Quick – which amount is larger: the difference between one in 32 and one in 13, or the difference between 3 percent and 8 percent?
If you know the answer, sit on your hands for a minute. If not, I’ll tell you shortly. But to understand why I’m asking, consider these two statements:
- Statement 1: “In 2008, roughly one out of 32 Tennesseans had a valid handgun permit. Now, it’s nearly one out of 13.”
- Statement 2: “The percentage of Tennesseans with a valid handgun carry permit has risen from 3 percent to 8 percent since 2008.”
I’d be willing to bet that the change described in the first statement sounds bigger to many people than the change described in the second. In fact, though, the second is larger – but by only a little. To figure out the first difference, divide 1 by 32. You’ll get 3.13 percent, which is 4.57 percentage points less than the 7.69 percent you get if you divide 1 by 13. To figure the second difference, subtract 3 percent from 8 percent, which gives you 5 percent. That’s a tad more than 4.57 percent, but not if you round to the nearest whole percentage.
So the answer is that it’s a trick question. The two differences are essentially identical.
If this doesn’t surprise you, great. Consider yourself a pretty savvy numbers person. But if it does surprise you, then you might need to take extra care when you read a story like “Handgun permits rise as legislators try to ease laws,” which appeared in the March 9, 2015 edition of The (Nashville) Tennessean.
The story opened with the same wording as Statement 1, went on to note that the number of permits has increased since 2008 in every one of the state’s counties, with some of the increases exceeding 200 percent, and said the head of a state-based gun rights advocacy organization “acknowledges the number of permits rose drastically since 2008.”
The story is the latest of several that state media outlets have published recently based on handgun permit data available from the Tennessee Department of Safety and Homeland Security. I’ve written here and here about some of the distortions in these reports. This report avoids most of the earlier issues (although it doesn’t account for population growth when reporting the county-level increases in permits). But in describing trends in the number of permit holders, the article uses language that obscures a seemingly important fact: While a growing percentage of Tennesseans have handgun permits, they remain a small minority statewide.
U.S. Census Bureau’s latest (2013) single-year population estimates for Tennessee
Tennessee Department of Safety and Homeland Security Handgun Carry Permit Statistics, Calendar Year 2013, p. 297.
That gray slice representing Tennesseans age 21 and older who hold handgun carry permits is 8.8 percent of the total – about the same, if a tiny bit larger, than the amount represented by the “one in 13” phrase in the opening sentence of the Tennessean story. It is perhaps a little less impressive, though, when viewed in this way.