Traditionally, artifacts are handled one of two ways in ERP studies: (1) rejection of affected segments and (2) correction via e.g. ICA. Threshold-based rejection is problematic because of the arbitrariness of the chosen limits and particular threshold criterion (e.g. peak-to-peak, absolute, slope, etc.), resulting in large researcher degrees of freedom. Manual rejection may suffer from low inter-rater reliability and is often done without appropriate blinding. Additionally, rejections are typically done for an entire trial, even if the ERP measure of interest isn't impacted by the artifact in question (e.g. motion artifact at the end of the trial). Additionally, fixed thresholds cannot distinguish between non-artifactual extreme values (i.e. those arising from brain activity and which have some 'signal' and some 'noise') and truly artifactual values (e.g. those arising from muscle activity or the electrical environment and which are essentially pure 'noise'). These aspects all become particularly problematic when analyzing EEG recorded under more naturalistic conditions, such as free dialogue in hyperscanning or virtual reality. By using modern, robust statistical methods, we can avoid setting arbitrary thresholds and allow the statistical model to extract the signal from the noise. To demonstrate this, we re-analyzed data from a multimodal virtual-reality N400 paradigm. We created two versions of the dataset, one using traditional threshold-based peak-to-peak artifact rejection (150µV), and one without artifact rejection, and examined the mean voltage at 250-350ms after stimulus onset. We then analyzed the data with both robust and traditional techniques from both a frequentist and Bayesian perspective. The non-robust models yielded different effect estimates when fit to dirty data than when fit to cleaned data, as well as different estimates of the residual variation. The robust models meanwhile estimated similar effect sizes for the dirty and cleaned data, with slightly different estimates of the residual variation. In other words, the robust model worked equally well with or without artifact rejection and did not require setting any arbitrary thresholds. Conversely, the standard, non-robust model was sensitive to the degree of data cleaning. This suggests that robust methods should become the standard in ERP analysis, regardless of data cleaning procedure.