Mastering SPSS – How to perform Paired Samples t-Tests in SPSS
This is the sixth post for SPSS beginners from the SPSS mastering series at Mastering SPSS.
Table of Contents
Introduction
In this video, I’m going to show you how to compare two means from two measurements of the same sample. This is called a within-subjects design, a repeated measures design, or a paired samples design. When we compare two related means with SPSS, we use a paired samples t-test.
As before, we will use the data set that we created in the first video. For this research project, we have a single sample that we have measured twice. You will often see this as a before-and-after design. You measure a group of people, then you give them a treatment, and then you measure them again a second time. If their scores on the post-test are higher than on the pretest, you know that the treatment had an effect.
Another time that we will have paired measures is when we have two measurements of the same group. In our data set, we measure the same people for both their height and their weight. Each person has a pair of measures. Of course, there is a fundamental flaw in this example, because height is measured in inches, and weight is measured in pounds, so, I’m comparing two completely different measurement scales. A much better example would be to have a before weight, and then put people on a calorie-restricted diet, and then six weeks later measure them again to see if they have lost weight; however, in order to show you how to conduct this type of test in SPSS, I’m going to go with this rather silly example, because these are the only two scale variables that I have.
Conducting the Paired Samples t-Test in SPSS
Conducting the Paired Samples t-Test in SPSS
We are going to use the paired-samples t-test, which means we need two scale variables. So go to Analyze -> Compare Means -> Paired Samples t-Test. Move over the variables that you want to compare. We want to compare height to weight: our two scale level variables. And when you’re ready, click OK.
The first table contains descriptive statistics for each variable. It has the mean, sample size, the standard deviation, and the standard error of the mean for each variable. Below that, in the second table, we see the correlation coefficient between the two variables. We do not really need this output right now, but you will use the correlation coefficient later, when we calculate the effect size. This third table has our inferential statistics. This is what we want to look at right now. On the far right, we see the t-value, the degrees of freedom, and the p-value that corresponds to a t-score of 17.4 with 9 degrees of freedom.
We are going to use the paired-samples t-test, which means we need two scale variables. So go to Analyze -> Compare Means -> Paired Samples t-Test. Move over the variables that you want to compare. We want to compare height to weight: our two scale level variables. And when you’re ready, click OK.
The first table contains descriptive statistics for each variable. It has the mean, sample size, the standard deviation, and the standard error of the mean for each variable. Below that, in the second table, we see the correlation coefficient between the two variables. We do not really need this output right now, but you will use the correlation coefficient later, when we calculate the effect size. This third table has our inferential statistics. This is what we want to look at right now. On the far right, we see the t-value, the degrees of freedom, and the p-value that corresponds to a t-score of 17.4 with 9 degrees of freedom.
Interpreting the Results
Interpreting the Results
So as before, we want to know are these means statistically significantly different? And we can answer that question in three ways:
- First, is the t-value greater than a critical value that we look up on Student’s t Table? With 9 degrees of freedom, I looked up that critical value; it was 2.262. This t-value of 17.4 is MUCH larger than 2.262.
- Second, is the p-value less than .05? Our p-value is .000, which is WAY less than .05.
- Third, does the 95% confidence interval cross zero? It does not. Both the upper and lower values are negative, so they are on the same side of zero. Therefore, we conclude that these means ARE statistically
So as before, we want to know are these means statistically significantly different? And we can answer that question in three ways:
- First, is the t-value greater than a critical value that we look up on Student’s t Table? With 9 degrees of freedom, I looked up that critical value; it was 2.262. This t-value of 17.4 is MUCH larger than 2.262.
- Second, is the p-value less than .05? Our p-value is .000, which is WAY less than .05.
- Third, does the 95% confidence interval cross zero? It does not. Both the upper and lower values are negative, so they are on the same side of zero. Therefore, we conclude that these means ARE statistically significantly different.
But as I told you, that is really not particularly surprising, because we are comparing inches and pounds. So let me say something more about that confidence interval. What is that? A confidence interval is a range in which the mean difference is likely to fall 95% of the time. You see, the mean difference of -67.2 is very precise, but it is also very likely to be wrong. If we drew another sample and tested it, most likely, the mean difference would be slightly different than -67.2. On the other hand, if I repeated this study 100 times, 95% of the time, the mean difference would be between -75.9 and -58.4. So, the mean is precise, but wrong. The confidence interval is much more certain, but also less precise. However, with good measurements and low variability, we can get both the mean and the confidence intervals as accurate as possible.
I also want to point out something about that t-value. Notice that the t is negative. All that means is that the second group had a higher mean than the first group. You interpret a positive t-value exactly the same way as you interpret a negative t-value. Let me show you. Go to Analyze -> Compare Means -> Paired Samples t-test. See that we have a space to do a second t-test? Let’s move over the height and weight variables, but this time in the opposite order. Click OK. When we examine the output, we see two t-tests. Notice that all of the output is exactly the same, except in places where it is just reversed, such as with this confidence interval. In one case, the t-value is negative, in the other case, it is positive. So, basically you do not need to focus on whether the sign is positive or negative, because the sign simply tells us which group was entered first or second. You SHOULD look at the actual means when you interpret these findings. And that is how we do a paired samples t-test in SPSS.
Further Learning
When you are ready to do your paired samples t-test for real, that I will teach you more about statistical theory, setting up the test, interpreting the results, and writing up your findings in APA in next posts style.
