Empirical Recovery of Response Time Decomposition Rules I. Sample-Level Decomposition Tests

E. N. Dzhafarov and R. Schweickert (1995, Journal of Mathematical Psychology, 39, 285-314) developed a mathematical theory for the decomposability of response time (RT) into two component times that are selectively influenced by different factors and are either stochastically independent or perfectly positively stochastically interdependent (in which case they are increasing functions of a common random variable). In this theory, RT is obtained from its component times by means of an associative and commutative operation. For any such operation, there is a decomposition test, a relationship between observable RT distributions that holds if and (under mild constraints) only if the RTs are decomposable by means of this operation. In this paper, we construct a sample-level version of these decomposition tests that serve to determine whether RTs that are represented by finite samples are decomposable by means of a given operation (under a given form of stochastic relationship between component times, independence or perfect positive interdependence). The decision is based on the asymptotic p-values associated with the maximal distance between empirical distribution functions computed by combining in a certain way the RT samples corresponding to different treatments.