A theoretical study of process dependence for critical statistics in standard serial models and standard parallel models

摘要

Long before the mathematical developments that led inexorably to the development of systems factorial technology, the somewhat arduous, but arguably requisite labors which precisely defined parallel and serial architectures had begun (e.g., Townsend, 1969, 1972). Both then and now, what are now referred to as standard serial models and standard parallel models not only play an important role in psychological science, they are often what non-mathematical psychologists are (sometimes in an unschooled fashion) referring to when they bring up architectural concepts. Interestingly, two strategic and critical properties, and therefore implicit predictions of the canonical serial and parallel models have witnessed little analysis. In this article, we address three issues: (1) Standard parallel models predict stochastically independent processing times and therefore total completion times. There is a partially valid intuition that standard serial models will predict positive dependence among totally completion times and standard serial models based on exponential processing time do predict this (Townsend and Ashby, 1983, p. 73). This also holds if only one order of processing is possible. However, if there is a mixture of processing orders, certain distributions can predict negative dependencies on this statistic. (2) Analogously, standard serial models predict independent and identically distributed processing times and therefore intercompletion times. Certain examples of standard parallel models (again, based on exponential processing times) suggest that the intercompletion times tend to increase over time and stages although there has been no information on their interdependence. Interestingly, we again find that there is an inclination for standard parallel models to emulate this behavior but that this tendency can be over-ridden by dramatically increasing parallel-channel hazard functions. (3) Are there psychological questions that pertain to these distinctions and are there any experiments that have emerged to assess the latter? With regard to experimental data on these issues, it turns out that there exists some data from categorical free recall that bear on some of the behavior of intercompletion times, which we discuss. To date, we know of no investigations that explore correlations of total completion times, although such analyses appear relatively straightforward. (C) 2019 Published by Elsevier Inc.