Customer Reviews

Calculated Risks: How To Know When Numbers Deceive You

5 star:		(12)
4 star:		(1)
3 star:		(3)
2 star:		(1)
1 star:		(0)

 

 

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.

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.

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).

I am always looking for materials to use to help non-specialist students understand some of the basic statistical errors that pharmaceutical advertisers exploit (and that so many otherwise educated and informed medical personnel also seem to misunderstand).

It's surprisingly difficult: some are way too technical and eccentric (Hacking). Others are too cute and breezy ("How to Lie..") Some are marred by the author's own (ungrounded) evolutionary conjectures (Taleb, "Fooled By Randomness....") Some just aren't clear enough.

Gigerenzer's book falls in that 'not clear enough' category. It fails to be clear for several reasons. First, as another reviewer has observed, it is badly overwritten. The analytical points, such as they were, were presented VERY early on in the book. The book should have been a pamplet. But, really, it is worse than that: instead of deepening the points, or providing more of a conceptual roadmap,the author repeated them, and in some cases clouded them with dubious interpretations/speculations, etc.

Some things should have been more carefully explained (in English as well as numbers), notably the misuse of statistics in interpreting evidence, both in the courtroom and in the interpretation of 'DNA fingerprints.' Some things should have been omitted. The chapter about HIV counseling really did not add very much. On the contrary: I think it may have detracted. It is VERY difficult to perform and interpret the sort of study that the author's student chose to perform; the student's methodology study was SERIOUSLY flawed, as any social science researcher is uncomfortably well aware.

Another candidate for deletion is the author's discussion of domestic violence. The statistical point is well made (and familiar): you have to have the right contrast class, or nothing you infer has any validity re: alleged connections between battering and killing. But the author's more 'philosophical' observations and speculations about violence against women....well, here again, I cringed. This IS an area in which there has been much examination, analysis, and--yes--speculation. The author's conjectures were painfully naive. I am sure he did not mean to appear flippant or to be laying claim to consideration as a serious investigator of the problem of domestic abuse. Still.....

I gave the book two rather than three stars at least in part because, in the end, there were serious audience questions: for WHOM was the author really writing? I honestly don't know. Not for me (a non-mathematician who nevertheless understands a fair amount). Not for my students, who are bright but more statistically naive. Not for the general layperson: the discussions are too mathematicized yet underexplained.

A good editor could have done wonders...

The author presents some important observations about calculated
risks, probabilities and statistical test inferences. He makes
clear the necessity to understand risks clearly at the outset
of any important decision. For instance, a physician must take
into consideration "false positive " test results so that
he/she does not over-react. An over-reaction could cause the
physician to take unnecessary precautions that could do more
to endanger the patient than help. In addition, the author
cautions against fabrication of certainty or the use of
statistics to prove a predetermined result. This book is
useful in arriving at a realistic design for a statistical
test or any other test from which an important scientific
inference will be made.

The book "Calculated Risk: How to Know When Numbers Deceive You", by Gerd Gigerenzer, will increase your risk aptitude. The 4 1/2 star (Amazon.com) book does not discuss statistical innumeracy from the IT perspective, but discusses innumeracy mainly in contemporary medicine, the justice system, and life in general.

Gerd describes four aspects of innumeracy as follows:
01) Illusion of certainty:
For example: Fingerprint and DNA testing.
02) Ignorance of relevant risks:
For example: "It is more likely that a young American male
knows baseball statistics than that his chances of dying on
a motorcycle trip is about 15 times higher than his chances
of dying on a car trip of the same distance."
03) Miscommunication of risks:
For example: One can communicate the chances that a test
will actually detect a disease in various ways ... The most
frequent way is in the form of a conditional probability: If
a person has cancer, the probability the he/she will test
positive on a screening is 90 percent. Many physicians
confuse that statement with this one: If a person test
positive on a screening, the probability that he/she has
cancer is 90 percent.
04) Drawing incorrect inferences from statistics:
For example: "Consider a newspaper article in which it is
reported that men with high cholesterol have a 50 percent
higher risk of heart attack. The figure of 50 percent
sounds frighting, put what does it mean? It means that out
of 100 fifty-year-old men without high cholesterol,
about 4 are expected to have a heart attack within ten years,
whereas among men with high cholesterol this number is 6. The
increase from 4 to 6 is the relative risk increase, that is,
50 percent. However. if one instead compares the number of
men in the two groups who are not expected to have heart
attacks in the next 10 years, the same increase in risk is
from 96 to 94, that is, about 2 percent (absolute risk). Now
the benefit of reducing one's cholesterol level no longer
looks so great."

Far from being a dry book on risk, uncertainty, and statistics, Gerd Gigerenzer is entertaining, provocative, irreverent and a bit of a maverick
.
" ... 1 out of every 90 Americans will lose his or her life in a motor vehicle accident by the age of 75. Most of them die in passenger car accidents."

" ... the terrorist attack on September 11. 2001, cost the lives of some 3,000 people. The subsequent decision of millions to drive rather than fly may have cost the lives of many more."

"... DNA ... match probability of 1 in 16 for a brother ... "

This book provides "tools for overcoming innumeracy that are easy to learn, apply, and remember."

This book illustrates two important concepts very well: Statistics confuse even intelligent people, and the meaning of "false negative" and "false positive" data, especially when reported as percentages, can be far from intuitive.

Why only three stars? Both of these ideas are thoroughly illustrated and then beaten to death by page 50 of this 300 page book. (You can get most of the information from reading one or two of the other reviews here on Amazon).

The remainder of the book uses various medical examples to make the point that a percentage of a percentage may sound more significant than it is (or less significant than it is). As Gigerenzer illustrates, doing the arithmetic to determine the actual numbers of each case represented will untangle most misunderstandings. After about a dozen of these, though, only a reader with an interest in the specific examples will remain engaged.

The writing is clear, the examples are all good, and the book does amply illustrate the quotation cited in Mark Twain's Autobiography: "There are three kinds of lies: lies, damned lies and statistics."

Heading for a medical exam? Wonder if those uncomfortable, expensive tests really make a difference? Skip the medical libraries and talk to the statisticians.

Gigerenzer bares the truth that doctors conceal because of ignorance or greed. Every woman should read his chapter on the risks and benefits of mammograms. The rate of false positives for mammograms is a whopping ninety percent. The cost is not measured by x-ray charges alone (although a radiologist huffed out of a meeting with a gynecologist who stopped recommending mammograms -- they make big bucks from those tests!). Think of the unnecessary biopsies -- and the unnecessary surgery because biopsies have error rates too.

Cancer tests do not cure or prevent cancer. They may reduce the risk of death, although a comparison between screened and unscreened populations shows that very few lives are actually saved this way. And there is no risk reduction unless early detection affords access to a cure.

AIDS tests also carry risks. The rate of false positives among a healthy, "safe-sex" population is about fifty percent. The author describes horror stories of disease-free people who were mis-diagnosed. They lost jobs, homes and friends; some sued for recovery but at least one committed suicide.

Our health care system spends millions on tests because both patients and doctors are ill-informed. We demand a cure and the medical system finds a way to give us the illusion of progress.

It's not just the US. The author found ignorance of false positives for AIDS tests in Germany. When I lived in Canada, the provincial health system bombarded us with propaganda for mammograms.

Gigerenzer has done the world a great service by writing this book and presenting data in a reader-friendly fashion. I suspect there is a human tendency to look for certainty and today's medical tests seems to be the equivalent of divining rods and astrology of three hundred years ago. Now I wish he'd take a look at academic and career tests, most of which also give a form of "false positives." We'd like a yes or no in this world, but alas, mostly we have to learn to live with the maybes.

This is an important work. It shows how to effectively reason about probabilities and risks and how to communicate them in a way that people can understand them. Many authors document the extent of statistical innumeracy among doctors and the general public. This book shows that this innumeracy is largely the result of ineffective forms of communicating probabilities and risks. The book has important implications about the teaching of statistics and should be read by all who want to improve their teaching of the subject. This book is also important for anybody who wants to improve their reasoning.

This book is incredible for a variety of reasons. First, it is written in such a way as to be easily digestible to people of varying backgrounds; it is written for the layperson, academic and professional alike. The author is able to discuss and describe with great clarity how probabilities are calculated and how they are often misinterpreted in the media, medical and law sectors. This book discusses issues that all of us will someday be faced with and affected by either firsthand or indirectly. The issues of breast cancer and prostate cancer screening, AIDS testing , DNA fingerprinting and other risk probabilities are meticulously discussed. Many reviewers have given low ratings for this book because they expected a different book or didn't understand the author's intention. The author wanted to write a book that would help people understand conditional probabilities, and that is exactly what he did.

Explaining statistics to a diverse audience is a daunting task for anyone. Dr. Gigerenzer performs his job with style and erudition. He is an incredible teacher, and he understands that conditional probabilities are complicated and easily confuse people. Yes, the author diligently and carefully explains the issues so that no one is left confused. Many readers become impatient and find this attention to detail annoying. The author is a conscientious teacher, hence his caution and vigilance when discussing difficult subject matter.
I found this to be a fascinating look into how statistics can be communicated clearly and in a very engaging way: by discussing pressing and relevant issues in our society. I did not find the author's level of detail or speed of progression to be a fault in any way. I read this book because I wanted to better understand conditional probabilities, how they're calculated and how they're often misunderstood and communicated. This book helped me fulfill every one of those goals.

One reviewer griped that only people who are interested in cancer and AIDS should read this book. I have two responses to that simple-minded comment. Everyone should be interested in those two issues because they greatly affect society, people we care about, and will probably affect many of us as we age. The other issue is that understanding how risk probabilities are calculated informs the public: information is empowering, it attenuates one's susceptibility to fear mongering and coercion. This book should be read by anyone who is a consumer of information or one whose job is to communicate information about risk. Knowledge is power and math is the ultimate vehicle for comprehension. This book will remove the barbs from understanding probabilities, and any book that can reduce one's fear of mathematical computation and information is something that should be pervasively hailed. This book will change the way you view many facets of the world, and that is the biggest complement I can give any author.