Systems factorial technology: Unconditional interaction contrasts for correct and incorrect responses

Response time is probably the most important metric in cognitive psychology. Many studies focus on average response time, but even more information can be obtained considering the shape of the response time distributions. In their seminal work, Townsend and Nozawa (1995) investigated the interaction contrast of response time distributions in two-factorial experiments for different cognitive architectures, including serial and parallel processing, with exhaustive and self-terminating stopping rules. They derived distinct, nonparametric predictions for the interaction contrast under fairly weak assumptions: selective influence of the factorial manipulations, and stochastic ordering of the processing times for the different factor levels. Their original theory is limited to tasks with ceiling accuracy. Extensions to more difficult tasks either conditioned the response time distributions on accuracy, which interferes with the assumption of stochastic ordering. Other approaches focused on a special case of the paradigm (i.e., redundant signals tasks). Here we show that with a slight extension of the stochastic dominance assumption, Townsend and Nozawa’s theorems can be generalized to difficult tasks that entail non-negligible error rates. We demonstrate statistical tests and illustrate methods to assess their power. We investigate additional generalizations of the theory to higher-order experimental manipulations and larger networks of serial and parallel processes. Interesting special cases such as redundant signals tasks and parametric experimental variations, as well as applications of the theory in areas outside cognitive psychology are proposed and discussed. More than 150 years after Donders, we can finally design and analyze interesting reaction time experiments with non-negligible error rates.