EMPIRICAL RECOVERY OF RESPONSE-TIME DECOMPOSITION RULES .1. SAMPLE-LEVEL DECOMPOSITION TESTS

E. N. Dzhafarov and R. Schweickert (1995, Journal of Mathematical Psyc hology, 39, 285-314) developed a mathematical theory for the decomposa bility of response lime (RT) into two component times that are selecti vely influenced by different factors and are either stochastically ind ependent or perfectly positively stochastically interdependent (in whi ch case they are increasing functions of a common random variable). In this theory, RT is obtained from its component times by means of an a ssociative and commutative operation. For any such operation, there is a decomposition test, a relationship between observable RT distributi ons that holds if and (under mild constraints) only if the RTs are dec omposable by means of this operation. In this paper, we construct a sa mple-level version of these decomposition tests that serve to determin e whether RTs that are represented by finite samples are decomposable by means of a given operation (under a given form of stochastic relati onship between component times, independence or perfect positive inter dependence). The decision is based on the asymptotic p-values associat ed with the maximal distance between empirical distribution functions computed by combining in a certain way the RT samples corresponding to different treatments. (C) 1996 Academic Prees, Inc.