Outgrowing the Procrustean Bed of Normality: The Utility of Bayesian Modeling for Asymmetrical Data Analysis

Psychological data often violate the normality assumptions made by commonly used statistical methods. These violations are addressed in a variety of ways such as transformations or assuming the employed method is robust to violations. Here we argue that data transformations are unnecessary at best and severely misleading at worst. An alternative approach is to use a Bayesian model that permits skewness and other perturbations to classical assumptions (e.g., heteroskedasticity). Through simulation, we demonstrate that a Bayesian skew-normal model has optimal frequentist properties (i.e., "type 1" error, "power", unbiasedness) compared to normal-assumptive models with or without transformation. Furthermore, the Bayesian skew-normal model has greater predictive utility, as indicated by posterior predictive checking and approximate leave-one-out cross-validation. After an applied example, we discuss practical implications of our findings for psychological science in general, and specifically how Bayesian modeling can improve reproducibility in psychology.