Ask anyone who uses SPSS to conduct t-tests, and they will likely tell you that
SPSS does not calculate Cohen's d effect size for t tests.
While it is still true that
SPSS has yet to provide a simple check box that would calculate
the most widely reported measure of effect size for t-tests
(come on IBM),
you can still calculate an effect size from the SPSS output.
Plus watch all the way to the end, and I will show you a little-known trick for getting
SPSS to actually calculate Cohen's d for you.
Let's review effect size.
Statistical significance tells us that an effect was not due to chance. The difference was real.
But statistical significance is really a function of sample size. With a large enough sample size,
almost any difference will be statistically significant.
So what we really need to consider is how big was the effect?
Effect size is a measure of how large the effect was.
Differences can be statistically
significant but not really all that
practically impressive. So if a statistical significance test tells us that the difference was real, the effect size
tells us if the difference was real big.
Jacob Cohen in his 1988 book,
Statistical Power Analysis for the Behavioral Sciences gave us a measure of effect size that we now call
Cohen's d.
This is the album cover to my band's single
Leonard Cohen's d, our song about Jacob Cohen's d to the tune of Leonard Cohen's "Hallelujah."
Cohen's d Is the most commonly used measure of effect size and what you should report anytime that you conduct a t-test.
Cohen's d standardizes the mean difference,
dividing the difference between the two means by a standard deviation.
Easy enough, right?
But the way that you calculate Cohen's d will differ depending on whether you are using an independent measures or
repeated measures design.
I'm going to show you how to calculate both types using the SPSS output.
Calculating effect size from independent samples SPSS output requires pooling the variance of the two samples. I have
another video about pooled variance,
so I will summarize here that when the variance or standard deviation of your groups is different and
one sample group is larger than the other.
then the variance of the larger sample will contribute more influence over the total variance.
To fix this we weight the variance of each group by the sample size of each group, and
that is called pooled variance.
Here is the formula for pooled variance and the information that we need to complete this formula is in the group
statistics for the independent samples t-test.
Here we have two groups, clicker training and food reward, which we will call Group 1 and Group 2,
respectively.
To calculate Cohen's d, we need the sample size,
mean, and standard deviation for each group.
Plug in these measures in their respective places in the formula.
When the data have been entered into the formula we use the PEMDAS
technique to solve the equation, and we get a Cohen's d of .79.
Calculating an effect size from paired-samples SPSS output is simpler.
There are two formulas that we could use, and I've included both of them here, so
we get the output for our paired-samples test. All of these descriptives are for paired differences,
so the mean difference is
1.25, and the standard deviation of the difference is 1.282.
Alternatively, we can use the t-value and the sample size.
Plug in the values to either formula and use the PEMDAS technique to solve the equation.
Either way we get a Cohen's d of .98
In the videos for both the independent samples t-test and the paired samples t-test,
I showed you how to compute Cohen's d
using the RStats effect size calculator for t-tests, available from RStats Institute.
But since calculating Cohen's d for independent samples is so complex, let me show you one other
SPSS trick to calculate Cohen's d.
I will tell you right off that this trick will begin to diverge from other calculations if you go out enough decimal places,
especially with smaller sample sizes. It is not perfect, but it gets you really close, and
you can win nerd bets with your friends when you tell them that you can make SPSS calculate Cohen's d.
This trick works better with a large sample size, preferably over 30 per group.
So I'm going to use a different data set. Job Satisfacton.sav
This is the data set that I use when I teach you about correlation and regression.
So first I'm going to run an independent samples t-test and calculate the Cohen's d
using the RStats effect size calculator for t-tests.
Go to "Analyze"
"Compare Means..."
"Independent Samples t-Test"
Right click on the variable names to show the variable labels.
I am going to use Job Satisfaction as the dependent variable, and I have a dichotomous variable,
Gender, to use for the groups. It is coded as 1 = Male, 2 = Female.
Click "OK"
Here in the output, double-click on the output for group statistics. Grab these first 6 cells and copy.
Now we will go to the our stats effect size calculator for t-tests.
Click on the sheet for effect size between.
Here I have a special place that you can just paste these values and click the tab key to analyze.
So here we see that the Cohen's d is a -0.36.
The negative sign just means that the first group has a lower mean, we interpret a negative effect size
exactly the same way as a positive effect size. The negative sign simply tells us the direction.
So now, let's go back to SPSS, and I will show you how to get SPSS to calculate Cohen's d.
Cohen's d is the standardized mean difference.
So we are going to use a shortcut to get SPSS to give us exactly that.
First, we need to standardize the scale scores. Convert them to z-scores. go to
Go to "Analyze"
"Descriptive Statistics"
"Descriptives"
We are using Job Satisfaction.
Notice that you have this little box that says "ave standardized values as variables"
Click that and "OK"
In the data set we now have a new variable called
ZJS which is the Job Satisfaction
converted to z-scores or
standardized.
Now run the independent samples t-test again, only this time we're going to use the standardized scores.
Go to "Analyze"
"Compare Means"
"Independent Samples t-Test"
Move Job Satisfaction out and replace it with this new ZJS variable.
Click "OK"
Remember that Cohen's d is the standardized mean difference.
We just ran an independent samples t-test on
standardized scores, so look at the mean difference.
-0.357, which rounds to the same
-0.36 as we calculated with the RStats effect size calculator for t tests, and
that is how you get SPSS to calculate Cohen's d.
This will only work with an independent measures design
if you did this with the repeated measures design
both of the scale variables would be standardized to have a mean of 0 and a standard deviation of 1,
so the mean difference 0 - 0 would be 0.
However, Cohen's d for repeated measures is easy enough to compute so you can use that formula instead.
Good luck and have fun with this trick.