THE STRUCTURE OF SIMPLE REACTION-TIME TO STEP-FUNCTION SIGNALS

Simple reaction time to a step-function signal of amplitude A can be additively decomposed into a signal-dependent component, T(A) (converging to zero as A increases), and a signal-independent component, R. The two components, however, are not mutually independent, they both are increasing deterministic functions of a single random variable; T(A) = T(A, C) and R = R(C). C is interpreted as a "criterion" or "inhibition factor" controlling simultaneously "readiness to detect" and "readiness to respond". The model is not based on a priori distributional assumptions. RT percentiles of a given rank P computed across RT distributions for different values of A, have a deterministic structure, RTP(A) = T(A, CP) + R(CP), where CP is the Pth percentile of C. Subtracting RTP(A*) for a very large A* from RTP(A), one gets an estimate of T(A, CP), the Pth percentile of T(A). Applying this to different values of P, one can a posteriori reconstruct the joint distribution of the two RT components. The asymptotic consequences of this model (for sufficiently large A) are corroborated by data on the RT to instantaneous displacements of a visual target. © 1992.