Thursday Tip: What's the point?

Many writers, even economists and statisticians who should know better, confuse percent and percentage point and thus their readers.

 
The abuse is common with rates, such as those of GDP growth:

 
Brazil's GDP growth increased by 2.5 percent in 2007.

 
If Brazil's GDP growth had been 5 percent in 2006 and increased by 2.5 percent, the growth rate for 2007 would be 5.125 percent. But if growth increased by 2.5 percentage points, the growth rate for 2007 would be 7.5 percent. A big difference.

 
The differences between two percentages are thus measured in percentage points not in percent, used for ratios and shares.

 
Consider these differences in the shares of three categories of voters from Wednesday's Washington Post:

 
An estimated 2 million Democrats voted, nearly triple the number who turned out in the past two presidential campaigns in the state. Clinton ran up big margins with her core constituencies, winning white voters with incomes under $50,000 by 32 points, voters over age 65 by 26 percent, and Catholic voters by 38 percent, more than countering Obama's strong showing among black voters and higher-income whites in Philadelphia and its suburbs.

 
For the 32 points, the writer should have made it clear that they are percentage points (this wasn't a basketball game that Clinton won by 32 points, with a score of 120-88).

 
And the 26 percent and 38 percent are plainly wrong. Both should have been percentage points, shortened to points if the first use had been 32 percentage points, specifying the kind of points.

 
If the margin among voters over age 65 had been 63 percent of the total to 37 percent, that would be 26 percentage points. But if Clinton had won those voters by 26 percent, her margin would have been 11.8 percentage points (0.37 x 0.32 = 0.118) and her share of the total 48.8 percent (0.37 + 0.118).

 
(Percent comes from the Latin per centum, by the hundred.)