Fun With Statistics

Statistics is the essential foundation for science-based medicine.  Unfortunately, it’s a confusing subject that invites errors and misunderstandings.  We non-statisticians could all benefit from learning more about statistics as well as trying to get a better understanding of just how much we don’t know. Most of us are not going to read a statistics textbook, but the book Dicing with Death: Chance, Risk, and Health by Stephen Senn is an excellent place to start or continue our education. Statistics can be misused to lie with numbers, but when used properly it is the indispensable discipline that allows scientists:

 …to translate information into knowledge. It tells us how to evaluate evidence, how to design experiments, how to turn data into decisions, how much credence should be given to whom to what and why, how to reckon chances and when to take them.

Senn covers the whole field of statistics, including Bayesian vs. frequentist approaches, significance tests, life tables, survival analysis, the problematic but still useful meta-analysis, prior probability, likelihood, coefficients of correlation, the generalizability of results, multivariate analysis, ethics, equipoise, and a multitude of other useful topics. He includes biographical notes about the often rather curious statisticians who developed the discipline. And while he includes some mathematics out of necessity, he helpfully stars the more technical sections and chapters so they can be skipped by readers who find mathematics painful. The book is full of examples from real-life medical applications, and it is funny enough to hold the reader’s interest.

What a Difference a Word Makes

Statistics (and probabilities) are frequently misunderstood, even by many scientists. Even what looks simple can turn out to be complicated and counter-intuitive.  Senn revisits an old question. If a man has 2 children and at least one of them is a boy, how likely is it that the other is a girl? Most people reason that there are only 2 possibilities, boy or girl, both equally likely, so there is a probability of 1 in 2, or 50%, that the other child is a girl. That’s wrong. In fact, there is a probability of 2 in 3: the other child is twice as likely to be a girl as a boy. The 50% answer is only true if you change the question slightly from “one of them is a boy” to “the firstborn is a boy.” If this doesn’t make sense to you, you really need to read the book.

Does Medical Research Discriminate Against Women?

He devotes a whole chapter to that question and answers it with a convincing NO. The Women’s Caucus complained that a lot of studies had only male subjects, that women were under-represented, that what we were learning about treating men might not apply equally to women. The perception that women were being neglected was not supported by the evidence; if anything, women have actually been over-represented. Nevertheless, they persuaded congress to pass a law requiring the director of the NIH to ensure that trials be designed to examine whether the variables being studied affect women or members of minority subgroups.  Senn explains how confounding factors like sex and race were already being dealt with adequately and why a strict enforcement of the new policy would be disastrous for research, requiring far greater numbers of subjects and greater expense. Fortunately, researchers have managed to continue their previous rational and appropriate practices while making a few token placatory noises to the grant-making bodies.

Applications Beyond Medicine

Medicine is the only profession that employs randomized controlled trials to evaluate the effects of its actions and systematically encourages publications about its errors. Evidence-based medicine is a good thing, and there’s no reason the methods of statistics couldn’t be used to develop similarly evidence-based approaches to educational, managerial, economic, and social policies.  He describes one intriguing application:  the process of religious conversion has been studied using infectious disease modeling.

Statistics in the Courtroom

The Dow Corning company manufactured silicone breast implants until statistical innumeracy allowed a flurry of successful lawsuits to bankrupt the company. Senn quotes the definition of dice from The Devil’s Dictionary:

Small polka-dotted cubes of ivory, constructed like a lawyer to lie on any side, but commonly on the wrong side.

He also includes this discouraging quote from Marcia Angell:

 I am occasionally asked by lawyers why the New England Journal of Medicinedoes not publish studies “on the other side”, a concept that has no meaning in medical research… Yet science in the courtroom, no matter how inadequate, has great impact on people’s lives and fortunes.

Statistics, MMR Vaccine, and Autism

In the last chapter he revisits the Wakefield fiasco, showing how misunderstandings of statistical principles have led to outbreaks of vaccine-preventable diseases. Statistics has an important role in determining rational public policies to protect the population, and through its sub-science of decision analysis has much to say about the ethical and economic aspects of vaccination.

Entertainment Value

Senn has a droll wit and an endearing fondness for puns. Who would have thought that a book on a dry subject like statistics could be so entertaining and even laugh-out-loud funny? He says the post hoc fallacy is so obvious that “almost any human being who is not a journalist can understand it.” Since it regularly gets by the average journalist, he renames it the “post hoc, passed hack” fallacy. He says that John Donne’s “no man is an island” is true, but if you capitalize Man it becomes “false, as anyone cognizant with the geography of the Irish Sea will surely aver.” In case geography-challenged readers don’t get this, he reluctantly explains it in the endnotes. He says such punctuation would be a capital offense. His puns extend to this tour de force:

 Poisson was attracted to magnetism, stretched his mind on the theory of elasticity, starred in astronomy and generally counted as one of the foremost mathematicians of his day.

His sources are wide-ranging and eclectic. He quotes Guernsey McPearson’s definition of a meta-analyst as one who thinks that if manure is piled high enough it will smell like roses. His quotes from Sinclair Lewis’s Arrowsmith inspired me to re-read that book (it’s available online and it’s just as pertinent today as it was in 1925.) One of his quotes from The Phantom Tollbooth is particularly applicable to some areas of CAM:

I only treat illnesses that don’t exist: that way if I can’t cure then, there’s no harm done.


The book reinforced my conviction that I don’t know enough about statistics and never will, so I will have to continue to rely on the experts. I confess that some of the material was over my head.  I couldn’t follow the formula for Russian roulette showing that the probability of death on the 5th attempt is 0.066 compared to 0.1 on the first attempt (no, the initial probability is not the 1 in 6 that you would suppose, since the weight of the bullet makes the spinning cylinder more likely to stop with the bullet at the bottom). I couldn’t follow his explanation of two different mathematical approaches to coin toss probabilities. But I do know more about statistics now than I did when I started reading. I learned much of value and was well entertained in the process.

I didn’t need any convincing, but I think even the most skeptical reader would come away convinced that:

the calculation of chances and consequences and the comprehension of contingencies are crucial to science and indeed all rational human activity.

This article was originally published in the Science-Based Medicine blog.

Dr. Hall is a contributing editor to both Skeptic magazine and the Skeptical Inquirer. She is a weekly contributor to the Science-Based Medicine Blog and is one of its editors. She has also contributed to Quackwatch and to a number of other respected journals and publications. She is the author of Women Aren’t Supposed to Fly: The Memoirs of a Female Flight Surgeon and co-author of the textbook, Consumer Health: A Guide to Intelligent Decisions.

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