Indices of Discriminability

Hammerton and Altham1 have pointed out the desirability of having a numerical measure for the discriminability of two stimuli, A and B, that does not depend upon the specific assumptions about the probability distributions of the internal events produced by A and B. Assuming that the data consist of confidence ratings for A and B, they have proposed an index C, which is equal to the difference between the average ratings for A and B divided by the difference in the ratings that represent “certainly A” and “certainly B”. Unfortunately their definition assumes that at least one rating can represent “certainly A” and at least one rating can represent “certainly B”. This often does not happen. For example2, when observers were permitted to develop their own rating systems for visual stimuli, it was found that for stimuli consisting of 55 and 66 quanta, on the average, at the cornea, there was not a single rating that meant certainly one stimulus or certainly the other. Another way of saying this is that there was never a single trial on which the observer was certain that the stimulus was the strong one.