- Paperback: 320 pages
- Publisher: Simon & Schuster; 1 edition (March 19, 2003)
- Language: English
- ISBN-10: 0743254236
- ISBN-13: 978-0743254236
- Product Dimensions: 6.1 x 1.1 x 9.2 inches
- Shipping Weight: 1.2 pounds (View shipping rates and policies)
- Average Customer Review: 36 customer reviews
- Amazon Best Sellers Rank: #169,753 in Books (See Top 100 in Books)
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Calculated Risks: How to Know When Numbers Deceive You 1st Edition
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In the tradition of Innumeracy by John Allen Paulos, German scientist Gerd Gigerenzer offers his own take on numerical illiteracy. "In Western countries, most children learn to read and write, but even in adulthood, many people do not know how to think with numbers," he writes. "I focus on the most important form of innumeracy in everyday life, statistical innumeracy--that is, the inability to reason about uncertainties and risk." The author wisely uses concrete examples from the real world to make his points, and he shows the devastating impact of this problem. In one example, he describes a surgeon who advised many of his patients to accept prophylactic mastectomies in order to dodge breast cancer. In a two-year period, this doctor convinced 90 "high-risk" women without cancer to sacrifice their breasts "in a heroic exchange for the certainty of saving their lives and protecting their loved ones from suffering and loss." But Gigerenzer shows that the vast majority of these women (84 of them, to be exact) would not have developed breast cancer at all. If the doctor or his patients had a better understanding of probabilities, they might have chosen a different course. Fans of Innumeracy will enjoy Calculated Risks, as will anyone who appreciates a good puzzle over numbers. --John Miller --This text refers to an out of print or unavailable edition of this title.
From Publishers Weekly
If a woman aged 40 to 50 has breast cancer, nine times out of 10 it will show up on a mammogram. On the other hand, nine out of 10 suspicious mammograms turn out not to be cancer. Confused? So are many people who seek certainty through numbers, says Gigerenzer, a statistician and behavioral scientist. His book is a successful attempt to help innumerates (those who don't understand statistics), offering case studies of people who desperately need to understand statistics, including those working in AIDS counseling, DNA fingerprinting and domestic violence cases. Gigerenzer deftly intersperses math lessons explaining concepts like frequency and risk in layperson's terms with real-life stories involving doctors and detectives. One of his main themes is that even well-meaning, statistically astute professionals may be unable to communicate concepts such as statistical risk to innumerates. (He tells the true story of a psychiatrist who prescribes Prozac to a patient and warns him about potential side effects, saying, You have a 30 to 50 percent chance of developing a sexual problem. The patient worries that in anywhere from 30% to 50% of all his sexual encounters, he is going to have performance problems. But what the doctor really meant is that for every 10 people who take Prozac, three to five may experience sexual side effects, and many have no sexual side effects at all.) All innumerates buyers, sellers, students, professors, doctors, patients, lawyers and their clients, politicians, voters, writers and readers have something to learn from Gigerenzer's quirky yet understandable book.
Copyright 2002 Cahners Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.
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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!
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.
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.
BE CAREFUL! This book is exactly the same as "Reckoning with Risk" by the same author. The two titles are merely U.S. and U.K. titles.
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