Book review: Calculated Risks, by Gerd Gigerenzer

Gigerenzer (2003) addresses statistical thinking, and the lack thereof, in medical and legal contexts, focusing on handling probabilities (risks). He identifies several issues and correctives:

• The illusion of certainty. For instance, most patients are not told that diagnostic medical tests can make mistakes, and are not informed of the error rates (false positive and false negatives).
• Ignorance of risk. Even if uncertainty is acknowledged, laymen and experts often do not know how great the level of risk is.
• Miscommunication of risk. Because of the peculiarities of human psychology, the way that risk information is usually communicated (using probabilities expressed as frequencies) can be misleading. For instance, absolute risk reduction, relative risk reduction, and number needed to treat are all mathematically equivalent ways to express the efficacy of a treatment. However, relative risk reduction is usually the way to communicate the results that leaves the best impression on the untutored mind.
• Clouded thinking. Even when risks are communicated properly, both experts and laypeople may not know how to reason with them. Expressing probabilities as natural frequencies forces us to focus on the reference class, and it allows people with little training to carry out Bayes Rule calculations easily.

The book provides a number of interesting case studies: the cases of breast cancer screening and AIDS counseling are particularly dramatic, and should be required reading for anyone taking a diagnostic medical test. Several other decision making heuristics that can result in misleading results are discussed, such as the "category effect". In general though, the book is not a complete discussion of the psychology of judgment and decision making applied to statistical thinking. Nonetheless, the author identifies a number of sub-optimal medical and legal practices in every day life.

Reference

Gerd Gigerenzer, 2003: Calculated Risks: How to Know When the Numbers Deceive You. Simon & Schuster.