Psychophysics of Causality: Detecting Contingencies Is like Detecting Signals

The contingency assessment situation and the signal detection situation are similar in that the information on which the decision is based is uncertain. Nevertheless the two research endeavours have progressed independently, each with its own traditions and each motivated by different theoretical perspectives. Recently, some researchers have integrated these two lines of research and have demonstrated the value of applying a signal detection analysis to contingency assessment. In the present paper, we describe a new method, the streamed-trial procedure, that is better suited to the study of contingency detection and discrimination than is the traditional contingency judgment task, and we present data from experiments using this new procedure. We also discuss future research with the streamed-trial procedure that could provide a better understanding of intriguing findings in the contingency judgment literature such as “depressive realism”. We must often make a decision even though the information we have is ambiguous or uncertain. One such situation is illustrated by a patient being treated by an allergist. The patient sometimes, but not always, develops hives after eating strawberries. Moreover, the patient sometimes develops hives even when strawberries are not eaten. Although the relationship between eating strawberries and developing hives is uncertain, the allergist must decide whether or not to recommend that the patient stop eating strawberries. Another type of ambiguous situation is illustrated by the task confronted by the radiologist. The radiologist must decide whether or not an x-ray indicates the presence of lung cancer. The signals seen in the x-ray are ambiguous, some consistent with lung cancer and others inconsistent with lung cancer. Even though the correct diagnosis is unclear, the radiologist must decide whether or not to recommend treatment. Despite the obvious similarities between the tasks, they have been treated quite differently. The allergy task has often been used by researchers interested in contingency assessment; that is, how humans judge that a cue (strawberry ingestion) imperfectly signals an outcome. The cancer task has often been used by researchers interested in signal detection; that is, how humans make decisions about the presence of a signal (cancer symptoms) in a noisy background. The contingency assessment situation and the signal detection situation are similar in that the information on which the decision is based is uncertain. Yet research concerned with contingency assessment and research concerned with signal detection have progressed independently, each with its own traditions and each motivated by different theoretical perspectives and models. Recently, Allan, Siegel, and Tangen (2005) and Perales, Catena, Shanks, and González (2005) demonstrated the value of applying a psychophysical analysis to contingency assessment. In the present paper, we describe a new procedure that is better suited to the study of contingency detection and discrimination than is the traditional contingency judgment task. Table 1: The 2x2 matrix for the cueoutcome pairings in a contingency assessment task. O ~O C a b ~C c d On each trial of the traditional contingency task, a cue either is presented (C) or is not presented (~C), and then the outcome either occurs (O) or does not occur (~O). For example, in the previously-described allergy task, the observer is shown whether the patient consumed or did not consume strawberries, and then is shown whether the allergic reaction occurred or did not occur. After a series of trials on which each of the four cue-outcome combinations are presented with a pre-defined probability, the observer is asked to rate the strength of the relationship between the cue and the outcome. Table 1 presents the 2 x 2 matrix for the cue-outcome pairings. 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. One measure of the contingency between the cue and the outcome is ΔP (Allan 1980), € ΔP = P(O | C) −P(O |~ C) = a