Chapter 3 reports some evidence that the facilitating influence of frequency formats for Bayesian reasoning problems is restricted to certain groups. A new study indicates that it is the most numerate people who benefit the most from frequency formats, as compared to standard probability formats. Chapman and Liu (2009) presented student participants with one frequency problem and one probability problem, and also asked them to complete the 11-item numeracy scale developed by Lipkus, Samsa, and Rimer (2001). Based on this last measure students were divided into high-numerate and low-numerate groups. Correct responses to Bayesian problems were rare, with the most frequent errors being to report a figure close to either the hit rate or the base rate. However, frequency formats did result in somewhat more correct answers, but this effect was largely restricted to the most numerate students.
References
Chapman, G.B., and Liu, J. (2009). Numeracy, frequency, and Bayesian reasoning. Judgment and Decision Making, 4 (1), 34-40.
Lipkus, I.M., Samsa, G., & Rimer, B.K. (2001). General performance on a numeracy scale among highly educated samples. Medical Decision Making, 21, 37-44.
Corrections and clarifications
There is an error in Figure 3.3. This is the tree diagram representing Eddy's (1982) medical problem. For the branch representing P(Negative | Cancer) the probability should be 0.208, NOT 0.028. Accordingly, the number at the rightmost end of the branch should be 0.0028, NOT 0.00028.
This does not affect the answer to the problem stated in the text, which remains 0.077.
My thanks to Chloe Turner (one of my students) for pointing this out.
Saturday 14 March 2009
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