortex is related to auditory working memory in humans and nonhuman primates

“…The comparison of grand mean waveforms across tasks requires homogeneous variance and a normal distribution of the underlying MEG data. We found that this could be achieved by a log-transformation of individual source waveforms, consistent with earlier studies ( König et al, 2015 ; Matysiak et al, 2013 ; Zacharias et al, 2011 ). To obtain the grand mean waveform, the log-transformed source waveforms were arithmetically averaged across subjects and this mean waveform was then back-transformed (by exponentiation) and plotted along a logarithmic axis.…”

“…They were seeded in the left and right AC, respectively, based on the anatomical MR image of each subject’s brain. To obtain the grand mean source waveforms, individual source waveforms were geometrically averaged across subjects, for reasons given elsewhere ( König et al, 2015 ; Matysiak et al, 2013 ; Zacharias et al, 2011 ). Source strengths were analyzed for correct trials (∼90%) only.…”

“…Average waveforms were obtained by arithmetically averaging the signals from epochs of trials with correct responses, separately for each subject, task and sensor. The use of the arithmetic average for this purpose is justified ( Zacharias et al, 2011 ; König et al, 2015 ). The average waveforms were then baseline-offset corrected.…”

Bis(4,4′-dimethyl-2,2′-bipyridine)oxidovanadium(IV) Sulfate Dehydrate: Potential Candidate for Controlling Lipid Metabolism?

“…Normal distribution was verified by Shapiro-Wilk test while homogeneity of variance was verified by Levene's test. In turn, Box-Cox transformation was used for variables which did not meet ANOVA assumptions [17, 18]. …”

Symmetric patterns with different luminance polarity (anti‐symmetry) generate an automatic response in extrastriate cortex

“…However, it is problematic to base theoretical conclusions on the absence of a significant effect. The traditional ANOVA method gives the probability 1 There has been some concern about the use of non-transformed data in hemispheric comparisons (König et al, 2015). However, the data used in this analysis were normally distributed (Shapiro-Wilk tests, p > .175) and applying the recommended ASINH transform did not change the results.…”