Source: Tables created by the author
This tutorial is going to teach you about using percentages wisely in statistics. People tend to throw around percentages without really thinking about what type of percentages they're talking about. So for instance, results and statistics are often expressed as percents but it's important to distinguish between percentage points and percents, which are used to describe relative change. Percentage points are used to measure absolute change. If you forgot what those terms are there's another tutorial on that.
Suppose a teacher gives a particularly difficult exam and these six students all failed it. The teacher graciously offered a retake to the students. So now, let's take a look at how these students did on the retake. Well they all passed, that's great. Jonathan scored an 88, Ryan scored a 78, Katherine scored an 84, et cetera. And look at Kelly, 95%. That was really nicely done.
We can express these changes in terms of percentage points and percent increase. So we'll talk about both of those. Which student had the highest increase in percentage points? Well, Jonathan went from 52% to 88%, that's an increase of 36 percentage points. Ryan went from 38 to 78, that's an increase of 40 percentage points. We can calculate that for all of them and see that it was Kelly who increased 47 percentage points.
Now, who had the highest percent increase? Well to that, we need to look at the raw numbers which were the increases. 36 points for Jonathan, 40 points for Ryan, 23 percentage points for Katherine, et cetera. And determine who had the highest percent increase over their old score. And so you begin with the 52 and determine how much of an increase 36% was over that 52.
So, Jonathan's score increased by 69%. Katherine's only increased by 38%, because she had a fairly high score to begin with. Which student had the highest percent increase? It was Ryan. He more than doubled his score. He started with a 38 and finished with a 78, a 40 percentage point increase. 40 percentage point increase over a score of 38, is over 100%. He more than doubled his old score.
Let's take a look at one more example. Suppose a politician's approval rating drops from 34.3% down to 26.9%. What was the absolute change in his approval rating? Pause the video and calculate it out. Well, it was 26.9 minus 34.3, or negative 7.4 percentage points. He dropped 7.4 percentage points.
What was his relative change, his percent change? Well we start with the negative 7.4 percentage point drop. How does that compare to his old percent of 34.3? It was negative 21.6%. It was a 21.6% decrease in his approval rating. That's a huge dip. He must have done something really, really wrong to drop from 34.3%, which wasn't high to begin with, all the way down to something like 27%.
And so to recap, when percentages are used in statistics it's important to know whether we're talking about absolute change or relative change. Absolute change is the difference in percentage points and relative change is a percent increase or percent decrease. The terms we used were percentage points and percent increase or decrease. Good luck, we'll see you next time.
An absolute increase or decrease in a percent value.
A relative increase or decrease in a percent value