Take this quiz:
If one candidate has 46 percent of the likely voters, and the other has 48 percent, what’s the gap between them?
If you said 2 percent, go to the back of the line. The gap between them is 2 percentage points. It’s a4 percent difference. (Either way, it probably falls in the margin of error, so don’t even think of saying one is ahead of the other).
Whenever there is an election, or a poll, there is often an “age” problem. It has nothing to do with how many birthdays a person has had, but with how numbers are treated. When it comes to what portion of the whole pie you have compared with someone else, there are two ways to measure it: In terms of “percent” and “percentage points.” And many times, news reports get it wrong.
Percentages are tricky, especially if you dozed off when they were taught. It doesn’t help that we speak of “percentages” even when we mean “percent.” If you think of that whole pie, it may make things easier.
Let’s say there are ten slices of the pie, representing 100 percent. You have four slices, and your friend has two. (The other four slices are still in the pie plate.) The first part is easy: You have 40 percent of the pie, and your friend has 20 percent. You can add two percent numbers together to see what portion of the whole they represent: Together you have 60 percent—six of the ten slices.
Now, you might think that, since you can add the two numbers together to come up with a total percentage of the pie, you can subtract one from the other to see the difference between you. If you subtract your friend’s 20 percent portion from your 40 percent, you have 20 percent more, right?
Um, no. If you think about it, you have twice as much pie as your friend has (piggy you!): Your four slices to your friend’s two. That’s 100 percent more: But you have 20 percentage points (or just points) more than your friend has—the simple mathematical difference between your portion, measured in percent, and your friend’s.
If you want to see the percentage difference, you need to do some division. Many of you probably learned this the hard way: ((y2 - y1) / y1)*100, where “y” is a value, “/” is divide and “*” is multiply. But there’s an easier way, by cutting out the middleman:
Take one number, subtract the other one, and divide by the other one. Which number you use for the first number will depend on what you want to measure.
For example, to see the percentage (proportional) difference between your share and your friend’s, take your share (40), and subtract your friend’s share (20). The difference is 20, and you divide it by your friend’s share (20). That equals 1.00; multiply by 100, or move the decimal two places to the right, and voilà: 100 percent. If you your friend wanted to know how much less pie she had, she would do the opposite: take her share (20), subtract your share (40), and divide by your share. That comes to -50 percent. She has half of what you have. (Remember, you can’t reduce anything by more than 100 percent.)
Now let’s turn to that poll. Take 48, subtract 46, and divide the result (2) by 48. You have .0417, or just over 4 percent. That’s what separates the two candidates.
This works for figuring out percentage changes in business reports, too. Take, for example, a company whose net income went from $3.5 million in the third quarter last year to $5.2 million in the third quarter this year. Take the new number (5.2), subtract the old number (3.5), and divide the result (1.7) by the old number (3.5), to get 0.486. The company’s net income went up by 48.6 percent. If those figures were switched, and this quarter was lower, the same calculation applies: New (3.5) minus old (5.3), yielding ¬-1.8, divided by old (5.3), equals -.340, or a drop of 34 percent.
There’s no percentage in getting it wrong.