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: MANGLING THE THREAT OF SECONDHAND SMOKE
In a press release, the British Heart Foundation’s director for Scotland was quoted as saying: “We know that regular exposure to second-hand smoke increases the chances of developing heart disease by around 25%. This means that, for every four non-smokers who work in a smoky environment like a pub, one of them will suffer disability and premature death from a heart condition because of second-hand smoke.”5
Well, no, that isn’t what it means–not at all. People often make this blunder when they equate a percentage increase (such as a 25 percent increase in risk of heart disease) with an actual percentage (25 percent will get heart disease). We can make this clear with a simple example (the numbers that I am about to use are made up). Suppose that, for every 100 nonsmokers, 4 have heart disease; that means the risk of having heart disease is 4 per 100. Now let’s say that exposure to secondhand smoke increases a nonsmoker’s risk of heart disease by 25 percent. What’s 25 percent of 4? One. So, among nonsmokers exposed to secondhand smoke, the risk of heart disease is 5 per 100 (that is, the initial risk of 4 plus an additional 1 [25 percent of 4]). The official quoted in the press release misunderstands what it means to speak of an increased risk and thinks that the risk of disease for nonsmokers exposed to secondhand smoke is 25 per 100. To use more formal language, the official is conflating relative and absolute risk.
The error was repeated in a newspaper story that quoted the press release. It is worth noting that at no point did the reporter quoting this official note the mistake (nor did an editor at the paper catch the error).6 Perhaps they understood that the official had mangled the statistic but decided that the quote was accurate. Or–one suspects this may be more likely–perhaps they didn’t notice that anything was wrong. We can’t count on the media to spot and correct every erroneous number.
Translating statistics into more easily understood terms can help us get a feel for what numbers mean, but it may also reveal that those doing the translation don’t understand what they’re saying.
C3Misleading Graphs
The computer revolution has made it vastly easier for journalists not just to create graphs but to produce jazzy, eye-catching displays of data. Sometimes the results are informative (think about the weather maps—pioneered by USA Today—that show different-colored bands of temperature and give a wonderfully clear sense of the nation’s weather pattern).
But a snazzy graph is not necessarily a good graph. A graph is no better than the thinking that went into its design. And even the most familiar blunders—the errors that every guidebook on graph design warns against—are committed by people who really ought to know better.7
| LOOK FORGraphs that are hard to decipherGraphs in which the image doesn’t seem to fit the data |
EXAMPLE: SIZING UP METH CRYSTALS
The graph shown here appeared in a major news magazine.8 It depicts the results of a study of gay men in New York City that divided them into two groups: those who tested positive for HIV, and those who tested negative. The men were asked whether they had ever tried crystal meth. About 38 percent of the HIV-positive men said they had, roughly twice the percentage (18 percent) among HIV-negative men.
Although explaining these findings takes a lot less than a thousand words, Newsweek decided to present them graphically. The graph illustrates findings for each group using blobs–presumably representing meth crystals. But a glance tells us that the blob/crystal for the HIV-positive group is too large; it should be about twice the size of the HIV-negative group’s crystal, but it seems much larger than that.
Graph with figures giving misleading impression.
We can guess what happened. Someone probably figured that the larger crystal needed to be twice as tall and twice as wide as its smaller counterpart. But of course that’s wrong: a figure twice as wide and twice as tall is four–not two–times larger than the original. That’s a familiar error, one that appears in many graphs. And it gets worse: the graph tries to portray the crystals as three dimensional. To the degree that this illusion is successful, the bigger crystal seems twice as wide, twice as tall, and twice as deep–eight times larger.
But what makes this graph really confusing is its use of different-sized fonts to display the findings. The figure “37.8%” is several times larger than “18%.” Adding to the problem is the decision to print the larger figure as three digits plus a decimal point, while its smaller counterpart has only two digits. The result is an image that manages to take a
