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The Relationship Between Variables: Correlation Coefficient & Scatterplots

The Relationship Between Variables: Correlation Coefficient & Scatterplots
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  • 0:05 Definition
  • 1:08 Scatterplots
  • 2:12 Coefficients and Plots
  • 4:09 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.

The focus of this lesson is on how both correlation coefficients and scatterplots convey the same message. Specifically, this lesson will explore how these two can reveal the same information but in different ways.

Scatterplots and Correlation Coefficients: Definitions

Scatterplots are cool because you can see them. Whenever math can be represented by a picture, it helps make things really easy to understand. Yeah, it's just a big open area with a bunch of dots in it, but it tells you a lot when you're able to interpret it. A scatterplot is a visual representation of the relationship between two variables. It is the thing you're looking at below. How you make one will be explored in a moment.

Example of a scatterplot
example of a scatterplot

These scatterplots are created to help a researcher visually see the relationship between two variables. This relationship between the two variables is called a correlation. The amount of correlation, or relationship, can be explained in a numerical form called a correlation coefficient. A correlation coefficient is defined as a numerical representation of the strength and direction of the relationship.

Scatterplots

To make a scatterplot is pretty simple. You have two numerical values for variables. Let's say number of hours slept and the amount of junk food eaten. Now, hours slept is an easy thing to keep track of. You slept two hours or four and a half - not a whole lot of controversy there. To measure junk food, we will have to get a little crafty because there are many ways you can go about this.

One option is the number of items of junk food (one pickle, one bag of chips, two sodas, three cupcakes), or we can count the number of calories (1,000 extra calories from junk food). I think the extra calories is a little more scientific and allows for a little more control because the piecemeal counting is kind of vague. Then, you draw an X-Y plane, and you make one side 'Hours Slept' and the other side 'Number of Calories.' And, plot your results. This is how you make a scatterplot.

Coefficients and Plots

Now how does the correlation coefficient come into this? A correlation coefficient is, again, a numerical representation of the relationship between the two variables. If there is a close relationship, meaning that as one moves, so does the other, then the coefficient is closer to 1 or -1. Remember that if the coefficient is negative, all this means is that when one variable increases, the other variable decreases. A coefficient closer to 0 means that there is less or no relationship between the variables.

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