Repeated exposure rivals lightweight training in Bayesian inference: accuracy, retention, and generalization

Bayesian inference is fundamental to interpreting diagnostic evidence, yet individuals often fail to integrate base rates and test characteristics when evaluating test results. Key questions are whether these difficulties can be attenuated by brief, scalable interventions, whether possible improvements are maintained over time, and whether they generalize to different probability judgments. We addressed these questions in an online experiment involving 256 laypeople who were presented with medical-screening Bayesian problems in a natural-frequency format and asked to estimate either positive predictive value (PPV) or negative predictive value (NPV). Participants were assigned to one of three conditions: repeated exposure to the problems, brief text-based training based on highlighted wording, or brief dynamic training based on animated visualizations. They completed the task before and after the intervention, and again in a delayed post-test administered 8-10 days later, which also assessed generalization to the predictive value not practiced during the intervention (namely PPV following NPV and vice versa). Performance improved reliably from pre-test to immediate post-test and remained elevated at delayed post-test. Moreover, improvements generalized to the unpracticed predictive value. However, neither training condition conferred a consistent advantage over mere exposure to plain text. Accuracy did not vary by predictive value, with comparable performance across PPV and NPV, and error analyses suggested that incorrect responses were heterogeneous and only weakly captured by standard non-Bayesian categories. Together, these findings suggest that modest but significant gains in Bayesian reasoning can emerge from repeated task exposure, whereas highlighted text, dynamic visualization, and feedback do not confer additional benefit.