How to Evaluate Phase Differences between Trial Groups in Ongoing Electrophysiological Signals.

Rufin Vanrullen

doi:10.3389/fnins.2016.00426

Abstract

A growing number of studies endeavor to reveal periodicities in sensory and cognitive functions, by comparing the distribution of ongoing (pre-stimulus) oscillatory phases between two (or more) trial groups reflecting distinct experimental outcomes. A systematic relation between the phase of spontaneous electrophysiological signals, before a stimulus is even presented, and the eventual result of sensory or cognitive processing for that stimulus, would be indicative of an intrinsic periodicity in the underlying neural process. Prior studies of phase-dependent perception have used a variety of analytical methods to measure and evaluate phase differences, and there is currently no established standard practice in this field. The present report intends to remediate this need, by systematically comparing the statistical power of various measures of “phase opposition” between two trial groups, in a number of real and simulated experimental situations. Seven measures were evaluated: one parametric test (circular Watson-Williams test), and three distinct measures of phase opposition (phase bifurcation index, phase opposition sum, and phase opposition product) combined with two procedures for non-parametric statistical testing (permutation, or a combination of z-score and permutation). While these are obviously not the only existing or conceivable measures, they have all been used in recent studies. All tested methods performed adequately on a previously published dataset (Busch et al., 2009). On a variety of artificially constructed datasets, no single measure was found to surpass all others, but instead the suitability of each measure was contingent on several experimental factors: the time, frequency, and depth of oscillatory phase modulation; the absolute and relative amplitudes of post-stimulus event-related potentials for the two trial groups; the absolute and relative trial numbers for the two groups; and the number of permutations used for non-parametric testing. The concurrent use of two phase opposition measures, the parametric Watson-Williams test and a non-parametric test based on summing inter-trial coherence values for the two trial groups, appears to provide the most satisfactory outcome in all situations tested. Matlab code is provided to automatically compute these phase opposition measures.

Highlights

Science has long sought to determine whether mental processes unfold continuously—like the flow of a river—or discretely over time—like the successive frames of a movie sequence (Stroud, 1956; VanRullen and Koch, 2003; VanRullen, 2016a,b)
It appears important to verify that all the statistical measures compared here share, at least, the ability to identify phase opposition in a real experimental situation, where the perceptual outcome is known to be modulated by ongoing oscillatory phase
We explored the performance of other phase opposition measures on this same dataset (Figure 4)

Summary

Introduction

Science has long sought to determine whether mental processes unfold continuously—like the flow of a river—or discretely over time—like the successive frames of a movie sequence (Stroud, 1956; VanRullen and Koch, 2003; VanRullen, 2016a,b). One convincing way to demonstrate such a rhythmic operation is by showing that the result of a given neural process varies, depending on the exact rhythmic phase at which this process is engaged. One convincing way to demonstrate such a rhythmic operation is by showing that the result of a given neural process varies, depending on the exact rhythmic phase at which this process is engaged1 This procedure has a history dating at least half a century (Callaway and Yeager, 1960; Dustman and Beck, 1965), in recent years there has been a surge of reports of such phase-dependent perception (VanRullen et al, 2011). Largescale physiological markers of perceptual processing such as ERPs (Dustman and Beck, 1965; Jansen and Brandt, 1991; Haig and Gordon, 1998; Barry et al, 2004; Gruber et al, 2014), TMSevoked motor potentials (Keil et al, 2014b), stimulus-evoked BOLD responses (Scheeringa et al, 2011), and fMRI network connectivity between areas (Hanslmayr et al, 2013) have been shown to depend on oscillatory phase at (or just before) the time of stimulus onset

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Discussion

Conclusion