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Using Percentages in Statistics

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Source: Tables created by Katherine Williams

This tutorial talks about using percentages in statistics. Percentages are a common way of reporting statistical results. There's many different things that we could be talking about when talking about percents, and it's important to understand the differences. That's what this tutorial will cover. They could be talking about percentage point or percent change, and one of those refers to an absolute change, while the other refers to relative change.

In this first example, the 2012 National Coffee Drinking Trends Report finds a 10% increase over 2011 in coffee consumption now puts coffee get a clear 14-point advantage over soft drinks. This is how the Trends Report is giving the results of their statistical study, and now, I need to break down what is meant by this 10% increase, and by the 14-point advantage. We need to know what that means in order to interpret the statement.

So first, let's look at percentage points. Percentage points is the simple difference between two percentages. The key is that it's an absolute change. It's simply the new value, subtract the old value.

So with the percentage point, you're just calculating the differences. So in our example, when we talked about the 14-point advantage, that 14-point advantage is referring to percentage point. So let's look at our data.

Here, in 2012, coffee had 64 votes, where soft drinks had 50 votes. So for the percentage point difference, we're doing a simple difference, and we're going to do 64 minus 50. And when we do that, we get 14. So coffee is at a 14-point advantage over soft drinks. That's where they're getting their statistic from.

Now, let's talk about percent change. Percent change is talking about how much a value changes relative to what it once was. So here, it's not absolute change, it's relative change.

So when we talk about percent increase or decrease, we're talking about the change relative to what the values once were. In order to calculate this, we do the absolute change, so the new value minus the old value, and then divide it by the old value. So in our example, where it talks about a 10% increase over 2011, they're doing the relative change there.

So let's look at our data again. So now, we're comparing coffee's value in 2012 with coffee's value in 2011, so 68 and 54. So for percentage change, we are going to be first calculating the absolute change. So 64 minus 58, and then dividing by the old value, dividing by 58.

So when we type that into the calculator, we're going to do 64 minus 58. We get 6. And then from there, we're going to divide by 58, and we get 0.103. To turn that into a percent, multiply it by 100. 10.3%.

Now, our statistic from before rounds this to a 10% increase, but that's pretty close. And they just rounded there. So when we're using percentages in statistics, it's important to decide whether we're looking at percentage points or percent change. One is referring to an absolute change, where the other is giving relative change, and they each might be appropriate, depending on your situation. This has been your tutorial on using percentages in statistics.