Comparing Bayes's Theorem to Frequency-Based Approaches to Teaching Bayesian Reasoning

John Ruscio, Elizabethtown College


Despite the conceptual simplicity of Bayesian reasoning, people often err when calculating or estimating conditional probability. These mistakes can have significant real-world consequences, and Bayes's Theorem is a notoriously difficult remedy to teach. Experimenters taught 113 students to use either Bayes's Theorem, 2 × 2 tables, frequency grids, or frequency trees to solve a sample mammogram problem. Immediately following written instruction, group demonstration, and a question-and-answer session, performance on new problems was equivalent across groups. However, when retested 4 weeks later, participants in the Bayes's Theorem group solved fewer problems and demonstrated a poorer understanding of Bayesian reasoning than participants in all other groups. Teaching a frequency-based approach to conditional probability appears to promote learning more effectively than teaching Bayes's Theorem.