Selective influence and response time cumulative distribution functions in serial–parallel task networks

We analyze sets of mental processes, some of which are concurrent and some of which are sequential, under the assumption that the processes are partially ordered, that is, arranged in a directed acyclic network. Information about the process arrangement can be discovered by examining the effects on response time of selectively influencing process durations. Previous work has mainly focused on analyses of mean response times. Here we consider analyses based on cumulative distribution functions, for one of the major classes of directed acyclic networks, serial-parallel networks. When two pro-cesses are selectively influenced, patterns in the cumulative distribution func-tions can be used to test whether the processes are sequential or concurrent and whether the task network has AND gates or OR gates. Cumulative dis-tribution functions are potentially more informative than means, and some previous results for means are shown to follow from our results for cumulative distribution functions. 2000 Academic Press Considerable evidence indicates that the mental processes involved in some information processing tasks are neither entirely serial nor entirely parallel. Many alternative forms of processing are conceivable; one of the plausible and useful forms is a directed acyclic network, such as the one in Fig. 1. The network represents a combination of sequential and concurrent processing. The stimulus is presented at o, and processes x and z begin immediately and concurrently. Process y begins as soon as x is finished. The response is made at r as soon as both y and z are finished, if there is an AND gate, or as soon as either y or z is finished, if there is an OR gate. There are many examples of tasks for which good accounts of response time data have been given by directed acyclic networks (although not always by that name). doi:10.1006jmps.1999.1268, available online a