The optimum decision rules for the oddity task

This paper presents the optimum decision rule for an m-interval oddity task in which m-1 intervals contain the same signal and one is different or odd. The optimum decision rule depends on the degree of correlation among observations. The present approach unifies the different strategies that occur with ''roved'' or ''fixed'' experiments (Macmillan & Creelman, 1991, p. 147). It is shown that the commonly used decision rule for an m-interval oddity task corresponds to the special case of highly correlated observations. However, as is also true for the same-different paradigm, there exists a different optimum decision rule when the observations are independent. The relation between the probability of a correct response and d' is derived for the three-interval oddity task. Tables are presented of this relation for the three-, four-, and five-interval oddity task. Finally, an experimental method is proposed that allows one to determine the decision rule used by the observer in an oddity experiment.