Before we calculate a correlation to see if two variables are linearly related
it is a good idea to look at a picture of our data. We do this using a scatterplot a
Scatter plot is used to graphically display correlational data.
The relationship between the variables is depicted with dots called data points.
Each data point is formed by a pair of x and y scores.
The sample size, n, is the number of pairs of x and y scores.
We have spoken before that correlation is measuring the direction and the strength of the relationship
between variables.
The relationship is said to exist when any given y-value tends to be paired with
one, and only one, value of x.
If every y-value was truly paired with one and only one x value there would be a perfect relationship
between the variables. In the real world, however, the relationships are less than perfect, so it is a good idea to add a
regression line to our scatterplot to better visualize
the relationship between the variables.
Now scatter plots can only show two variables at a time.
You can correlate multiple variables in SPSS,
but the scatter plots will only be two at a time.
It is possible to create multiple scatter plots among multiple variables using a matrix
scatterplot, and we will create a matrix scatter plot in SPSS a little later.
All of the scatter plots will use interval or ratio level data. These are called scale level data in SPSS
because they all refer to quantitative, continuous data.
You should create a scatter plot of your data before you begin doing hypothesis testing so that you will have a better idea
about the relationship between the variables.
Visualizing with scatter plots used with a correlational data set as part of exploratory data analysis.
We're going to create a scatterplot in SPSS.
Let me show you the basics here. The scatter plot begins with an x and y axis in a graph.
Set up your x and y axes and label them.
The x-values, the predictor values, go on the horizontal axis.
The y-values, the criterion variable or outcome variable, will go on the vertical axis.
This tells us that x is being used to predict y.
You begin your scatter plot by plotting each pair of x and y values
or coordinates. You go over x points and up y points.
Each pair of scores is represented by a single point.
Again, n equals the number of pairs of scores.
in this simple example we have seven pairs of scores for students: age and their pulse rate.
We will create a scatter plot from these data by placing age on the x-axis and
pulse rate on the y-axis
so we will see if age predicts pulse rate.
We will create our first dot by going over
20 points on the x-axis and up 72 on the y-axis.
Next, go over 25 and up 62.
Over 35 and up 86.
Over 45 and up 64
Over 40 and up 80.
Over 45 and up 74.
And that is how you create a scatterplot.
Now that you understand the basics of a scatterplot, let's create a correlational scatterplot in SPSS.
We will be using the data set Job Satisfaction.sav.
These are data from 200 mental health counselors.
The first four variables are job satisfaction score, burnout score,
compassion fatigue score, with compassion fatigue being the negative emotional consequence of counseling people who have been traumatized, and
gender (male and female).
We are going to create three types of scatterplots.
We will use a simple scatter plot to answer, "How is burnout related to job satisfaction?"
Then we will use a group scatterplot to answer whether the relationship between burnout and job satisfaction
differs from men and women.
Third, we will create a matrix scatterplot to determine how burnout is related to job satisfaction and
compassion fatigue all at once.
So now we are ready to go to SPSS.
Here in SPSS we have opened the data set Job Satisfaction.sav
To create a simple scatter plot go to 'Graphs'
'Chart Builder...'
If when the chart builder opens you are seeing variable labels, you can right-click to show variable names.
In the gallery select 'Scatter/Dot'
And then drag 'Simple Scatter Plot' into the canvas.
We are going to use burnout to predict a job satisfaction.
Drag your predictor variable, Burnout, to the x-axis.
Drag your criterion variable, Job Satisfaction, to the y-axis, and now click OK.
The output window will pop up.
Scroll down, if necessary, until you find a scatterplot. It will not have a regression line in it, so you'll have to add one.
Double-click anywhere in the middle of that chart to open the chart editor.
Click on the icon 'Add a Fit Line At Total.' It's the fifth button from the left on the bottom row of buttons.
A line will appear in the chart editor window.
Close the chart editor by clicking on the red X for P, or the red circle for Mac.
We can see a negative relationship between these variables.
As burnout increases, job satisfaction decreases.
This is what we expected, however,
We may want to know whether the relationship between burnout and job satisfaction is different for males and females.
Perhaps when females burn out on their job, their job satisfaction doesn't decrease as much as it does for males
Let's find out.
Go to 'Graphs.'
"Chart Builder..."
In the gallery, click 'Reset' so we're clearing out anything from the previous analysis.
Now drag 'Grouped Scatterplot' into the canvas.
We are still using burnout to predict job satisfaction, so drag your predictor variable, burnout,
to the x-axis.
Drag your criterion variable, Job Satisfaction, to the y-axis.
You now have a third drop zone titled 'Set color' where you can add a
categorical variable to split the scatterplot.
Drag gender to 'Set color.'
Now we will have two overlaid scatter plots, one for men and one for women. Click OK.
The output window will pop up again. It will not have a regression line on it,
so you'll have to add one. Only this time we want two regression lines: one for men and the other for women.
Double-click anywhere in the middle of this scatterplot to open the chart editor.
Click on the icon 'Add Fit Line At Subgroup'. It's the sixth button from the left on the bottom row.
Two lines will appear on the chart editor window. The blue one is for men and the green for women.
You will also see that the men's scores are plotted with blue dots, and the women's scores are plotted with green dots.
Close the chart editor by clicking on the red X for PC or red circle for Mac.
We can see that these two lines are very similar.
They're parallel and almost on top of each other, that means that the relationship between burnout and job satisfaction is
pretty much the same for men as it is for women. If these lines went in different directions,
then the relationship between the variables would be different for men and women.
These lines are almost on top of each other, so the relationship between the variables is pretty much exactly the same regardless of gender.
Let's do one more scatter plot to figure out
how burnout is related to job satisfaction and compassion fatigue all at once. This is called a scatterplot matrix.
Go to 'Graphs'
'Chart Builder...'
In the gallery click 'Reset' so we clear out the previous analysis.
Drag scatter plot matrix into the canvas.
Now this time you only have one drop zone. It's labeled Scattermatrix.
With this version you can drag them in sequentially. Drop them in this order: Job Satisfaction,
Burnout, and Compassion Fatigue.
And now click OK.
Let's go back to the slides to Interpret this scatterplot matrix.
We are not going to add any regression lines to these scatterplots.
The purpose of the scatterplot matrix is to allow us to see the general pattern of the data.
It allows us to look for potential problems.
You remember that we used three variables, but we have six scatterplots.
And that's because each variable is plotted against the other twice.
For each pairing, one variable is placed on the x-axis and then later on the y-axis,
and this creates a variety of scatterplots that are really more than we need.
The important thing to notice here is that we really have three pairs of scatterplots.
These pairs are the same only with the variables rotated.
We are going to see this same pattern when we look at the correlation matrix in SPSS.