Dr. Andreas Eenfeldt is 6\u20197\u201d tall \u2013 a fact I\u2019ve managed to work into two pre-cruise roasts, as well as the speech I gave on this year\u2019s cruise. You can always spot the man in a crowd, unless he happens to be standing amidst an NBA team.<\/p>\n
You might expect that his brother is equally tall, or that he\u2019ll have a son someday who\u2019s as tall or taller. But that expectation would be wrong. His brother (an affable guy I\u2019ve met on two cruises) is 6\u20193\u201d \u2013 still tall, but four inches shorter than Andreas. That\u2019s because Andreas is an anomaly. He\u2019s proof of the statistical principle that given enough chances, chance happens<\/em>. And what happened in his case was probably a genetic quirk that produced some extra human growth hormone.<\/p>\n In his book How Not To Be Wrong: The Power of Mathematical Thinking<\/a>, math professor Jordan Ellenberg explains how anomalies can produce study results that are statistically significant, but nonetheless due entirely to chance. I recounted those points in a previous post<\/a>.<\/p>\n In a later chapter, Ellenberg describes how we can fooled by the flip-side of given enough chances, chance happens<\/em>: regression to the mean. After chance happens, things tend to return to normal.<\/p>\n Ellenberg begins the chapter (titled The Triumph of Mediocrity<\/em>) by recounting the work of a professor of statistics named Horace Secrist. After examining data on hundreds of businesses in the 1920s, Secrist wrote an influential paper with a rather startling conclusion: the competitive forces of American capitalism lead to mediocrity in business. Secrist\u2019s evidence was that when businesses produced record-high profits one year, they tended to produce average profits in subsequent years. Likewise, firms that produced record-low profits tended to show higher profits in subsequent years. Therefore, something about capitalism must produce middle-of-the-road mediocrity, Secrist concluded.<\/p>\n But as Ellenberg explains, what Secrist\u2019s data demonstrates isn\u2019t an inherent flaw in competitive capitalism, but the simple fact that anomalies tend to be followed by a regression to the mean. A business can have a bang-up year for any number of reasons: a disaster that affects the competition, a temporary surge in demand, etc. When the temporary conditions that produced the record profits go away, so do the record profits.\u00a0 It’s business as usual again.\u00a0 That doesn\u2019t mean the company\u2019s management drifted into mediocrity.<\/p>\n Or on the subject of height:<\/p>\n People drawn from the tallest segment of the population are almost certain to be taller than their genetic predisposition would suggest. They are born with good genes, but they also got a boost from the environment and chance. Their children will share their genes, but there\u2019s no reason the external factors will once again conspire to boost their height over and above what heredity accounts for. And so on average, they\u2019ll be taller than the average person, but not quite so tall as their beanpole parents. That\u2019s what causes regression to the mean: not a mysterious mediocrity-loving force, but the simple workings of heredity mixed with chance.<\/span><\/p>\n I don\u2019t know how Dr. Eenfeldt would feel about being called a beanpole, but you get the idea. It\u2019s not likely that he\u2019ll produce a son who is 6\u20197\u201d or taller.<\/p>\n Ellenberg points out that regression to the mean is also common in sports. An NFL running back has a record-setting year, scores a huge contract as a result, then never puts up those stratospheric numbers again. Grumbling fans assume that with all those guaranteed millions in the bank, the running back lost his desire or work ethic. In fact, it\u2019s probably just a case of regression to the mean. The running back was never going to have another season like the record-breaking one, fat contract or not.<\/p>\n As a personal example that doesn\u2019t involve fat contracts or money of any kind, I saw regression to the mean during the past five days, when I played several rounds of disc golf against my buddy Jimmy Moore. Last year I kept our scores in a spreadsheet. My average at the end of that week was 6 under par on the dot.\u00a0 (It’s an easy course, by the way.)<\/p>\n In one game yesterday, I tossed a 10 under par \u2026 four strokes better than average, and my lowest score ever when playing against Jimmy. The next game (a mere 90 minutes later), I finished just two under par \u2026 four strokes worse than average.\u00a0 When I tabulated all my scores for the five days we played, my average was \u2026 wait for it \u2026 5.8 under par. I have good games and not-so-good games, but I always seem to drift back to right around 6 under par.<\/p>\n So what does all this have to do with diet and health? Plenty. Here\u2019s an example from Ellenberg:<\/p>\n Almost any condition in life that involves random fluctuations in time is potentially subject to the regression effect. Did you try a new apricot-and-cream-cheese diet and find you lost three pounds? Think back to the moment you decided to slim down. More than likely it was a moment at which the normal up-and-down of your weight had you at the top of your usual range, because those are the kinds of moments when you look down at the scale, or just at your midsection, and say Jeez, I\u2019ve gotta something<\/em>. But you might well have lost three pounds, apricots or no apricots, when you trended back toward your normal weight.<\/span><\/p>\n Okay, so maybe a loss of a few pounds that would have happened anyway fools people into continuing with a wacky diet for awhile. That\u2019s not a big concern in my opinion. The real concern is when regression to the mean fools doctors and researchers, or gives researchers a chance to fool doctors and the public at large.<\/p>\n Ellenberg doesn\u2019t get into the subject, but Chris Masterjohn did in an article from 2011<\/a>. You can read the entire article if you want the details, but here\u2019s the main point: regression to the mean can exaggerate the reported efficacy of drugs and other treatments.<\/p>\n Suppose researchers are screening subjects for a trial on a cholesterol-lowering drug. Part of the screening process is a lipid panel. Because of the principle that given enough chances, chance happens<\/em>, some people are going to have a spike in cholesterol on the day of the screening. So they\u2019re now labeled as people with high cholesterol and enrolled in the study. When they\u2019re screened again later, their cholesterol is lower \u2013 which it would have been anyway because of regression to the mean. But the lower number is attributed entirely to the drug.<\/p>\n As Masterjohn points out, if it\u2019s a large enough study and the subjects were properly randomized, the regression-to-the-mean effect should be roughly equal in both groups, because both groups would include equal numbers of people whose first screening occurred on a day when their cholesterol was spiking. But smaller studies and studies in which subjects weren\u2019t carefully randomized are particularly prone to the regression-to-the-mean effect. To quote from Masterjohn\u2019s article:<\/p>\n And thus we see that many published research findings are false. Some of these false findings exist because we would inevitably expect by the laws of probability for a small handful of well conducted, thoroughly reported, and appropriately interpreted studies to uncover apparent truths that are really false simply by random chance. This emphasizes the need to look at the totality of the data. Some will be false because of regression to the mean. This emphasizes the need to critically evaluate the data in each study.<\/span><\/p>\n