Judgements of a 2 × 2 contingency table: Sequential processing and the learning curve

Shanks (1985) has used a video game to investigate how subjects estimate the effect of their behaviour in a task defined by a 2×2 contingency table. The subjects were able to distinguish positive and negative contingencies from zero contingencies. In addition, they showed a learning curve and a bias to rate zero contingencies with a high outcome density higher than low-density zero contingencies. He interpreted these data as being consistent with associative models derived from animal learning. In Experiment 1 we replicated these results using a task and instructions similar to his. In a second experiment we showed that the subjects' tendency to overestimate high-density zero contingencies did not arise because the “game” was so difficult that it interfered with processing the events. In this experiment subjects were given tables of the outcome frequencies that had been determined by the earlier subjects. These subjects were, if anything, less accurate in rating the zero contingencies. We point out several logical problems with Shanks's initial task. The task did not represent a true 2×2 contingency, and aspects of it were physically impossible. In Experiment 3 we modified the task to represent a true 2×2 contingency. Using this task, we found a similar pattern of results, except that there was no evidence of the learning curve predicted by the associative models. We conclude that there is little in our data to rule out a “rule-based” analysis of contingency judgements.