When intuitive Bayesians need to be good readers: The problem-wording effect on Bayesian reasoning

Abstract

Are humans intuitive Bayesians? It depends. People seem to be Bayesians when updating probabilities from experience but not when acquiring probabilities from descriptions (i.e., Bayesian textbook problems). Decades of research on textbook problems have focused on how the format of the statistical information (e.g., the natural frequency effect) affects such reasoning. However, it pays much less attention to the wording of these problems. Mathematical problem-solving literature indicates that wording is critical for performance. Wording effects (the wording varied across the problems and manipulations) can also have far-reaching consequences. These may have confounded between-format comparisons and moderated within-format variability in prior research. Therefore, across seven experiments (N = 4909), we investigated the impact of the wording of medical screening problems and statistical formats on Bayesian reasoning in a general adult population. Participants generated more Bayesian answers with natural frequencies than with single-event probabilities, but only with the improved wording. The improved wording of the natural frequencies consistently led to more Bayesian answers than the natural frequencies with standard wording. The improved wording effect occurred mainly due to a more efficient description of the statistical information-cueing required mathematical operations, an unambiguous association of numbers with their reference class and verbal simplification. The wording effect extends the current theoretical explanations of Bayesian reasoning and bears methodological and practical implications. Ultimately, even intuitive Bayesians must be good readers when solving Bayesian textbook problems.

Keywords: Bayesian reasoning; Mathematical problem-solving; Natural frequencies; Wording effect.