(Photo: John Foxx)
It’s an embarrassing episode. The opening sentence of James B. Stewart’s Tangled Webs: How False Statements Are Undermining America is:
“We know how many murders are committed each year — 1,318,398 in 2009.”
But this is false. As Jeffrey Rosen notes in a savage New York Times review, there were 15,241 murders in 2009. The cited number isn’t just wrong, it’s wrong by two orders of magnitude. Where did the 1,318,398 come from? It’s the number of violent crimes, which includes robbery, rape and assault. And only a small proportion of all violent crimes — a little more than 1 in 100 — are murders.
And so this provides a useful teaching moment for thinking about numeracy. How can you avoid such errors?
- Don’t use numbers when words will do. The rhetorical point that Stewart was trying to make is simply that there are a lot of murders. Too many. You don’t need numbers to say this.
- Don’t use numbers that are hard to comprehend. We have everyday experience in thinking in dozens. But we’re hopeless when it comes to millions, billions, or at the other extreme, tiny fractions. For instance, no one ever made the mistake of saying there are 12,000 eggs in a typical carton. But plenty of journalists confused the $700 billion TARP bailout, describing it as a $700 million plan.
- Scale matters: Big (and small) numbers only make sense relative to something else. Is 15,241 murders a lot for a country the size of the U.S.? Find a scaling that gives this some meaning (and avoids the artificial precision of 5 significant figures). Perhaps: Last year around 1 in 20,000 people were murdered. But how can you get your reader to picture 20,000 people? Easy, it’s roughly the number of people who attend a typical MLB game.To over-simplify: Look around an average NBA basketball stadium. If the crowd is representative of the streets, someone in this crowd will be killed this year.
- The laugh test: When you really think about your number, does it seem plausible, or is it laughably wrong? My basketball stadium analogy conveys the true extent of the U.S. homicide problem. If Stewart had followed this advice, he would have seen that his wrong number implied that 1 in 230 people is killed each year. Straight away he would realize that he isn’t grieving the murder of one of his Facebook friends every year or two.
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This article echoes precisely my sentiment whenever big numbers are thrown out there to illustrate a point. Especially points 1, 2 and 3. Also what irritates me is that many people like those who will read James B. Stewart will assume his statement true just because they see him as a credible source. Heck, the entire country thought Iraq had WMD’s just because the Bush Administration fed us a few BS satellite pics, but I’m digressing.
My point is go check the facts, be it numbers or statements.
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“we know” is also a loaded preamble- auto inclusives to knowledge are often rhetorical manipulators regardless of (true) content
well, when there’s nothing better, a false debt ceiling is better than no ceiling at all. But I still say- we need to pay our bills. China won’t be happy if we do. But wow, imagine a debt free America. Sell bonds if we have to do so. What is the problem. I see it now. a false understanding of Post-industrial society as functional without producing anything. In a way, am I any different? Produce or perish.
I think that keeping your units constant is key in giving perspective when dealing with really large or really small numbers. Going from million to billion, almost interchangeably, can be very misleading. I feel XKCD has a comic that perfectly exemplifies this point, as usual.
http://xkcd.com/558/
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Good points, but I might choose to avoid the NBA analogy, due to basketball’s being primarily an urban game, and murder being associated with urban settings. It would sound different if you made a baseball or soccer analogy. It would sound different if you said “imagine all the people attending a Broadway show tonight – on average one of them will be murdered this year.” It would sound different if you tied the number to the SXSW festival. Context matters.
Hot debate. What do you think?
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“We know how many murders are committed each year…”
But – and I’m sure every reader of murder mysteries would argee – we don’t know how many murders are committed. We know how many deaths are reported and labeled as murders in the crime statistics. Some fraction (one hopes a small one) of those are really natural & accidental deaths that were mislabeled, another fraction of deaths were filed as natural/accidental (or not reported at all), because the murderer took sensible precautions…
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We do math all day here at work. If we are wrong, we lose money…sometimes lots of money. Our best skill is that we can smell a bad number. To some degree, this is a learned skill but mostly, I think, it is a skill you are simply born with.
The two guys I work with are amazing at “smelling a rat”. They don’t teach this at school very well and most people just write down whatever the calculator says.
One guys here still complains about 6th grade when the teacher would mark down his score for not “showing his work” despite getting the correct answer while rewarding those with absurdly wrong answers because they “showed their work” properly.
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I’m off to lunch.
I’ll be back in three thousand seconds.
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