A Phase Transition Model for the Speed-Accuracy Trade-Off in Response Time Experiments
Article first published online: 8 NOV 2010
Copyright © 2010 Cognitive Science Society, Inc.
Volume 35, Issue 2, pages 211–250, March 2011
How to Cite
Dutilh, G., Wagenmakers, E.-J., Visser, I. and van der Maas, H. L. J. (2011), A Phase Transition Model for the Speed-Accuracy Trade-Off in Response Time Experiments. Cognitive Science, 35: 211–250. doi: 10.1111/j.1551-6709.2010.01147.x
- Issue published online: 10 FEB 2011
- Article first published online: 8 NOV 2010
- Received 2 February 2010; received in revised form 2 July 2010; accepted 21 July 2010
- Reponse times;
- Speed-accuracy trade-off;
- Sequential sampling models;
- Fast guess model;
- Phase transitions;
- Catastrophe theory
Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction—hysteresis in the transitions between guessing and stimulus-controlled behavior—was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction—bimodal RT distributions—was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding.