A tandem random walk model of the SAT paradigm: response times and accumulation of evidence

The speed-accuracy trade-off (SAT) paradigm forces participants to trade response speed for information accuracy by presenting them with a response signal at variable times after the onset of processing to which they must give an immediate response (within 300 ms). The processes that underlie the paradigm, especially those affecting response times, are not completely understood. Also, the extent to which the paradigm might affect the evidence accumulation process is still unclear. By testing several different sets of assumptions, we present a random walk model for the SAT paradigm that qualitatively explains both accuracy and response time data. The model uses a tandem random walk, with two possible continuations in a second phase which begins after the response signal. If a boundary is not reached during phase one, the walk transfers the current sum (relative to the size of the boundaries) from phase one to phase two in the form of bias, with drift rate equal to zero. If, however, a boundary is reached in phase one, the second phase starts from zero (no bias) with a strong drift rate towards the previously reached boundary. The model also incorporates a psychological refractory period: a delay in the onset of a second task when two tasks are presented in close succession. The model is consistent with the idea that information about the evidence accumulation rate is not contaminated by the paradigm.