Stat-Spotting. Joel Best
distinction and that we ought to reconceptualize sex as a continuum rather than a dichotomy. Just how common is intersexuality? One widely cited estimate is that 1.7 percent of people are intersex: “For example, a city of 300,000 would have 5,100 people with varying degrees of intersexual development.”8 (The Internet circulates claims that the actual proportion may be closer to 4 percent.)9
However, many of the people included in these estimates live their entire lives without discovering that they are intersex. The most common form of intersexual development is late-onset congenital adrenal hyperplasia (LOCAH–estimated to occur in 1.5 percent of all people, and therefore accounting for nearly 90 percent of all intersex individuals: 1.5 ÷ 1.7 = .88). Babies with LOCAH have normal genitalia that match their chromosomes; their condition may never be identified.10 In other words, the most common variety of intersex–accounting for the great majority of cases–is subtle enough to go undiscovered. In contrast, “true hermaphrodites”–babies born with obviously ambiguous genitalia–are in fact rare; there are only about 1.2 per 100,000 births.
Intersexuality, then, displays the pattern common to so many phenomena: the most dramatic cases are relatively rare, whereas the most common cases aren’t especially dramatic.
| PART 2 | |
| VARIETIES OF DUBIOUS DATA |
C
BLUNDERS
Some bad statistics are the products of flubs—elementary errors. While some of these mistakes might involve intentional efforts to deceive, they often reflect nothing more devious than innocent errors and confusion on the part of those presenting the numbers. For instance, after Alberta’s health minister told students at a high school that they lived in the “suicide capital of Canada,” a ministry spokesperson had to retract the claim and explain that the minister had spoken to a doctor and “misinterpreted what they talked about.” In fact, a health officer assured the press, the local “suicide rate is among the lowest in the region and has been on a steady decline since the mid-1990s.”1
Innumeracy—the mathematical equivalent of illiteracy—affects most of us to one degree or another.2 Oh, we may have a good grasp of the basics, such as simple arithmetic and percentages, but beyond those, things start to get a little fuzzy, and it is easy to become confused. This confusion can affect everyone—those who produce figures, the journalists who repeat them, and the audience that hears them. An error—say, misplacing a decimal point—may go unnoticed by the person doing the calculation. Members of the media may view their job as simply to repeat accurately what their sources say; they may tell themselves it isn’t their responsibility to check their sources’ arithmetic. Those of us in the audience may assume that the media and their sources are the ones who know about this stuff, and that what they say must be about right. And because we all have a tendency to assume that a number is a hard fact, everyone feels free to repeat the figure. Even if someone manages to correct the mistake in newspaper A, the blunder takes on a life of its own and continues to crop up on TV program B, Web site C, and blog D, which can lead still more people to repeat the error.
And yet it can be remarkably easy to spot basic blunders. In some cases, nothing more than a moment’s thought is enough to catch a mistake. In others, our statistical benchmarks can provide a rough and ready means for checking the plausibility of numbers.
C1The Slippery Decimal Point
The decimal point is notoriously slippery. Move it just one place to the right and—wham!—you have ten times as many of whatever you were counting. Move it just one digit to the left and—boom!—only a tenth as many. For instance, the Associated Press reported that the final Harry Potter book sold at a magical clip on the day it was released, averaging “300,000 copies in sales per hour—more than 50,000 a minute.”3 Of course, the correct per-minute figure was only 5,000 copies, but this obvious mistake was overlooked not only by the reporter who wrote the sentence but also by the editors at AP and at the various papers that ran the story unchanged.
Misplacing a decimal point is an easy mistake to make. Sometimes our sense of the world—our set of mental benchmarks—leads us to suspect that some number is improbably large (or small), but errors can be harder to spot when we don’t have a good sense of the correct number in the first place.
| LOOK FORNumbers that seem surprisingly large–or surprisingly small |
EXAMPLE: HOW MANY MINUTES BETWEEN TEEN SUICIDES?
“Today, a young person, age 14–26, kills herself or himself every 13 minutes in the United States.”–Headline on a flyer advertising a book
When I first read this headline, I wasn’t sure whether the statistic was accurate. Certainly, all teen suicide is tragic; whatever the frequency of these acts, it is too high. But could this really be happening every 13 minutes?
A bit of fiddling with my calculator showed me that there are 525,600 minutes in a year (365 days × 24 hours per day × 60 minutes per hour = 525,600). Divide that by 13 (the supposed number of minutes between young people’s suicides), and we get 40,430 suicides per year. That sure seems like a lot–in fact, you may remember from our discussion of statistical benchmarks that the annual total number for suicides by people of all ages is only about 38,000. So right away we know something’s wrong.
In fact, government statistics tell us that there were only 4,010 suicides by young people age 15–24 in 2002 (the year the headline appeared).4 That works out to one every 131–not 13–minutes. Somebody must have dropped a decimal point during their calculations and, instead of producing a factoid, created what we might call a fictoid–a colorful but completely erroneous statistic. (Sharp-eyed readers may have noticed that, in the process, the age category 15–24 [fairly standard in government statistical reports] morphed into 14–26.)
You’ve probably seen other social problems described as occurring “every X minutes.” This is not a particularly useful way of thinking. In the first place, most of us have trouble translating these figures into useful totals, because we don’t have a good sense of how many minutes there are in a year. Knowing that there are roughly half a million–525,600–minutes in a year is potentially useful–a good number to add to our list of benchmarks. Thus, you might say to yourself, “Hmm. Every 13 minutes would be roughly half a million divided by 13, say, around 40,000. That seems like an awful lot of suicides by young people.”
Moreover, we should not compare minutes-between-events figures from one year to the next. For instance, below the headline quoted above, the flyer continued: “Thirty years ago the suicide rate in the same group was every 26 minutes. Why the epidemic increase?” The problem here is that the population rises each year, but the number of minutes per year doesn’t change. Even if young people continue to commit suicide at the same rate (about 9.9 suicides per 100,000 young people in 2002), as the number of young people increases, their number of suicides will also rise, and the number of minutes between those suicides will fall. While we intuitively assume that a declining number of minutes between events must mean that the problem is getting worse, that decline might simply reflect the growing population. The actual rate at which the problem is occurring might be unchanged–or even declining.
C2Botched Translations
It is not uncommon for people to repeat a statistic they don’t actually understand. Then, when they try to explain what this number means, they get it wrong, so that their innumeracy suddenly becomes visible. Or, at least it would be apparent if someone understood the blunder and pointed it out.
| LOOK FORExplanations that convert statistics into simpler language with surprising implications |
EXAMPLE: