Psychologists interested in such diverse areas as scientific reasoning, attribution theory, depression, and judgment have central to their theories the ability of people to judge the degree of covariation between two variables. We performed seven experiments to help determine what heuristics people use in estimating the contingency between two dichotomous variables. Assume that the two variables are Factor 1 and Factor 2, each of which may be present or absent. In Experiment 1 we hypothesized that people assess contingency solely based on the number of instances in which both Factor 1 and Factor 2 are present. By manipulating column and row tables of a 2x2 matrix, we were able to place various values in this "present-present" cell, also called Cell A. If subjects do base their contingency estimate on Cell A, we would expect a monotonic relation between Cell A frequency and the contingency estimate. This test of the Cell A heuristic led us to conclude that it could not represent a complete explanation of contingency estimation. Although Experiment 2 resulted in a rejection of one possible explanation of the results of Experiment 1, Experiment 2 and 3 together provided us with an essential finding: Very low cell frequencies are greatly overestimated. In Experiment 4 participants in a contingency estimation task involving no memory demands used rather complex heuristics in judging contingency. When the memory demands were increased in Experiment 5, the comparatively simple Cell A heuristic emerged as the modal strategy. Two factors, the use of simple heuristics by most subjects and the overestimation of small cell frequencies, combined to explain the results of Experiments 2 and 3. In Experiment 6 we showed that in a contingency estimation task, salience can augment the impact of one type of data but not another. In Experiment 7 we learned that the versus at the end of the data stream, can influence the final estimate. From this group of experiments we concluded that the "framing" of the task affects the contingency estimate; a number of factors that bear no logical relation to the contingency between two factors nevertheless influence one's perception of the contingency. Finally, we related our findings to a variety of analogous findings in the research areas of memory, attribution theory, clinical judgment, and depression.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education