The subtitle of this book is Learning to Live with Uncertainty, and I had assumed it would focus on the "irrational" way that humans behave in the face of risk, such as avoiding airplane journeys even though they are statistically safer than cars, etc.. Well, it is about that a bit, but the main thrust of the book is to try to educate the reader on how to interpret, and better understand, the kinds of statistical information which are so often used in society today.

According to Gigerenzer, a major problem is clouded thinking, which he defines as "a form of innumeracy, in which a person knows about the risks but not how to draw conclusions or inferences from them." His argument is that clouded thinking is something that can be countered, if one learns various techniques, or mind tools, to use when presented with a series of seemingly complicated statistical data.

The book contains chapters describing several cases where statistical data is available and yet hard to understand, and he shows how the use of mind tools can clarify the data and make it easier to assess the cost/benefits of a particular decision. He also shows how in many cases statistics are used in a misleading way, either deliberately or through ignorance.

Gigerenzer quotes various statements that have been made on risks, and shows how, although they may be correctly stating statistical data, the terms used, and confusion between such things as absolute and relative probability makes it quite difficult to determine exactly what they mean. In contrast, when he translates these statements into "natural frequencies", the same data becomes much more clear.

For example, the two statements below contain the same information, but the second one makes it a lot easier to deduce how likely it is that a positive test means a woman actually has breast cancer (from p41):

1. The probability that one of these woman has breast cancer is about 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram.

and

2. Eight out of every 1,000 woman have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don't have breast cancer, some 70 will still have a positive mammogram.

Some other things I highlighted when reading the book:

• In a survey, 1,000 Germans were asked what "40 percent" means. About one third did not choose the right answer from:
  1. one quarter
  2. 4 out of ten
  3. every 40th person
  [p23]
• Probability can mean different things, e.g.
  1. degrees of belief, e.g. "I think it's 80% certain that I'll pass my driving test"
  2. propensities, e.g. "the die has a 1 in 6 chance of showing a 4"
  3. frequencies, e.g. "half of people who smoke die of a tobacco-related illness"
  and it is important to understand which kind of probability is being used [p26]
• People asked to estimate values will give different answers depending how alternative options are presented. For example, asked to assess a value on a linear scale from 0 to 100%, a different average was obtained from when the same question was asked with a scale that ran linearly from 0 to 40, with one extra section marked ">40%". [p192]
• There's a big difference between relative risk and absolute risk, although the distinction isn't always made clear. For example, the absolute risk of a thromboembolism as a side effect of birth-control pills is 2 in 14,000 instead of 1 in 14,000. But in relative terms, the risk doubles. [p207]
• number needed to treat is another useful piece of information which is not always made available. For example, if you prescribe cholesterol-lowering drugs to 1,000 people, and the result is one death fewer, then NNT is 1,000. [p35]

Studies (by the author and others) show that "natural frequencies" are a much better way of communicating information. Rather worryingly, many of these studies show that professionals such as surgeons and lawyers "switch off" when presented with a statement containing percentages, or are happy to admit that they don't understand numbers. More hopefully, studies also show that once people are taught how to use mind tools, they remember the tools and continue to apply them. In fact after the first part of the book I found myself using natural frequencies to tackle some of the statements in later sections, so with any luck it's helped me too.

He does seem to have a bit of a bee in his bonnet about breast cancer, and while the data he provides does seem quite compelling, I don't feel I know enough about that subject to criticise what he says. But whether he's right or not about this, the techniques he describes make the book worth reading.

Completed : 27-Sep-2004