Assessing the amount of violation of the race model inequality

Hans Colonius, Department of Psychology University of Oldenburg

Abstract
The race model inequality (RMI) proposed in Miller (1982) has become a standard testing tool in many multisensory reaction time (RT) studies. It stipulates that the RT distribution function for bimodal stimuli is nowhere larger than the sum of the RT distributions for the unimodal stimuli. Its violation indicates that RTs in the bimodal condition are faster than predicted by a race model assuming that the termination of the first of several parallel processes determines the response, and it is interpreted as an indicator of a neural summation (or coactivation) mechanism. A single-valued index of the amount of violation is desirable when several different experimental conditions are to be compared. A widespread practice is to take the area under the function obtained by subtracting the right-hand side of the RMI from its left-hand side. Here we show that this area is equal to the mean RT predicted by a race model with maximally negative dependence between the processes, minus the observed bimodal mean RT. We also present an extension of this result to trimodal stimulation.

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