Writers Talk About Writing
I'll Take the Percent Increase for $84, Please
When the US government finally signed a deal to avoid the fiscal cliff, I was quickly confused about what the deal was. On the airwaves, I heard that part of the deal would be a 2% increase in payroll taxes, yet in print, I read that there was to be a 2 percentage point increase.
There can be a big difference between 2% and 2 percentage points.
Proportion and Precision
Percent is a specific portion of a given value, with the whole of the value being 100%. For example, if I invite 50 people to a party, and the portion who actually come is 60%, then 30 people attend my party:
50 * 0.60 = 30
A percentage is an unspecified portion of a given value. I could say A percentage of the people I invited actually came to the party. Although rare, a numerical value can be listed in related to percentage, but the number comes after percentage, as the object of a preposition, rather than as a modifier of percentage:
She hit 22 homers on the season, with a slugging percentage of .968, and posted a record of 20-3 on the mound. — San Francisco Chronicle
Pretty straightforward, right? Language users get percent and percentage right without thinking too hard about it.
But here's what we often miss: percentage point is, as Mark Allen said in Become a Numbers Person, "a point along a 100-point scale related to the whole scale rather than related to a number being compared."
We're talking about two different measurements here. A percent change is a proportional change, that does not, as the AMA Manual of Style points, "indicate the actual beginning or ending values or the magnitude of the change." A percentage point change is a mathematical, or numerical, change, which does give you an idea of the magnitude of the change.
$84 vs. $2,000
Let's go back to our original example. The US payroll tax rate in 2012 was 4.2%. That is, 4.2% of your income went to Uncle Sam. For the sake of simplicity, let's say you earned $100,000 in 2012. Of that amount, you paid 4.2%, or $4,200, in payroll taxes:
100,000 x 0.042 = $4,200
If the payroll tax were going to be 2% higher in 2013, that would mean the rate would be increasing a portion of the starting rate. That is, we would be paying 2% of 4.2% plus the original 4.2%, or 4.284%.
Again for simplicity, let's say your salary will stay the same in 2013. This year, you'll pay $4,284 instead of $4,200 ($100,000 x 4.284%). That's not a bad increase.
But that's not what's happening. Look closely, and you'll see that the new payroll tax rate is 6.2% — a two percentage point increase. What will you pay out in payroll taxes in that case?
$100,000 x 0.062 = $6,200
Numerically speaking, a $2,000 increase is substantially different from a $84 increase!
Here's the big question: is the usage distinction between percent and percentage point recognized outside of industry texts, such as financial reports and medical studies? In other words, does a general audience understand what is meant when they hear that there will be a 2% payroll tax increase?
It's not unusual for industry definitions to become less precise and more generic when they are co-opted by a general audience. That audience doesn't know all the ins and outs, just the summary information. And though it drives those who know the difference crazy, that's just the way life works.
In this case, those who don't know the distinction between percent and percentage point seem to be making a leap in logic and coming up with the right answer. At least according to the reports I've heard. Perhaps the inclusion of the new and old rates, 4.2% and 6.2%, helps in that leap.
Printed news stories about the payroll tax increase are more precise, however, using percentage point. I've only heard reference to a percent increase, not read it. So at least in print, we are opting to be more precise. It makes sense. In print we have the time to do the math and think about the logic. Plus readers can't ask for clarification and get it quickly. Without the precision in print, we risk a potentially huge misunderstanding.
But even in formal speech, we should be careful. Again, listeners might not have an opportunity to ask for clarification. It's important for writers and speakers to not only know their facts but also communicate them in a way that eliminates confusion or misunderstanding as much as possible.
Numbers can be confusing, particularly when you don't know all the details behind them. For clarity's sake, use the precise meanings of percent and percentage point to get your message across.