This is the sixth video in SPSS for Beginners from the RStats Institute
at Missouri State University. 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.
So 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 in 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. We are going to use the
paired-samples t-test, which means we need to 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, a 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. 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. I will tell you more about that negative
sign here in a minute. 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. When you are ready to do your paired samples
t-test for real, check out these other videos from RStats Institute, that
will teach you more about statistical theory, setting up the test, interpreting
the results, and writing up your findings in APA style.