Overcoming difficulties in Bayesian reasoning: A reply to Lewis and Keren (1999) and Mellers and McGraw (1999)

Bayesian reasoning can be improved by representing information in frequency formats rather than in probabilities. This thesis opens up applications in medicine, law, statistics education, and other fields. The beneficial effect is no longer in dispute, but rather its cause and its boundary conditions. C. Lewis and G. Keren (1999) argued that the effect of frequency formats is due to "joint statements" rather than to "frequency statements." However, they overlooked the fact that our thesis is about frequency formats, nor just any kind of frequency statements. We show that joint statements alone cannot account for the effect. B. A. Mellers and A. P. McGraw (1999) proposed a boundary condition under which the beneficial effect is reduced. In a reanalysis of our original data, we found this reduction for the problem they used but not for any other problem. We conclude by summarizing results indicating that teaching frequency representations fosters insight into Bayesian reasoning.