ASA 127th Meeting M.I.T. 1994 June 6-10

4aPP26. Optimal decision rules for the oddity task.

Niek J. Versfeld

TNO Inst. for Human Factors, P.O. Box 23, 3769 ZG Soesterberg, The Netherlands

Huanping Dai

David M. Green

Univ. of Florida, Gainesville, FL 32611-2065

In the most general oddity task, m-1 stimulus alternatives are the same and one is different. The decision maker must identify the odd stimulus. Two likelihood-ratio decision rules are derived by treating the stimuli as Gaussian random variables with means that depend on the stimulus conditions. The two rules depend on the correlation between the observations generated by the stimuli. For m=3, which is by far the most popular oddity task, two extreme cases are discussed. If the observations are highly correlated, the optimum decision rule is equivalent to the so-called triangular rule. The other decision rule is slightly different, and is optimum when the stimulus observations are independent. Different rules are applicable to experiment using fixed versus random standards. A COSS (conditional on a single stimulus) analysis provides a convenient way of estimating the rule actually used by a decision maker in a typical decision task. [Work supported by the Dutch Ministry of Defence and by the U. S. AFOSR.]