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

#### Abstract

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.

*This paper has been withdrawn.*