On the Interpretation of Response Time vs Onset Asynchrony Functions: Application to Dual-Task and Precue-Utilization...

The central bottleneck model of dual-task performance (H. Pashler and J. C. Johnston, 1998, Quarterly Journal of Experimental Psychology, 46A, 51-82) and the serial processing model of precue utilization (R. Gottsdanker, 1992, Acta Psychologica, 79, 21-43) are based on a common formal structure: They both represent response time as RT(tau)=max(X-tau, Y)+Z, where X, Y, Z denote the duration of certain processing stages specified by the models and tau denotes the onset asynchrony (SOA) between two stimuli. We consider this model within a stochastic framework in which the stage durations are random variables following an arbitrary joint distribution and derive properties of the function relating E[RT(tau)] to SOA. We present a distribution-free result which relates the slope of this function to the distribution of the random durations of the assumed processing stages. Our results allow for a direct, model-based interpretation of data from related experiments; specifically, they show how the slope of the SOA-function depends on experimental factors which selectively influence individual processing stages. We explain the implications of our results for models of dual-task performance and precue utilization and illustrate their application to data obtained by M. C. Smith (1969, Acta Psychologica, 30, 220-231) and R. Gottsdanker (1992, loc. cit.) Copyright 2001 Academic Press.