Abstract
In three experiments on joint probability estimation, gist representations were manipulated with analogies, and the suboptimal strategy of ignoring relevant denominators was counteracted with training in using 2βΓβ2 tables to clarify joint probability estimates. The estimated probabilities of two events, as well as their conjunctive and disjunctive probabilities, were assessed against two benchmarks, logical fallacies and semantic coherenceβa constellation of estimates consistent with the relationship among sets. Fuzzyβtrace theory (FTT) predicts that analogies will increase semantic coherence, and a table intervention affecting denominator neglect will both increase semantic coherence and reduce fallacies. In all three experiments, analogies increased semantic coherence. In both experiments training participants to use 2βΓβ2 tables, such tables reduced fallacies and increased semantic coherence. As the relations among sets in the problem materials progressed in cognitive complexity from identical sets, mutually exclusive sets, and subsets to overlapping sets, fallacies generally increased, and semantic coherence generally decreased. These findings indicate that denominator neglect is pervasive, but that it can be remedied with a straightforward intervention that clarifies relations among sets. Further, intuitive gistβbased probability estimation can be improved through the use of simple analogies. Copyright Β© 2009 John Wiley & Sons, Ltd.