
Gigerenzer explains that a major obstacle to our understanding of numbers is that we live with an illusion of certainty. Many of us believe that HIV tests, DNA fingerprinting, and the growing number of genetic tests are absolutely certain. But even DNA evidence can produce spurious matches. We cling to our illusion of certainty because the medical industry, insurance companies, investment advisers, and election campaigns have become purveyors of certainty, marketing it like a commodity. To avoid confusion, says Gigerenzer, we should rely on more understandable representations of risk, such as absolute risks. For example, it is said that a mammography screening reduces the risk of breast cancer by 25 percent. But in absolute risks, that means that out of every 1,000 women who do not participate in screening, 4 will die while out of 1,000 women who do, 3 will die. A 25 percent risk reduction sounds much more significant than a benefit that 1 out of 1,000 women will reap. This eye-opening book explains how we can overcome our ignorance of numbers and better understand the risks we may be taking with our money, our health, and our lives.
Gerd Gigerenzer has a nice book, Reckoning with Risk (or Calculated Risks: How to Know When Numbers Deceive You in the US), in which he calls for people to stop using percentages and to use natural numbers numbers instead.
When you say that someone's risk has increased by 33% they usually have no idea what that means, but they think it's scary. But if the risk used to be 0.001% then a 33% increase isn't much to worry about.
The book has many examples from real world medicine of people having great disruption caused because they took medical treatment based on a faulty understanding of the numbers. It wasn't just lay people making the mistakes either; many doctors and consultants were getting the numbers wrong.
http://www.amazon.com/Calculated-Risks-Know-Numbers-Deceive/...
for readable training in rational thinking. Interestingly, Gigerenzer's more recent books have focused more on strategies for using standard human thought processes, which may not be strictly rational, to reach correct decisions. I haven't read those books yet as closely as I have read Calculated Risks.
