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# Scatter Plots

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What do all the points mean? What does the line mean? What even is a scatter plot?

• What is a scatter plot?
• What are the different types of scatter plots?
• What are some uses for scatter plots?

## Scatter Plot in Psychology Definition

Scatter plots are used to determine if there is a relationship between the two variables being studied. If there is a relationship between the two variables, it will be shown on the scatter plot. In order for data to be shown on a scatter plot, it has to be measured in numerical values.

On the x-axis of the scatter plot graph is one variable and on the y-axis is the other variable. Remember, these variables have to be numerical! You can’t have a scatter plot that has one numerical variable and one non-numerical variable.

For example, you wanted to study the relationship between a subject and the rates of students enrolled in that subject. You collected data and tried to show the relationship between the two variables in a scatter plot. However, it doesn’t work since the subject is not a numerical value. A graph that would better represent this data would be a bar graph which would display comparisons between the people enrolled in each subject. If you were set on using a scatter plot as your graph, you would have to change the nonnumerical variable. Your new study could look at the relationship between tuition and the rates of students enrolled in the school.

When looking at a scatter plot, look left to right to determine if there is a relationship between the variables. There will be points scattered around the graph but if there is a relationship, you will see the majority of the points either trending upward or downward.

### Line of Best Fit

So there’s a bunch of points that look like they’re going to the top right or bottom right corner of the graph but you’re not fully sure of the direction of all the points. What do you do?

Line of best fit to the rescue!

The line of best fit is a line that shows the relationship between all the points.

Think of the line of best fit as an estimate. The line of best fit will most often not actually go through every single point on the scatter plot; otherwise, it wouldn’t be a line! It’s just showing the general idea of how the points would look if they were averaged. In some cases, the points on the scatter plot and the line of best fit are all very close together which is great because that means there’s not a whole lot of variation in your data. However, it does happen that your line of best fit has some points around it, but a couple of points that are nowhere near it. That’s okay! Those are just your outliers.

## Types of Scatter Plot in Psychology

### Positive Scatter Plotsin Psychology

The first type of scatter plot is a positive or rising scatter plot. Here, when looking from left to right at the data, the points will, for the most part, trend upwards. If you were to insert a line of best fit in a positive scatter plot, the slope would be positive. Easy enough to remember!

Data that results in a positive scatter plot has both variables either increasing or decreasing together. They have to move in the same direction!

An example of data that would result in a positive scatter plot would be minutes spent in a pool and calories burned (if you were lap swimming). The more minutes you spend in the pool working out, the more calories you burn. If you chose to show this relationship on a scatter plot, the slope of the line of best fit would be positive and all the points would trend upwards from the bottom left to the top right corner.

Positive scatter plot. wikimediacommons.

### Negative Scatter Plots

As you might guess from the name, the points for a negative scatter plot will trend downwards when looking at the graph from left to right. The slope of the line of best fit would also be negative.

Data that results in a negative scatter plot has to have one variable increasing and one variable decreasing.

Sticking with the example of swimming, an example of data that would result in a negative scatter plot would be years spent swimming and 100 freestyle time. For the most part, as the number of years that someone has swum increases, their time in the 100 freestyle will decrease since they are getting faster. This will cause the data and the line of best fit to trend downward.

Negative scatter plot. wikimediacommons.

### No Relationship

No correlation means that the points are all over the place. When you look at a scatter plot of data that shows no correlation, there will be no method to the madness of the points. The points will be randomly over the graph and you will not be able to tell if they all tend to go upwards or downwards. There is no relationship between the two variables.

An example of two variables with no relationship would be shoe size and SAT scores. Since these variables don’t increase together or go in opposite directions, they have no relationship. The points on this scatter plot would be all over the place.

No relationship scatter plot. wikimediacommons.

## Examples of Scatter Plot in Psychology

Psychologists use scatter plots most often for correlational research. Correlational research collects data from two different variables and determines the relationship between the two variables. Unlike experimental research, correlational research does not manipulate variables, but rather simply looks at or collects data for the variables.

By putting the correlational data in a scatter plot, researchers can look at the data and determine if there is a relationship. When variables are correlated, they change at the same time (either they both increase together or one increases while the other decreases).

Remember with correlational research, correlation does not equal causation! Just because two variables are correlated, it does not mean that one variable causes the change in the other. Correlational studies can only show that variables are related. If they are, researchers would then have to conduct an experimental study to determine causation.

All of the examples above would be considered correlational research.

## Scatter Plot Correlation Coefficient

In scatter plots and correlational research, there is an important value called the correlation coefficient.

The correlation coefficient is a numerical value ranging from -1.00 to +1.00 that shows how strong a correlation is.

A scatter plot whose line of best fit has a negative slope will have a negative correlation coefficient. When there is a scatter plot with a positive slope, the correlation coefficient will be positive.

A correlation coefficient of -1.00 or 1.00 would be the strongest possible correlations. -.90 or .90 would still be strong correlation coefficients -- anything below -.80 and above .80 would be considered significant correlation coefficients. For the coefficients that fall outside of that range, they might show correlation, but it would not be considered statistically significant.

## Scatter Plots - Key takeaways

• Scatter plots are graphs that are used to determine if there is a relationship between two variables
• A positive scatter plot means both variables are increasing. The line of best fit would have a positive slope.
• A negative scatter plot means one variable is increasing and one variable is decreasing. The line of best fit would have a negative slope.
• No relationship means that there is no relationship between the variables. A line of best fit is unable to be made.

In psychology, a scatter plot means that the two variables shown are being studied using correlational research.

A scatter plot would be used to show the relationship between time working out and amount of sweat produced.

Scatter plots are used for correlational research in psychology.

To create a scatter plot, you plot out each point of data through the x-axis and y-axis.

The characteristics of a scatter plot are points from the data, axes, and a line of best fit.

## Final Scatter Plots Quiz

Question

What is a scatter plot?

A graph that shows the relationship between two variables

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Question

When is a scatter plot used in psychology?

Correlational research/studies

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Question

How do you read a scatter plot?

From left to right!

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Question

What is the line of best fit?

A line that shows the relationship between the two variables (and best summarizes the data)

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Question

Does the line of best fit go through all the points?

Yes

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Question

Does the line of best fit have to be straight?

Yes, it's a line

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Question

What relationship between the variables does a positive scatter plot show?

Both variables increase

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Question

What relationship between the variables does a negative scatter plot show?

One variable increases and one decreases

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Question

The slope of line of best fit for a positive scatter plot would be ___________

Positive

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Question

The slope of line of best fit for a negative scatter plot would be ___________

Positive

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Question

What does a scatter plot with no relationship look like?

The points are scattered all around the graph

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Question

What does a scatter plot with no relationship mean?

There is no relationship between the two variables being studied

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Question

What type of scatter plot would this example have:

Food eaten and weight gained

Positive

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Question

What type of scatter plot would this example have:

Temperature and clothes worn

Positive

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Question

What type of scatter plot would this example have:

Body muscle and intelligence

Positive

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