“Statistics Are Elusive Things”
Most journalists aren’t number people. If they were, they’d be much less likely to wind up in a profession dominated by words. We’re trying to ameliorate the situation, at least a little, by cosponsoring CARR training sessions here in Missouri with the Heritage Foundation, the Sunlight Foundation, and the Missouri Broadcasters Association. These sessions help to give journalists some basic grounding in computer-aided statistical reporting.
A recent article in The Washington Missourian about property tax assessments (I found the link via John Combest’s always useful page) highlights the need for journalists to check, doublecheck, and triplecheck their numbers — and always get another pair of math-savvy eyes to inspect their work:
Kim and Steve Obenauer were shocked last week when they found out their real estate tax bill has increased by nearly 87 percent this year. […]
The tax bill for the lot with the mobile home was $79.08 in 2006. This year’s tax bill for the property is $605.41.
Wait a second, I thought — wouldn’t that be an increase of more like 600 to 700 percent? I called up Windows’ trusty calculator, and found that, indeed, moving up from $79.08 to $605.41 constitutes an increase of 665.57 percent. Why such a large discrepancy between the actual figure and the reported figure, I wondered? I figured it was probably just a typo, and moved on. Then I found this sentence:
One woman’s tax bill increased 61 percent, from $390.63 in 2006 to $1,009.10 this year, Emmons said.
But that would be an increase of well over 100 percent! Sure enough, a quick trip to the calculator revealed an increase of 158.33 percent. That’s when I realized what the Missourian piece was doing wrong — it was taking a backward look at the numbers, as though the new tax figures were starting points.
Take the first set of numbers, $79.08 and $605.41. If a homeowner were assesed $605.41 one year and $79.08 the next, that would constitute a decrease of 86.94 percent — or, rounded up, 87 percent. The problem is, that same figure doesn’t apply in reverse. Percentage changes are relative, depending on which number is the starting point, so even though $79.08 is only 13.06 percent of $605.41, calculating the reverse shows that $605.41 is 765.57 percent of $79.08 — or, after subtracting the original 100 percent, an increase of 665.57 percent more than the original $79.08.
The same is true of the second set of numbers. Moving from $1,009.10 one year to $390.63 the next would be a decrease of 61.29 percent, but the reverse, moving up from $390.63 to $1,009.10, is an increase of 158.33 percent. In other words, if you take the difference between the lower figure and the higher — that difference being $618.47 — you can fit $390.63 into it 1.5833 times, which is where we get the 158.33-percent-increase figure. If you take that same difference and try to fit $1,009.10 into it, you’ll find that it fits 0.6128 times, which is where we get the 61.28-percent-decrease figure.
I don’t write this as an unfriendly challenge to anybody at the Missourian. Rather, I simply hope it illustrates that, as Judge J. Smith Henly wrote, "Statistics are elusive things at best," and nudges Missouri journalists toward using a little more care when working with figures.
