A permutation test for the race model inequality

When participants are asked to respond in the same way to several stimulus identities, responses are often observed to be faster if two stimuli are presented simultaneously as opposed to when a single stimulus is presented (redundant signals effect; Miller, 1982). An important issue of such experiments is whether the observed redundancy gains can be explained by parallel processing of the two stimuli in a race-like fashion. To test the parallel processing model, Miller derived the well-known race model inequality which has become a routine test for behavioral data in experiments with redundant signals. Several statistical procedures have been used for testing the race model inequality. However, the commonly employed procedure does not control the Type I error. In this article a permutation test is described that keeps the Type I error at the desired level. Simulations show that the power of the test is reasonable even for small samples. The scripts discussed in this article may be downloaded as supplemental materials from http://brm.psychonomic-journals.org/content/supplemental.