Rejoinder: combining speed and accuracy to assess error-free cognitive processes

Abstract

yale university Carlos J. Morales worcester polytechnic instituteWe welcome Rouder's thoughtful comments, which provide valuable context for our work. We especially appreciate the amount of time that he has placed into examining features and properties of our model. Rouder points out the close connection of our modeling framework with the deadline model framework of Ollman and Billington (1972). In doing so, he explains some of the difficulties that have been discovered with deadline models, summarizing work by Ruthruff (1996) as well as his own with Ratcliff (Ratcliff and Rouder, 1998). Our response to Rouder's discussion allows us to clarify a bit further the assumptions underlying our model.While Rouder is correct in noticing that our error-free statistical model is nearly identical to the deadline model of Ollman and Billington (1972), our model is, in fact, different in a crucial respect. The deadline model, like our error-free modeling framework, assumes a race between two processes. The process of interest, the discrimination process, infallibly produces correct responses. The model assumes that a participant's underlying discrimination time distribution depends only on the type of stimulus presented, so that it is not affected by the relative stress on speed versus accuracy. Meanwhile, the deadline time process is under control of the participant, and is manipulated by the individual according to the demands of a trial. In other words, the deadline time is set by a participant before a trial begins, and is meant to capture the relative demands on speed versus accuracy.In our modeling framework, we also posit two processes that are in a race; one, the error-free process, which always produces correct responses, and the other, the guessing process, which randomly produces correct responses. But unlike the deadline model, our error-free modeling framework assumes that the two processes occur in parallel, and are meant to reflect all cognitive processes that are participant-specific for a fixed experimental condition. Thus, by contrast, our framework allows for the possibility that both processes can be affected by speed versus accuracy demands, not just one of the two processes (i.e., the guessing process). If speed or accuracy demands are experimentally manipulated (e.g., by asking the participant to be as accurate as possible rather than as quick as possible), then they can affect the error-free process insofar as changing speed or accuracy demands constitutes a change in the experimental condition. In our framework, all differences in an experimental setting, whether they are explicit changes in stress on speed versus accuracy, change in the difficulty of the task, change in induced emotion, etc., are