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.