- 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: #185,798 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!
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.
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.
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.
Gigerenzer uses logic, math, and common sense to explain the fascinating pull of statistics used by those who try to influence us. As a "Medical Minimalist" I have often encountered resistance from doctors who have insisted I follow the proscribed schedule of "screening" tests. This book is an invaluable tool for understanding what is meant when someone says "One in Five........"