A new nonparametric test for the race model inequality

Abstract

The race model inequality (RMI), as first introduced by Miller (Cognitive Psychology, 14, 247–279, 1982), entails an upper bound on the amount of statistical facilitation for reaction times (RTs) attainable by a race model within the redundant-signals paradigm. A violation of RMI may be considered as empirical evidence for a coactivation model rather than a race model. Here, we introduce a novel nonparametric procedure for evaluating the RMI for single participant analysis. The statistical procedure is based on a new probabilistic representation that highlights some neglected, but important distributional features of the RMI. In particular, we show how the reconstructed distribution function under maximal statistical facilitation for a race model is characterized by a specific truncated-type property. The results of two Monte Carlo simulation studies suggest that our procedure efficiently controls for type I error with reasonable power. Finally, unlike previous proposals for single participant analysis (e.g., Maris and Maris (Journal of Mathematical Psychology 47, 507–514, 2003)), our approach is also more consistent with the typical way to collect RT data in experimental works. R script functions for running the statistical analysis on single participant data are made freely available to the readers on a dedicated web server.