The Canon (12 page)

In her class, Deborah Nolan also brings the bell curve to life by playing tailor to her students. "I take many different measurements of them, height, shoulder width, the distance from the shoulder to elbow, the elbow to the fingertips, the distance from the pinkie to the thumb." Plotting the results of each tally on the blackboard for her five or six dozen students, she shows them how nature adores a good hump.

The same bell curve contour would define the results of coin-flipping bouts. If you performed 1,000 bouts of 100 coin flips, you'd have a sprinkling of really skewed ratios of, say, 71 heads and 29 tails, or even a freakish 80-something tails, teen-something heads, but the great bulk would be in the neighborhood of fifty heads and fifty tails.

Finding the contours of a normal distribution for a given problem is part of what science is all about. What's your mean value, and how do you know when you've got it? If you're trying to figure out the average alcohol consumption among students at a local college, how many people must you interview to feel confident you haven't inadvertently sampled a few too many frat boys, liars, or Seventh-day Adventists? When do you know you've amassed a large enough sample that the midpoint of your bell curve has meaning, that it captures the representative slice of reality you're after? You don't want to end up like the three statisticians out on a duck hunt: the first one fired a shot that sailed six inches over the duck, the second fired a shot six inches under the duck, and the third one exulted, "We got it!" The rules for determining the statistical soundness of a sample size are complex and depend on the particulars of the problem, but a couple of tenets generally apply: the sample should be as large as is practically and economically possible; and once the sample population is settled on, the net should be as finely meshed as you can make it. Nothing tarnishes the credibility of a sample like the desire to be sampled, which is why the results of a sex survey of the readers of
Maxim
magazine may be far less revealing than any of the garments on the females displayed therein. A good pollster will hound and rehound the very people who least want to cooperate.

The fact that so many things in life, from the length of a human pinkie to a roll of the dice, conform to a bell curve pattern of data points says something fundamental, if potentially dispiriting, about life: that it's much easier to be ordinary—that is, to dwell somewhere within the normal distribution of whatever category you're measuring—than to be outstanding (or, for that matter, grossly inadequate). Parents want each of their offspring to be what Gertrude Stein is purported to have called "an immortal something or other"; and inspirational spots on public television always feature children dreaming of being great successes—the next Thomas Edison, a world-famous chef, the first astronaut on Mars. Yet distribution theory reveals that values cluster around midpoints, and that mediocrity loves company. As a result, the only way for most children to be "outstanding," "genius material," or even merely "gifted and talented" is to redefine your terms ("of course you're extraordinary: there's never been anybody in the history of the human race with precisely your DNA!"), inflate your grades, or dump your rankings altogether.

Bell curves aren't cast in bronze, and their midpoints can be coaxed over a bit in a preferred direction, usually gradually, sometimes dramatically. With a few changes in public health practices, for example, like pumping sewage out of town instead of slopping it out the window, and encouraging doctors to scrub their hands between patients, the average life span in the United States nearly doubled between the mid-1800s and the mid-1900s. In another twentieth-century great leap upward, the American-born-and-fed children of immigrants soon towered over their parents, pushing the two bulges of the bell curves for height—one for women, one for men—rightward by several inches. Average IQ scores also have risen in the past half century, for reasons that remain unclear.

Whichever way a bell curve swings, there is always a big fat greedy bulge somewhere, sucking up the bulk of the population. Indeed, the pull of the bell's bulge is so relentless that it's been given its own term: regression to the mean. By this principle, the extraordinary tends to lose its edge over time. If two unusually tall parents have a child, the child is likely to be taller than average, but slightly shorter than his or her same-sex parent; the child, in other words, will regress toward the mean. Why should this be so? Because the parents reached their imposing stature through a combination of genetics and a series of small happenstances during development that all shook out in favor of added verticality; and though they may pass along genes that generally enhance height, the chance settings that accentuated their loftiness will be reset to zero with the new generation and are unlikely to reposition themselves as a series of pluses once again. It can happen, but the odds are against it, just as they are against a mother flipping five heads in a row, handing the coin to her daughter, and having her daughter promptly repeat the trick. While population averages in height or intelligence may advance over time, regression to the mean serves as a counterweight, a stabilizing trend that helps keep cockiness in check.

John Allen Paulos proposes that regression to the mean could explain the legendary
Sports Illustrated
jinx: the long-standing observation that quite often, after an athlete appears on the cover of
Sports Illustrated,
that person goes into decline, fumbling the ball, botching the serve, assaulting the fans. Such unstellar turns could result from the pressures of fame, or a superstition subsumed into self-fulfilling prophecy, but Paulos thinks otherwise. "When do you appear on the cover of
Sports Illustrated
? When you've done extraordinarily well for a period of time and are at the top of your game," he said. "By implication, you're not going to be able to maintain your outlier status for very much longer." You are going to start regressing, however slightly, back toward the mean streets of the mean.

The same might be said for many a miracle cure in the annals of alternative medicine. People often resort to alternative therapies when they have been ill for some time, and have failed to find relief in a mainstream medicine chest. They are at their wits' end, desperate for relief. A friend recommends bee pollen, or shark cartilage, or powdered bear
carbuncle, and they decide to give it a swallow. A week later, they're largely healed; after two, enzealed. Why didn't their physician recommend bear carbuncle in the first place? Was it because the pharmaceutical industry can't patent or profit from it and so hasn't distributed educational literature and free samples? Or was the doctor too narrow-minded to consider a therapy that looks like the sort of thing you can order through the back pages of the
Utne Reader?
Perhaps. Or perhaps the cure had nothing to do with the ingested novelty item, and instead represented another instance of regression to the mean. After many weeks precariously poised on the outlier tail of illness, people slip back into the comfortable lap of health, the physiological norm that our immune system grants us most of the time and that we take for granted until it is gone.

That people readily attribute a spontaneous recovery to some bold move, some agency, on their part, demonstrates the human desire to feel in control of one's destiny, yes. But it also underscores our readiness to conflate correlation with causation, which brings us to yet another way in which we may be snookered by statistics. Just because two traits or events are frequently found in the same package doesn't mean that one is responsible for the other. Sometimes the independence of oft linked items is easy to discern. In Sweden, many people are blond and blue-eyed, but obviously the Viking coolness of their gaze is not what blanched their hair, or vice versa. At other times, conjoined traits seem more portentously causal, but one must take great care before sketching out the flowchart. For example, many high school dropouts smoke cigarettes. Among adults in the United States, 35 percent of those who never finished high school are regular smokers, compared to 14 percent of those with a college degree. But does one characteristic in this correlation cause the other, and if so who does what to whom? Do high school dropouts smoke at two and a half times the rate of college graduates because they left school before learning just how bad the habit is? Do they smoke comparatively more because they're likelier to be in dead-end jobs that make them depressed, and nicotine, as a compound that both stimulates and relaxes, is just the sort of double-edged drug depressives crave? Or did their addiction to cigarettes prompt them to drop out in the first place—to get a job to support an increasingly expensive habit, or to escape the chronic censure of their teachers? Or are dropping out of high school and smoking cigarettes useful as signs of sedition, to advertise one's hostility toward society? Or are dropping out and smoking signs of submission, to advertise one's fealty to a gang?

Drawing causal arrows from one behavior or outcome to another is often fraught with danger, but that doesn't stop people from trying. In
How to Lie with Statistics,
Darrell Huff cites an example from a Sunday supplement called "This Week," in which an editor answered a reader's question about the effect that going to college has on one's odds of remaining unmarried. "If you're a woman, it skyrockets your chances of becoming an old maid," the editor replied. "But if you're a man, it has the opposite effect—it minimizes your chances of staying a bachelor." The editor then quoted from a Cornell University study of 1,500 "typical middle-aged college graduates," in which 93 percent of the men were married, compared to 83 percent for the general population, while only 65 percent of the women were married. "Spinsters were relatively three times as numerous among college graduates as among women of the general population," the editor ominously concluded. The lesson for the 1950s gal was clear: going to college, like getting fat or contracting a mild case of polio, can seriously diminish one's romantic opportunities. Boys do not wed the bookish coed.

Hold your Miss Havishams, huffed the progressive-spirited Darrell. Before we breezily turn a correlation into an open-and-shut case of cause-and-effect, who's to say that all those "old maids" in the Cornell survey pined to get married in the first place? They could very well have seen college as a way to escape matrimony and gain economic independence. For that matter, if college-bound women are relatively more single-minded than other women to begin with, who knows what impact their university experience may have had on them; perhaps even fewer of the Cornell coterie would have gotten married if they hadn't gone to college. All these possibilities are equally valid conclusions, said Huff. "That is, guesses."

Those who are statistically sophisticated can, if they choose, squeeze a number set until it squeals "Ninety-six Tears." Sir Richard Peto, an epidemiologist at the University of Oxford, made this point absurdly clear when the editors at
The Lancet
asked him to perform additional statistical analyses on a landmark report he and his colleagues had just submitted to the British medical journal. In their study, the researchers showed that heart attack victims had a comparatively better chance of surviving if they were given aspirin within a few hours of the attack.
The Lancet
editors wanted the epidemiologists to break the data down into subgroups, to see whether different patients might benefit more or less from aspirin depending on their age, previous health status, or other characteristics. Sir Richard balked. He knew that if you fiddled with and whittled down your numbers long enough, all sorts of spurious connections might arise through chance alone. The editors insisted. Finally, Peto relented, and gave them the subsidiary calculations they desired—but only on condition that they include in the publication one statistical "link" he'd uncovered that would drive home the need to regard the whole subgroup massage exercise with appropriate skepticism. Welcome back to the zodiac. Aspirin may be a lifesaver for heart attack victims born under ten of the twelve astrological signs, Peto wrote, but for those who happen to be a Libra or a Gemini, so sorry, the drug appears to be worthless. (Note to Libras and Geminis with current or suspected cardiac activity: consult your doctor, astrologer, or local cable company about whether "salicylic acid" might be a better choice for you; but under no circumstances should you contact Dr. Peto, who is a Taurus.)

In a similar bid to demonstrate the dangers of crackpot correlations, Sherman Silber, a reproductive surgeon in St. Louis, and two colleagues published the results of their willfully whimsical fishing expedition through a database of twenty-eight infertility patients. They used a computer program to identify any traits whatsoever that might link those women who had succeeded in becoming pregnant. Bless my speculum, what have we here: those patients whose last names began with the letters G, Y, or N were significantly more likely to end up bearing a child than were their less auspiciously surnamed peers. After admitting to a certain amount of ego gratification at the coincidence, Dr. Silber warned that many a "statistically significant" correlation in the scientific and medical literature may be just as specious as his game of GYN-ecology, but that few, unfortunately, will be as "patently ridiculous" and thus as easy to defrock.

If it's hard for the workaday doctor or researcher to recognize every sham correlation that might pop up on PubMed, none of us can escape the occasional hoodwink. And as tempting as it might be to defend yourself proactively by damning all statistics indiscriminately, the great statistician Frederick Mosteller had a point when he said, "It is easy to lie with statistics, but it is easier to lie without them." Nevertheless, there are some steps you can take to, as Huff put it, "talk back to a statistic." Among the biggies recommended by many scientists is to ask a simple question: Does the figure, finding, or correlation make sense, that is, accord with what you know of objective reality? "You have to look at the biological plausibility," said James L. Mills, chief of the pediatric epidemiology section of the National Institute of Child Health and Human Development. "A lot of findings that don't withstand the test of time didn't really make any sense in the first place."