Implications of Latency Data for Threshold and Nonthreshold Models of Signal Detection1

Two detection cum latency models are constructed by combining sets of plausible assumptions about latency with, in the first instance, the model of the Theory of Signal Detection and, in the second instance, a general threshold model. The aim of this paper is to show that latency statistics can be used to provide sharp tests for distinguishing between the two models. The two statistics studied are the reaction time operating characteristic (RT-ROC) and the plot of average reaction time against response probability (RT-probability curve). It is shown that, under the first detection model, the RT-ROC lies below the ROC derived from detection rates except at the “yes-no” point, and the RT-probability curve is decreasing whereas, under the second model, the RT-ROC coincides with portions of the latter ROC, and decreasing RT-probability curves do not arise naturally, The effect of criterion variability on the ROC is discussed in detail and conditions are given under which the RT-ROC is equivalent to a ROC generated by variable criteria.