Figure 2.

Comparison between standard trial-averaged ERP, overlap-corrected regression-ERP (rERP), and overlap-corrected factored rERP, using regression design. A) Standard ERPs time-locked to stimulus onset and button response events may be calculated separately by using separate STIM and RESP matrices substituted for the trial design matrix $X$, separately across different trial types (e.g., congruent correct, incongruent correct, congruent error, etc.). Here, each row of $X$ corresponds to each latency $L$ in the continuous EEG recording $y$, and each column of $X$ corresponds to each latency within the chosen epoch for which the ERP is to be calculated (e.g., 2 seconds before and after each stimulus or response event) of length $J$. An element of $X$ takes the value of 1 (small black squares) if it corresponds to a latency within the event-related epoch on a given trial number of a given trial type, and 0 otherwise. As trial RTs vary, so do overlapping non-zero elements of $STIM$ and $RESP$. Note that the standard ERP does not account for temporal overlap among stimulus and response epochs (see magenta and cyan demarcations alongside the EEG recording $y$), and therefore stimulus- and response-locked standard ERPs are temporally confounded. B) Overlap-correction among stimulus and response processes is achieved by horizontal concatenation of STIM and RESP into a single matrix $X$ for each trial type. Here, periods within the continuous EEG recording where stimulus- and response-locked epochs overlap are highlighted in yellow. C) Concatenating task design matrices from multiple trial types may be used to explore processes that are unique to a given trial type. Using trial type 1 (white block of $X$) as the reference type in a treatment coding framework, the degree to which waveforms deviate from trial type 1 as a function of trial type 2 (light gray) or trial type 3 (dark gray) may be explored. For example, in our study we used congruent correct trials as the reference type (white block) and explored how rERPs deviated as a function of incongruent flanker stimuli (light gray) or errors (dark gray).