On using the fixed-point property of binary mixtures to discriminate among models of recognition memory

A variety of different recognition-memory models make different psychological assumptions, but similar predictions about ROC curves in old–new recognition-memory experiments. Some models assume that recognition responses are produced by a unitary process and other models assume they are a binary mixture of two qualitatively different types of responses. This note shows that despite their similar ROC predictions, the binary-mixture models make some striking predictions that the unitary models do not make. Specifically, in any experiment that includes conditions in which the mixture probability varies but the component distributions do not, the binary-mixture models predict that all response time probability density functions must intersect at the same time point (if they intersect at all). Similarly, they also all predict that if the ROC curves intersect, they must also all intersect at the same point.