Empirical Discriminability of Two Models for Stochastic Relationship Between Additive Components of Response Time

Abstract

Dzhafarov (1992,J. Math. Psych.36, 235–268) analyzed additive decompositions of simple response time (RT) into two random variables: a signal-independent component and a component stochastically decreasing and 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 stochastically independent sources of random variability, Dzhafarov proposed 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 patterns of the asymptotic RT behavior on a population level. Our computer simulations show, however, that if Dzhafarov's test based on this difference is applied to RT samples generated according to the stochastic independence model, the results can sometimes mimic the asymptotic predictions 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 applies the test to a sequence of nested regions of large signals. Our computer simulations show that with this approach the two models can be reliably discriminated on realistically sized RT samples