On measuring the minimum detection time: a simple reaction time study in the time estimation paradigm.

Kornblum's time estimation paradigm, together with the so-called 'race model', provides an appealing alternative for measuring the 'cut-off' which separates 'true' reaction times from anticipatory reaction times. However, the model is not precise enough to reveal the relation between the signal intensity and the 'cut-off'. Accordingly, Kornblum's model is extended with an emphasis on the measure of the 'cut-off'. Another aspect of the extension is to use a parametric method to analyse the data. In particular, it is assumed that the time estimation-induced latency is gamma distributed and the signal-induced latency is Weibull distributed, with the latter shifted by the 'cut-off'. The rationale behind the parametric assumption is discussed. For illustrative purposes, two pieces of experimental work are presented. Since the core of the race model is the assumption of an independent race between the time estimation process and the detection process, the first experiment tests whether, for the same signal intensity, the signal-induced latency distribution is invariant across different time intervals; the second experiment tests whether, for the same time interval, the time estimation-induced latency distribution is invariant across different signal intensity conditions. The data from the second experiment are also used to test various parametric assumptions in the model, which include the signal effect on the 'cut-off'. The new model fits the data well.