The effect of representations of binary variables on judgment of influence

Studies concerned with judgments of contingency between binary variables have often ignored what the variables stand for. The two values of a binary variable can be represented as a prevailing state (nonevent) or as an active state (event). Judgments under the four conditions resulting from the combination of a binary input variable that can be represented as event-nonevent or event-event with an outcome variable that can be represented in the same way were obtained. It is shown in Experiment 1, that judgments of data sets which exhibit the same degree of covariation depend upon how the input and output variables are represented. In Experiment 2 the case where both the input and output variables are represented as event-nonevent is examined. Judgments were higher when the pairing of the input event was with the output event and the input nonevent with the output nonevent that when the pairing was of event with nonevent, suggesting a causal compatibility of event-event pairings and a causal incompatibility of event-nonevent pairings. Experiment 3 demonstrates that judgments of the strength of the relation between binary input and output variables is not based on the appropriate statistical measure, the difference between two conditional probabilities. The overall pattern of judgments in the three experiments is mainly explicable on the basis of two principles: (1) judgments tend to be based on the difference between confirming and disconfirming cases and (2) causal compatibility in the representation of the input and output variables plays a critical role.