Interaction contrasts for choice responses

Townsend and Nozawa (1995, Journal of Mathematical Psychology) investigated the shape 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 showed that the different architectures predict distinct shapes of the interaction contrast of the distribution functions under fairly weak assumptions, namely, selective influence of factorial manipulations on the processing times, and stochastic ordering of the processing times for different factor levels. The theory is limited to experimental tasks with ceiling accuracy, however. In this presentation, I show that with a slight extension of the stochastic dominance assumption, the original theorems can be generalized to more difficult tasks that entail non-negligible error rates (e.g., choice responses). Moreover, statistically powerful predictions can be derived for the interaction contrasts of the subdistributions of correct and wrong responses. I also apply the new method to interesting special cases such as parametric experimental variations and redundant signals tasks, and I discuss applications of the method in other areas than cognitive psychology.