Calculated Risks: How to Know When Numbers Deceive You

This is a very clearly written book. It demonstrates many numerical errors the press, the public, and experts make in interpreting the accuracy of medical screening test (mammography, HIV test, etc...) and figuring out the probability of an accused person being guilty. At the foundation of the above confusions lies the interpretation of Baye's rule. Taking one example on page 45 regarding breast cancer. Breast cancer affects 0.8% of women over 40. Mammography correctly interprets 90% of the positive tests (when women do have breast cancer) and 93% of the negative ones (when they don't have breast cancer). If you ask a doctor how accurate this test is if you get a positive test, the majority will tell you the test is 90% accurate or more. That is wrong. The author recommends using natural frequencies (instead of conditional probabilities) to accurately interpret Baye's rule. Thus, 8 out of every 1,000 women have breast cancer. Of these 8 women, 7 will have a positive mammogram (true positives). Of, the remaining 992 women who don't have breast cancer, 70 will have a positive mammogram (false positives). So, the accuracy of the test is 7/(7+70) = 10%. Wow, that is pretty different than the 90% that most doctors believe! What to do? In the case of mammography, if you take a second test that turns positive, the accuracy would jump to 57% (not that much better than flipping a coin). It is only when taking a third test that also turns positive that you can be reasonably certain (93% accuracy) that you have breast cancer. So, what doctors should say is that a positive test really does not mean anything. And, it is only after the third consecutive positive test that you can be over 90% certain that you have breast cancer. Yet, most doctors convey this level of accuracy after the very first test!What applies to breast cancer screening also applies to prostate cancer, HIV test, and other medical tests. In each case, the medical profession acts like the first positive test provides you with certainty that you have the disease or not. As a rule of thumb, you should get at least a second test and preferably a third one to increase its accuracy.The author comes up with many other counterintuitive concepts. They are all associated with the fact that events are far more uncertain than the certainty that is conveyed to the public. For instance, DNA testing does not prove much. Ten people can share the same DNA pattern. Another counterintuitive concepts is associated with risk reduction. Let's say you have a cancer that has a prevalence of 0.5% in the population (5 in 1,000). The press will invariably make promising headline that a given treatment reduces mortality by 20%. But, what does this really mean? It means that mortality will be reduced by 1 death (from 5 down to 4). The author states that the relative risk has decreased by 20%; but, the absolute risk has decreased by only 1 in 1,000. He feels strongly that both risks should

The author presents some important observations about calculatedrisks, probabilities and statistical test inferences. He makesclear the necessity to understand risks clearly at the outsetof any important decision. For instance, a physician must takeinto consideration "false positive " test results so thathe/she does not over-react. An over-reaction could cause thephysician to take unnecessary precautions that could do moreto endanger the patient than help. In addition, the authorcautions against fabrication of certainty or the use of statistics to prove a predetermined result. This book isuseful in arriving at a realistic design for a statisticaltest or any other test from which an important scientificinference will be made.

Gerd Gigerenzer has written several books dealing with "bounded rationality"--how humans use their brains to understand the world around them, make decisions, and determine the risks associated with a given course of action. This book is easily his most accessible. It is clear and easy to read, with most(but not all)the examples drawn from the field of personal health.Gigerenzer provides the simple mental tools that allow anyone to make sense of the statistics that bombard us daily in the media. It is exactly his point that one does not need to be a rocket scientist (or professional statistician) to understand the numbers used by professionals, from personal physicians to DNA experts, that affect our lives and livelihoods.If I could recommend only one book to address "numerical illiteracy," this would be it. You will learn some essential skills in a clearly informative and entertaining way.

In a valiant effort to educate professionals and lay people alike, the author of this book clearly explains how to interpret risks and risk data (statistics) in a useful and understandable way. For example, anyone who is wondering about whether or not to undergo screening for breast cancer, prostate cancer, HIV, etc. should do themselves a great big favor and read this book. The author also discusses legal issues such as how evidence may presented in court in order to support a given side of a case just by presenting statistical data, e.g., fingerprints, DNA evidence, etc., in certain ways. In addition, the author discusses a variety of other matters from advertising gimmicks to TV game show strategies. Using the techniques given in this book, readers will be much less likely to be fooled. Clearly written in plain english and in an engaging style, this book should be required reading for everyone - from professionals who provide statistical (risk) information (they would learn how to be more clearly understood) to those receiving the information (they would learn to see through any smoke screens or awkward presentations and thus make better decisions).