EMPIRICAL DISCRIMINABILITY OF 2 MODELS FOR STOCHASTIC RELATIONSHIP BETWEEN ADDITIVE COMPONENTS OF RESPONSE-TIME

Dzhafarov (1992, J. Math. Psych. 36, 235-268) analyzed additive decomp ositions of simple response time (RT) into two random variables: a sig nal-independent component and a component stochastically decreasing an d vanishing as signal magnitude increases. The asymptotic behavior of RT (the dependence of RT of a given quantile rank on signal magnitude in the region of sufficiently large signals) was shown to be different under different models of stochastic relationship between the two RT components. As a simple alternative to the more traditional stochastic independence model, according to which the two RT components have sto chastically independent sources of random variability, Dzhafarov propo sed a single-variate RT decomposition model (SVRT) according to which the two components are increasing functions of a single common source of random variability. The two models predict distinctly different pat terns of the asymptotic RT behavior on a population level. Our compute r simulations show, however, that if Dzhafarov's test based on this di fference is applied to RT samples generated according to the stochasti c independence model, the results can sometimes mimic the asymptotic p redictions of the SVRT model. This happens because of the uncertainty in determining the range of signals that are ''sufficiently large'' to warrant asymptotic approximations, This difficulty can be overcome if instead of choosing a fixed range of large signals one repeatedly app lies the test to a sequence of nested regions of large signals. Our co mputer simulations show that with this approach the two models can be reliably discriminated on realistically sized RT samples. (C) 1996 Aca demic Press, Inc.