Data-driven approach
A mass-univariate non-parametric randomization procedure was used as a first statistical assessment of the EEG data (Maris, 2004; Maris and Oostenveld, 2007). For this procedure, a Delaunay triangulation was used to define clusters of neighbouring electrodes over a 2D projection of the electrode montage, connecting nearby electrodes independently of the physical distance between them. Clusters were defined in order to contain a minimum of two electrodes. Two dimensional (time, electrode) analyses were conducted on the ERP amplitudes between 0 and 400 ms post-stimulus.
For each of the comparisons performed, the amplitude at each time point and electrode underwent a 2-tailed dependent t-test. The significance probability (p-value) of the t-statistic was determined by calculating the proportion of 2D samples from 10000 random partitions of the data that would have a larger test statistic as a result than the actually observed test statistic (Monte Carlo method). Then, clusters were created by grouping adjacent 2D points exceeding a significance level of 0.05 (two-tailed). A cluster-level statistic was calculated by taking the sum of the t-statistics within every cluster. The significance probability of the clusters was assessed with the described non-parametric Monte Carlo method. Corrected values of p below 0.05 were considered significant. For each significant cluster we report its temporal spread, cluster statistic and p value.
Using this procedure, statistical comparisons were conducted both in acquisition and test sounds comparing the agent and the observer conditions (subtracting observer from agent condition) to test for agency effects and comparing the early and late learning stages (subtracting early from late learning stages) to test for learning effects. Subsequently, we tested for interactions between agency and learning stage comparing the difference between agent and observer across learning stages and the difference between learning stages across agency conditions. In test sounds, we tested for effects of congruency contrasting congruent and incongruent sounds. Finally, we investigated if congruency effects were modulated by the factors agency and learning stage by comparing the difference between congruent and incongruent trials (incongruent subtracted from congruent) in the agent versus observer condition, and in the late versus early learning stage.
As discussed frequently (e.g. Sassenhagen & Draschkow, 2019), cluster-based statistical analyses controlling for multiple comparisons (Maris, 2004; Maris and Oostenveld, 2007) may lead to an overestimation of the temporal and spatial characteristics of the effects, so it is recommendable to avoid very specific time-space claims about the data. We are aware of these limitations, and we try to relate the findings from the cluster-based analysis to classic ERP components based on the shapes and scalp topographies of the obtained waveforms.