Calculated Risks: How To Know When Numbers Deceive You [Hardcover]

Gerd Gigerenzer (Author)

Book Description

Publication Date: June 5, 2002

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 electioncampaigns 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.

Editorial Reviews

Amazon.com Review

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

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.

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Product Details

• Hardcover: 320 pages
• Publisher: Simon & Schuster (June 5, 2002)
• Language: English
• ISBN-10: 0743205561
• ISBN-13: 978-0743205566
• Product Dimensions: 9.3 x 6.4 x 1.2 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (17 customer reviews)
• Amazon Best Sellers Rank: #990,452 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

29 of 29 people found the following review helpful:

5.0 out of 5 stars How to interpret test results better than your Doc!, June 2, 2004

By 

Gaetan Lion - See all my reviews
(TOP 1000 REVIEWER)    (REAL NAME)   

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This review is from: Calculated Risks: How To Know When Numbers Deceive You (Hardcover)

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.

19 of 19 people found the following review helpful:

5.0 out of 5 stars Be an Informed Consumer in the Age of Numbers, May 28, 2003

By 

J. Williamsen "jackwill" (De Pere, WI USA) - See all my reviews
(REAL NAME)   

This review is from: Calculated Risks: How To Know When Numbers Deceive You (Hardcover)

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.

18 of 18 people found the following review helpful:

5.0 out of 5 stars Required reading for everyone!, July 10, 2002

By A Customer

This review is from: Calculated Risks: How To Know When Numbers Deceive You (Hardcover)

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).