The black line represents the time course of the predictive value of theta phase (same data as shown in Figure 3a). To test whether the early and the late peaks in the theta predictive value reflected one or two independent phenomena, we ran logistic regression analyses in which we used both the early (estimated at −1.4 s) and the late theta phase (estimated at −0.1 s) as predictors of the perceptual performance. We performed this analysis in two versions. In a first version, the logistic regression analysis was performed channel-by-channel (as described in the paper for the original analysis), and we used the early and the late theta phases estimated at corresponding EEG channels. Both the early and the late theta phases predict perception, with an almost identical pattern as the original analysis, both with respect to topography (top graphs) and effect size (bottom graph, cyan symbols). This indicates that the two effects are independent. However, because the early and the late effect have different topographies, the channel-by-channel analysis is unlikely to include the relevant phases (the ones for which one has to partial out) for every channel. Therefore, we also ran a second analysis, in which we partialled out for the phases of the other effect measured at its best channel, i.e., the channel with the highest effect size in the original analysis for the early and the late effect (channels are marked in red in the top graphs; early effect: AF3; late effect: CP5). Also in this case, both effects (red symbols) are significant (early effect, AF3: p<0.001; late effect, CP5: p<0.001), confirming their statistical independence.