Calculated Risks: How to Know When Numbers Deceive You
|Publisher:||Simon & Schuster|
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.
This book was also released under the title Reckoning With Risk: Learning to Live With Uncertainty.
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