Interpreting the Correlation Coefficient

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  • 0:07 Definition
  • 2:34 Perfect and No Correlation
  • 5:03 Real Correlations
  • 6:44 Lesson Summary
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Lesson Transcript
Instructor: Devin Kowalczyk

Devin has taught psychology and has a master's degree in clinical forensic psychology. He is working on his PhD.

This lesson explains the process of interpreting and analyzing a correlation coefficient both as a figure and as a context by discussing common and easy to understand examples.

Correlation Coefficient and Related Definitions

Did you know that as ice cream sales increase, so do murder rates? It's insane; it's crazy; but it's true. As ice cream sales increase, so does murder. As murder rates decline, so do ice cream sales.

A correlation is defined as a relationship between two variables. So, in our example, there is a relationship between ice cream sales and murder. As one goes up, the other goes up. As one goes down, the other goes down.

A perfect correlation is defined as a perfect relationship between two variables. This means that the two variables we are looking at move at the same time. If variable one moves up, then variable two also moves up. If variable two moves twice, then variable one moves twice. A perfect correlation looks like a line.

However, we are starting to limit ourselves here. A relationship can happen when one variable increases while another variable decreases. For instance, the more time a student spends watching TV is inversely related to his or her GPA. More TV, lower GPA. Higher GPA would mean less TV.

We will explain those a little bit better in a second. First, we need to explain a few more definitions. A scatterplot is a visual representation of the relationship between two variables. It is the thing below.

Example of a scatterplot
example of a scatterplot

It is done by placing one variable on axis Y and the other variable on axis X. The individual points of data are then marked. If you have a low variable X and a high variable Y, then it is placed in the upper left-hand side. A high X and a low Y means it goes onto the far right side. You never really do escape geometry, do you?

A correlation coefficient is defined as a numerical representation of the strength and direction of the relationship. It is usually represented by a lowercase 'r.' The correlation coefficient is a number that represents how similar the two variables are. It ranges from -1 to 1.

OK, enough definitions. Let's start bringing this all together: what is, and how do you interpret, a correlation coefficient?

Perfect and No Correlation

This is going to get a little tricky here, so please pay very close attention. Correlation coefficients have some basic facts; it's just how they are. Here they are in list form:

  • Coefficients range from -1 to 1, which describes how scattered the data is. The more like a line it is, the closer it is to 1 (or -1).
  • Negative implies an inverse correlation, or that when one variable goes up, the other variable goes down.
  • A 0 means there is no correlation.

OK? Probably not, so we will use some examples. Let's say (and I am making these numbers up) that there is a perfect correlation between ice cream and murder as well as between TV and GPA (yes, we are using both). That would mean there is a 1 or a -1 correlation coefficient.

If, for every murder, there was one box of ice cream sandwiches sold, then 15 murders mean 15 boxes of ice cream sandwiches sold. This means that as one increases, the other will increase in an equal way. After some fancy math, our correlation would look like this: r = 1.

In our TV and GPA example, let's say that for every 5 hours of TV, your GPA will drop by 1. So, if you watch 10 hours of TV, your GPA will drop by about 2. After your fancy math, your correlation coefficient would look like this: r = -1. Please note that the negative means that there is an opposite interaction - as one goes up, the other goes down.

This is worth having on the screen: A negative correlation is just as strong as a positive correlation. The only difference between a negative and a positive correlation is the interaction.

Examples of negative and positive correlations
example of negative and positive correlations

Positive means both go up and down at the same time, while negative means they go up and down at opposite times.

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