Welcome to the fourth video in SPSS for beginners from the RStats Institute at Missouri State University.
Now that we have learned how to examine each variable using descriptive statistics and graphs,
I'm going to show you how to do some simple analyses. So this video will show you the basics of doing correlation.
When you're ready to do a correlation for real,
watch the other are stats Institute videos to learn more about the theory the analysis and
how to write up your findings in APA style.
We're still using the same
SPSS data set that we created in the first video, however, I deleted the z-score variables that we created last time.
Now I'm going to show you how to calculate
correlations in
SPSS
The correlation that we are doing is called Pearson's r.
A Pearson's correlation describes the relationship between two variables.
Pearson's r ranges between -1 and +1.
0 indicates no relationship at all.
The closer that the correlation is to either +1 or -1, the stronger the relationship
between the variables.
We are interested in the relationship between height and weight.
Notice how the data have already been set up. Each person has a pair of scores.
Your height should be paired with your weight, it makes no sense to pair your height with my weight.
So it's very important that each pair stays together
We have 10 pairs of scores. Our sample size is 10. Each pair counts as one case.
So remember that we have two people without height and weight scores.
They are not going to be included in this analysis.
In fact, SPSS will simply ignore those cases with missing values. So let's do a correlation.
Go to Analyze
Correlate
A Pearson's r correlates two variables, so choose Bivariate...
As before all of our variables are here on the left. The two that we want to correlate are height and weight.
So we need at least two
variables.When you move over the first, the "OK" is still not available until you move over the second.
And we could add additional variables, but each would be correlated only two at a time.
We have some additional options here as well. We could calculate Kendall's tau or
Spearman's Rho if we had different data, but for now let's just stick with Pearson's r.
SPSS assumes that we want two tailed significance tests and
that we want to flag significant correlations.
We haven't talked about significance tests yet,
so for now just know that significance tests tell us something important about the variables. In this case, our
correlation is statistically significantly different than 0. If it is,
SPSS will flag it. All of the default settings are just the way we want them, so click OK to run the analysis.
The box that we see is called a "correlation matrix."
The correlation matrix shows the correlation coefficient for every combination of variables.
So we have two rows: one for height, one for weight.
And we have two columns: one for height, one for weight.
Where each row and column intersect, we see the correlation coefficient between those two variables.
So in this quadrant of the matrix we see the correlation coefficient between height and
itself.
No surprise. It's 1. It's a perfect correlation.
We see another perfect correlation down here on the lower right which is the correlation between weight and itself.
SPSS will compare every combination of variables
including each variable and itself.
Now these correlations are not very interesting because we already know that
every variable will always correlate with itself at a +1, no matter the variable.
The interesting correlations are in these off diagonals.
The top left box is the correlation coefficient.
It will always be between +1 and -1.
Below that is the significance level.
Significance levels smaller than .05 are statistically significant.
Below that is the N, or the sample size, which is our 10 pairs of scores. So let's look at this coefficient.
Notice that the off diagonal correlations are the same because height correlates with weight exactly the same as weight
correlates with height. In this case it's a .574 which is pretty strong,
but not significant because the sample size of 10 is pretty small.
You are always more likely to find significance with larger sample sizes.
If this correlation was significant, we would see some asterisks next to the coefficient.
So as I mentioned, you can correlate more than two variables at a time,
and you could even use correlation with nominal variables as long as it only has two levels. In fact, let me show you.
Go to Analyze
Correlate
Bivariate
All we're going to do is throw in a third variable, Gender, and this is actually called a point biserial correlation,
more on all of that later. For now, just click OK.
We get another correlation matrix, but this time it's bigger. It has three rows and three columns.
The correlations between height and weight are exactly the same as before,
but we also have correlations with gender.
Because the correlations are negative, as one variable goes up the other goes down.
Remember that we coded males as 1, females as 2. So the 1 is smaller. We see this negative
correlation, the smaller numbers are associated with larger values. So basically the males were taller and weighed more.
And here we also see a significant correlation that's been flagged.
The biserial correlation between weight and gender has two asterisks, so what does that mean?
We can see that this correlation is significant at the .01 level. In fact, the p-value is .009.
So there' is a statistically significant relationship between weight and gender.
So there's one more thing that I want to show you with correlations,
and that is how to make a picture of them. The picture is called a scatter plot,
and it is created using a new tool called the chart builder. And here's how we do it.
Instead of the Analyze menu, we're going to use the Graphs menu. So go to Graphs
Chart Builder
We will learn more about the chart builder later when we learn about graphing.
For now, let's just have some fun and make a scatter plot.
Start by clicking on the word Scatter/Dot in the gallery.
Now we see our eight options. If you hover your cursor above them, SPSS will tell you what they are.
We want this first option: Simple Scatter
Click and drag it into the blank area known as the canvas.
You will see that we now have two drop zones: one for the x axis and one for the y axis.
So let's use height to predict weight.
Drag height to the x axis drop zone
weight to the y-axis drop zone.
And that is all you have to do. Click OK.
And there is our scatter plot of all 10 of the pairs of scores.
There is much more that we could do with correlation, so for instance, we could format the scatter plot in APA style.
We could do other types of correlations.
We could even use some variables to predict other variables using a technique called
regression
To learn more about correlation, scatter plots, simple regression, and multiple regression check out these other videos
from RStats Instiutue.
Correlations are about relationships between variables,
but we might also be interested in
differences between variables. So next we're going to learn about t-tests.