Generalizations of the race model inequality.

In redundant signals tasks, participants respond in the same way to two different stimuli which are presented either alone or in combination (redundant stimuli). Responses to redundant stimuli are typically faster than responses to single stimuli. Different explanations account for such redundancy gains, including race models and coactivation models. Race models predict that the cumulative response time distribution for the redundant stimuli never exceeds the summed distributions of the single stimuli (race model inequality, RMI, Miller, 1982). Based on work by Townsend and Nozawa (1995) we demonstrate that the RMI is a special case of a more general interaction contrast of response time distributions for stimuli of different intensity, or stimuli presented with onset asynchrony. The generalization of the RMI is, thus, suited for a much wider class of experiments than the standard setup in which response times for single stimuli are compared to those for double stimuli. Moreover, predictions can be derived not only for the race model, but for serial, parallel, and coactive processing modes with different stopping rules. Compared to the standard RMI, statistical power of these interaction contrasts is satisfactory, even for small onset asynchronies.