data were rank-transformed because this method cannot be used with negative-valued data. Two issues inherent in magnitude scaling and phase distribution require a non-parametric intervention prior to group-level statistical analyses. The first issue is that non-transformed magnitudes are difficult to interpret because they scale with the data (reaction time or luminance values), which was different across subjects (this can be contrasted with inter-trial phase coherence, described above, for which the average vector magnitudes have a maximum of 1.0 and are inherently interpretable). The second issue is that if phase values are non-uniformly distributed across trials (as would be expected if there is, e.g., stimulus-induced phase reset), the distribution of reaction time would be artificially non-uniformly distributed. To counteract both of these issues, we applied permutation testing, in which the observed reaction time and phase values were shuffled with respect to each other. This provides a data-driven test of the null hypothesis that there is no consistent relationship between reaction time and phase angle. Five hundred iterations with shuffled reaction time–phase pairings were performed at each point in time–frequency–electrode–condition space, thus creating a distribution of reaction time–phase modulations under the null hypothesis. Finally, the standardized distance between the observed modulation and
