Calculated Risks: How to Know When Numbers Deceive You Paperback – March 19, 2003

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!

Older 2002 version of the author's 2014 Risk Savy book that largely replaced this one. I thought I was buying the newer book until I realized there were two similar books with different titles.

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 be conveyed to the public.The author shows how health agencies and researchers express benefits of treatments by mentioning reduction in relative risk. This leads the public to grossly overstate the benefits of such treatment. The author further indicates how various health authorities use either relative risk or absolute risk to either maximize or minimize the public's interpretation of a health risk. But, they rarely convey both; which is the only honest way to convey the data.If you are interested in this subject, I strongly recommend: "The Psychology of Judgment and Decision Making" by Scott Plous. This is a fascinating book analyzing how we are less Cartesian than we think. A slew of human bias flaws our own judgment. Many of these deal with other application of Baye's rule.

No math knowledge required to understand the concepts presented. The author communicates fairly complex probability ideas in clear prose.Here is a teaser. Suppose you take a routine blood test for disease X (you have no symptoms or reason to suspect you have disease X). You receive a positive result. The test is "95% accurate". What is the probability you have disease X?

Although we are living in the era of so-called "big data", most people are still surprisingly incapable of understanding uncertainties in their situations and making decisions out of it. This is particularly problematic when it comes to medical problems, which this book mostly concentrates on; mammography and HIV tests are taken as examples, and the author's demonstration of how misinterpreted these tests are by doctors and the general public came as a great shock to me. The author argues, however, that by realizing the uncertainty and representing it as natural frequencies, we can greatly improve our ability to cope with uncertainties.The book is very clearly written with rich & convincing examples; I would strongly recommend this book to my friends. However, I felt first few chapters already delivered most of the message and the rest of the book was repeating the same story again and again; it could've been written more concisely with better organization, but maybe the author wanted to dumb down as much as possible as his main purpose of writing this book is to educate the general public.

Non è un libro da studio ma un libro da lettura per passatempo

The only people who should not read this book are high school students. They would be wrongly scared about studying Math.LOL!

眼から鱗でした。数学に弱い医者がいかに多いかということが驚きでした。ここでは結核について主に取り上げていますが、偽陽性、偽陰性、罹患確率など、今の新型コロナ、COVID-19についての検査などについてメディアが騒いでいる現象に重ね合わすことができました。文系の人間としては、やや読みづらいものの非常に勉強になりました。

This book is an eye opener. It can be easily understood, enabling critical thinking and cross examination of what we are told by the medical profession. Very good 'other side of the coin' training for when we inevitably have to make life long committed decisions with our medical practitioners.

In the beginning, I was a bit torn about this book. Yet another book about Bayes Theorem. And the first 100-150 pages pretty much is about that. But it does have merit in explaining and representing statistics in ways people can understand it. By using frequencies instead of probabilities. This is very important as documented by the examples concerning cases in health care, law etc. Pretty scary actually. So even highly educated people can benefit from this book - if they don't feel comfortable with statistics. This will help most people forward.If you are comfortable with Bayes theorem, false positives/negatives etc - then you will learn more about presentation than statistics. So I thought initially it was a 2 star, but will actually lift it to 4 stars - as most people will benefit from reading it . Go read it - it is easy to get through.