Receiver-Operating Characteristics Determined by a Mechanical Analog to the Rating Scale

In one portion of a fixed-interval-observation experiment, observers indicated their certainty that a 500-cps signal had been presented in a thermal-noise background by positioning a slider after each interval. In a second portion of this experiment, the observers responded by making binary decisions. Slider positions were treated as typical confidence ratings; the conditional probability of a given rating or of one indicating greater confidence, given signal plus noise, was plotted against the probability of these ratings, given noise alone. Functions produced in this manner, for a rating scale divided into thirty-six positions, were fit closely by the receiver-operating characteristics (ROC's) of the theory of signal detectability. A psychophysical model using two straight-line segments did not provide a good approximation to these data. Values of d′ were generally lower for the rating procedure than for the binary-decision procedure. The use of a large number of rating categories did not result in large increases information transmitted by the observers, but it did provide the desired fine resolution of the ROC's.