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Empirical Recovery of Response Time Decomposition Rules II. Discriminability of Serial and Parallel Architectures

Among the possible response time (RT) decomposition rules, three are of a traditional interest: addition (serial RT architecture), minimum (parallel-OR architecture), and maximum (parallel-AND architecture). Given RT samples, one can decide which of these three operation is the true decomposition rule by choosing the operation producing the smallest Smirnov distance between the RT samples combined in a certain way, as described by E. N. Dzhafarov and J. M. Cortese (1996, Journal of Mathematical Psychology 40, 185-202). By means of Monte-Carlo simulations, we determine at what sample sizes this decision identifies the true decomposition rule reliably. The results indicate that for a broad class of RT distribution functions the sample sizes required are by an order of magnitude larger when the component times are stochastically independent than when they are perfectly positively stochastically interdependent. In both cases, however, the required sample sizes are realistically achievable in an experiment, provided the experimental factors selectively influencing component times are sufficiently effective. Addition and maximum are generally more difficult to discriminate than addition and minimum, which in turn are more difficult to discriminate than maximum and minimum.