of physical abuse, and only a small fraction of cases of physical abuse involve fatal injuries. Now, one can argue that every case of child abuse and neglect is bad, but most people would probably agree that being beaten to death is worse than, say, not having clean clothes to wear to school.
Or take crime. In 2011, there were about 700,000 motor vehicles stolen, but fewer than 15,000 murders.6 Stealing a car and killing someone are both bad, but almost everyone thinks that murder is worse than car theft.
Most social problems display this pattern: there are lots of less serious cases, and relatively few very serious ones. This point is important because media coverage and other claims about social problems often feature disturbing typifying examples: that is, they use dramatic cases to illustrate the problem. Usually these examples are atrocity stories, chosen precisely because they are frightening and upsetting. But this means they usually aren’t typical: most instances of the problem are less troubling than the example. Still, it is easy to couple a terrible example to a statistic about the problem’s scope: for instance, a report of an underage college student who died from acute alcohol poisoning (a terrible but rare event) might be linked to an estimate of the number of underage college students who drink (doubtless a big number).7 The implication is that drinking on campus is a lethal problem, although, of course, the vast majority of student drinkers will survive their college years.
| LOOK FORDramatic examples coupled to big numbers |
EXAMPLE: THE INCIDENCE OF BEING INTERSEX
A person’s sex–male or female–strikes most people as the most fundamental basis for categorizing people. Classification usually occurs at the moment of birth (if not earlier, thanks to ultrasound imagery): “It’s a girl!” or “It’s a boy!” This seems so obvious and natural that most of us rarely give it a thought.
Still, there are babies who don’t fit neatly into the standard male/female framework. Some babies have ambiguous genitalia; they can be recognized as hermaphrodites at birth. Others have less visible conditions that may take years to be recognized. People with androgen insensitivity syndrome, for instance, have the XY chromosomes found in males, but because their cells do not respond to testosterone, they develop female genitalia; the condition is usually not discovered until puberty. There are several such conditions, and people with any of them may be categorized as intersex.
Some advocates argue that intersex people are common enough to challenge the naturalness of the male/female 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
