The project described was supported by Award Number R21CA149796 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Health. We thank the National Cancer Institute for its support.
Semantic Coherence and Inconsistency in Estimating Conditional Probabilities
Version of Record online: 27 MAR 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Journal of Behavioral Decision Making
Volume 26, Issue 3, pages 237–246, July 2013
How to Cite
Wolfe, C. R., Fisher, C. R. and Reyna, V. F. (2013), Semantic Coherence and Inconsistency in Estimating Conditional Probabilities. J. Behav. Decis. Making, 26: 237–246. doi: 10.1002/bdm.1756
- Issue online: 25 JUN 2013
- Version of Record online: 27 MAR 2012
- conditional probability;
- semantic coherence;
- probability estimation;
- Bayes' theorem;
Two studies examined semantic coherence and internal inconsistency fallacies in conditional probability estimation. Problems reflected five distinct relationships between two sets: identical sets, mutually exclusive sets, subsets, overlapping sets, and independent sets (a special case of overlapping sets). Participants estimated P(A), P(B), P(A|B), and P(B|A). Inconsistency occurs when this constellation of estimates does not conform to Bayes' theorem. Semantic coherence occurs when this constellation of estimates is consistent with the depicted relationship among sets. Fuzzy-trace theory predicts that people have difficulty with overlapping sets and subsets because they require class-inclusion reasoning. On these problems, people are vulnerable to denominator neglect, the tendency to ignore relevant denominators, making the gist more difficult to discern. Independent sets are simplified by the gist understanding that P(A) provides no information about P(B), and thus, P(A|B) = P(A). The gist for identical sets is that P(A|B) = 1.0, and the gist of mutually exclusive sets is that P(A|B) = 0. In Study 1, identical, mutually exclusive, and independent sets yielded superior performance (in internal inconsistency and semantic coherence) than subsets and overlapping sets. For subsets and overlapping sets, interventions clarifying appropriate denominators generally improved semantic coherence and inconsistency, including teaching people to use Euler diagrams, 2 × 2 tables, or relative frequencies. In Study 2, with problems about breast cancer and BRCA mutations, there was a strong correlation between inconsistency in conditional probability estimation and conjunction fallacies of joint probability estimation, suggesting that similar fallacious reasoning processes produce these errors. Copyright © 2012 John Wiley & Sons, Ltd.