Robust Bayesian hypothesis testing with the hierarchical EZ-DDM

The EZ-diffusion model (EZ-DDM) uses a method of moments to provide closed-form estimators for the three-parameter drift-diffusion model from summary statistics. In previous work, we showed that using the sampling distributions of these statistics enables the implementation of hierarchical EZ-DDM extensions, supporting scalable Bayesian inference in cognitive psychometrics applications. However, the summary statistics used in EZ-DDM implementations (the mean and variance of the response time distribution) are sensitive to contaminant data points, limiting its utility in real-world applications. To address this, we propose a variation on the EZ-DDM implementation in which the summary statistics are replaced with robust alternatives, substituting mean RT with median RT and RT variance with an estimate derived from the interquartile range. We explore and evaluate the effectiveness of this substitution through simulation studies using a within-subject t test design across varying sample sizes and effect sizes. We show that the robust variant matched the diagnostic accuracy of the EZ-DDM implementation on uncontaminated data while maintaining diagnostic accuracy under contamination, unlike the standard model. This extension preserves efficiency while adding robustness in real-world applications. We recommend using the robust EZ-DDM in practical applications.