Calculated Risks: How to Know When Numbers Deceive You By Gerd Gigerenzer

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Author: Gerd Gigerenzer

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At the beginning of the twentieth century, H. G. Wells predicted that statistical thinking would be as necessary for citizenship in a technological world as the ability to read and write. But in the twenty-first century, we are often overwhelmed by a baffling array of percentages and probabilities as we try to navigate in a world dominated by statistics.Cognitive scientist Gerd Gigerenzer says that because we haven't learned statistical thinking, we don't understand risk and uncertainty. In order to assess risk -- everything from the risk of an automobile accident to the certainty or uncertainty of some common medical screening tests -- we need a basic understanding of statistics.Astonishingly, doctors and lawyers don't understand risk any better than anyone else. Gigerenzer reports a study in which doctors were told the results of breast cancer screenings and then were asked to explain the risks of contracting breast cancer to a woman who received a positive result from a screening. The actual risk was small because the test gives many false positives. But nearly every physician in the study overstated the risk. Yet many people will have to make important health decisions based on such information and the interpretation of that information by their doctors.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.

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Uncertainty in life is accepted. We are forced to deal with it regularly in our daily lives. But do we really understand the risks associated with this uncertainty? For most of us, I'd say probably not. In many cases certainty is an illusion according to Gigerenzer. We are generally beset by what he calls innumeracy - a lack of understanding of numbers and what they mean. For example, when we are presented with the risks of, let's say, treatment with a statin drug, there are three ways to present the benefits - absolute risk reduction, relative risk reduction, and something called number needed to treat (NNT). In this case relative risks make something seem better, or worse, than it really is, but this is usually the numbers we are given by the medical profession. Gigerenzer shows through diagrams, charts and tables, and something called natural frequencies just how we can be misled by the way probabilities are presented.He follows this introduction with a chapter on breast cancer screening. This chapter was an eye-opener. I think the information presented here should be required reading for any woman who has a mammography on a regular basis as a prophylactic measure. Misunderstanding of the results of the test can lead to unnecessary trauma and hardship. As Gigerenzer notes, "Women who are contemplating prophylactic mastectomy should know these numbers in order to be able to make an informed decision. [...] Ignorance of risks seems to be the rule rather than the exception." This problem is related to the concept of "informed consent." The author then shows how to turn this ideal of informed consent into reality. This requires education of not only the patient, but also the physician.In subsequent discussion about colorectal cancer and prostate cancer screening, he drives home the difference between conditional probabilities and natural frequencies. Through numerous examples, charts, and diagrams, he clearly make the case for the use of natural frequencies (these avoid the use of percentages and probabilities), which is so much clearer and is necessary for what he calls "informed consent." In the next chapter on AIDS counseling, we learn about the importance of certain parameters such as sensitivity, false positives, prevalence, and positive predictive value. Gigerenzer explains the importance of all of this and exposes the principle deficits of counseling. He compares responses from nineteen counselors to these parameters; the disparity in the responses is truly amazing. Again, before one agrees to AIDS testing, I recommend reading this chapter. He follows with very interesting chapters on wife battering and DNA fingerprinting. In the chapter on DNA fingerprinting, he explains the "chain of uncertain inference." This is a sequence that goes as follows: reported match > true match > source > present at crime scene > guilt. Gigerenzer gives a detailed analysis of each of these steps leading from a DNA match to the proof of the guilt or innocence of the defendant. It's all very interesting.Not surprisingly, innumeracy can be exploited. Representations can be chosen that mislead the innumerate without being inaccurate. For instance, Gigerenzer shows a sample from an information leaflet written by 12 physicians that was available in the waiting rooms of German gynecologists. The leaflet (on hormones and cancer) demonstrated the potential cost (increased risk of breast cancer) as an absolute risk while showing the potential benefit (a decreased risk of colon cancer) as a relative risk. This clearly made the cost appear smaller and the benefit larger. This was not inaccurate, just misleading. Caveat lector!In the chapter on "Fun Problems," I enjoyed the Monty Hall problem. This is based on the show Let's Make a Deal. Suppose you have three doors to choose from, and you pick number one. The host shows that door three has a goat; should you switch to door number two? You will find the answer, and the explanation of the answer, enlightening. Gigerenzer follows this up with a three prisoner problem which is similar. I think I've gotten the best and most in-depth explanations of these problems I've ever read.The author ends with a chapter showing us how to teach clear thinking when it comes to the numbers game, and includes a glossary of all the technical terms used in the book. I actually read all the definitions in the glossary as they were very informative. You can learn a lot from this book.I hope I have been able to give you a flavor for what's in this book. The point to take home is that there is so much uncertainty in numbers, especially in matters that can be life altering, that I definitely recommend this book as required reading for anyone who faces the risks discussed in this book. It could be a matter of life or death - really!

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Special Edition Calculated Risks: How to Know When Numbers Deceive You with FREE EASY Reading!

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