SDT and Contingency Assessment 116 Applying Signal Detection Theory to Contingency Assessment

In studies of contingency assessment a participant is asked to judge the relationship between events, a cue and an outcome. Although there are various forms of the task, a discrete trial format with a single cue and a single outcome often is used. On each trial, a cue may, or may not, be presented, following which an outcome may, or may not, be presented. Various cues and outcomes have been used. For example, the cue may consist of information that clouds have or have not been seeded, and the outcome consists of information that it has or has not rained (Ward & Jenkins, 1965); the cue may consist of information that a putative leavening agent has or has not been added to bread dough, and the outcome consists of information that the dough has or has not risen (Shaklee & Mims, 1981); the cue may consist of information that a patient has or has not a particular symptom, and the outcome consists of information that a patient does or does not have a particular disease (Smedslund, 1963). More generally, the stimuli presented to a participant can be summarized as a 2x2 matrix (see Table 1a). On each trial the cue either is presented (C) or is not presented (~C), and then the outcome either does occur (O) or does not occur (~O). The letters in the cells (a, b, c, d) represent the joint frequency of occurrence of the four cue-outcome combinations in a block of trials. Preparation of this paper was supported by research grants from the Natural Sciences and Engineering Research Council of Canada to SS and LGA. We thank Rolfe Morrison for assistance with the proof in Appendix 1, and Jennifer Heisz for her insightful comments during laboratory meetings. Correspondence concerning this manuscript should be addressed to either Shepard Siegel ([email protected]) or Lorraine Allan ([email protected]). The address for Shepard Siegel, Lorraine G. Allan, and Samuel D. Hannah is: Department of Psychology, Neuroscience and Behaviour, McMaster University, Hamilton ON L8S 4K1, Canada. The address for Matthew J. C. Crump is: Psychology Department,Vanderbilt University, PMB 407817 2301,Vanderbilt Place, Nashville, TN 37240-7817, USA. Volume 4, pp 116-134 2009