A new nonparametric test for the race model inequality

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.