How to Teach Bayesian Reasoning: an Empirical Study Comparing Four Different Probability Training Courses

Background: Bayesian reasoning is understood as the updating of hypotheses based on new evidence (e.g., the likelihood of an infection based on medical test results). As experts and students alike often struggle with Bayesian reasoning, previous research has emphasised the importance of identifying supportive strategies for instruction. Aims: This study examines the learning of Bayesian reasoning by comparing five experimental conditions: two "level-2" training courses (double tree and unit square, each based on natural frequencies), two "level-1" training courses (natural frequencies only and a school-specific visualisation "probability tree"), and a "level-0" control group (no training course). Ultimately, the aim is to enable experts to make the right decision in high-stake situations. Sample: N = 515 students (in law or medicine) Method: In a pre-post-follow-up training study, participants' judgments regarding Bayesian reasoning were investigated in five experimental conditions. Furthermore, prior mathematical achievement was used for predicting Bayesian reasoning skills with a linear mixed model. Results: All training courses increase Bayesian reasoning, yet learning with the double tree shows best results. Interactions with prior mathematical achievement generally imply that students with higher prior mathematical achievement learn more, yet with notable differences: instruction with the unit square is better suited for high achievers than for low achievers, while the double tree training course is the only one equally suited to all levels of prior mathematical achievement. Conclusion: The best learning of Bayesian reasoning occurs with strategies not yet commonly used in school.