Testing the race model inequality in redundant stimuli with variable onset asynchrony.

In speeded response tasks with redundant signals, parallel processing of the signals is tested by the race model inequality. This inequality states that given a race of two signals, the cumulative distribution of response times for redundant stimuli never exceeds the sum of the cumulative distributions of response times for the single-modality stimuli. It has been derived for synchronous stimuli and for stimuli with stimulus onset asynchrony (SOA). In most experiments with asynchronous stimuli, discrete SOA values are chosen and the race model inequality is separately tested for each SOA. Due to the high number of statistical tests, Type I and II errors are increased. Here a straightforward method is demonstrated to collapse these multiple tests into one test by summing the inequalities for the different SOAs. The power of the procedure is substantially increased by assigning specific weights to SOAs at which the violation of the race model prediction is expected to be large. In addition, the method enables data analysis for experiments in which stimuli are presented with SOA from a continuous distribution rather than in discrete steps.