A Note on the Stop-Signal Paradigm, or How to Observe the Unobservable

Department of Psychological SciencesPurdue UniversityA new theoretical analysis of the stop-signal paradigm is proposed. With the concepts of crude andnet hazard functions, the nonobservable control-latency distribution can be estimated from observ-able reaction times. This result allows a test of Logan & Cowan's (1984) model without any simplify-ing assumptions.In studies using response time as the major dependent vari-able, the stop-signal procedure has been used by several investi-gators in an attempt to reveal the time course of hypothesizedunderlying sensory or cognitive processes or both (e.g., LappinE Oilman, 1973). In this paradigm, subjects aregiven a primary reaction time task to perform, and a stop signalthat tells subjects to withhold their responses is sometimes pre-sented shortly after the primary stimulus. Logan and Cowan(1984) presented a theory of inhibition of thought and actionthat focuses on this paradigm. The purpose of this note is topresent a new theoretical analysis of the stop-signal paradigmthat allows a more stringent test of Logan and Cowan's modeland, in fact, of all theories based on this paradigm.Logan and Cowan-'s (1984) model accounts for response inhi-bition in terms of a "horse race" between two sets of processes,one that generates a response for the primary task and one thatreacts to the stop signal:If the primary-task process finishes before the stop-signal process,the response is executed; if the stop-signal process finishes beforethe primary-task process, the response is inhibited. To model thissituation, the finishing times of the primary-task and the stoppingprocess are assumed to be independent random variables, (pp.298-299)Note that the primary-task processing time is observable bothin the normal condition (i.e., the no stop-signal condition) andin the stop-signal condition given it "wins the race"; because ofthe nature of this paradigm, however, the stop-signal processingtime can never be observed. A major goal of a formal analysisof this paradigm, then, is to derive an estimate of this unobserv-able control latency. Logan and Cowan achieved this by assum-This note is based on a talk presented at the Hoosier Mental LifeConference, Indiana University, Bloomington, May 1989. The work waspartially supported by a grant from Stiftung Volkswagenwerk.I thank James Townsend and Richard Schweickert for their helpfulcomments on an earlier version of this note.Correspondence concerning this article should be addressed to HansColonius, Department of Psychological Sciences, Purdue University,West Lafayette, Indiana 47907.ing the stop-signal processing time to be constant. Assuming, inaddition, that the control-latency distribution peaks around itsmean, they offered an argument that this constancy assumptionyields a reasonable approximation to what would follow froma true horse-race mechanism. In a later article, Logan and Bur-kell (1986) introduced specific parametric assumptions for thecontrol-latency distribution.Rather than arguing about the soundness of this approxima-tion, in what follows I demonstrate that under the assumptionsof Logan and Cowan's (1984) race model, the entire distribu-tion of control latencies can be estimated in a straightforwardmanner from directly observable reaction times (observing theunobservable, so to speak). Moreover, this analysis permits anoverall test of the assumptions of the race model that is moredirect than in previous analyses.