Compute Paired-Samples t-Tests
Let’s see the steps for computing a paired-samples t-test.
Recall from Week 5 that data do not need to be reformatted for paired-samples tests as they are already
located in separate columns.
We will hypothesize that participants’ scores on Anxiety are lower Post-treatment than they are Pre-
treatment. We have given a direction, so this is a one-tailed test. Each participant has a score for pre-
treatment and a score for post-treatment, so we need to run a paired-samples test.
1. Open your data file, click on Data, and click Data analysis.
2. Scroll down and select t-Test: Paired Two Sample for Means. Click OK.
3. In Variable 1 Range, put the range for the first of your two variables, including the label. In Variable 2
Range, put the range for the second of your two variables, including the label.
a. Check the box next to Labels.
b. Make certain your Alpha is set to 0.05
c. Select the radio button for New Worksheet.
d. Click OK
4. A new worksheet will open. Right click on the worksheet tab and rename it to identify the analysis you
are conducting.
5. Reformat your data to the appropriate font and number format (change general to number). You will
see the output in the following format:
These data give you the mean, the variance, and the number of participants (observations) for each variable.
Note you will need to compute the SD, which is the square root of the variance. This is followed by the
Pearson correlation, hypothesized mean difference (null hypothesis), and df (needed for your APA-formatted
formal report). Following df is the information that will enable you to interpret this test. You are interested in
the t-statistic and the p-value for the one-tail and the two-tail tests along with the critical value.
Here we conducted a one-tailed test hypothesizing lower scores post-treatment. Our t has an absolute value
of |7.48|, with p = 0.00 and a critical value of 1.80 for a one-tailed test. Because t = |7.48 |is greater than the
critical value, we can conclude that there are significant differences between the two means. This is
confirmed by the p-value of 0.00, which is less than the required 0.05 for significant differences. For this data,
your p-value is less than 0.05; so, you will reject the null hypothesis and interpret the data output as having
significant differences between pre- and post-treatment scores.
In your report, these data would be written in APA format as follows:
Results
The participants were tested on anxiety prior to beginning therapy and again three months later to see
whether their levels of anxiety changed significantly. To test the hypothesis that therapy was effective, a
paired-samples t-test was run, which indicated that scores did change significantly (t(11) = 7.48, p < .000). So,
the null was rejected. The mean anxiety score at the beginning of therapy was 22, SD = 3.41. Three months
later, anxiety significantly decreased, with mean = 11.33, SD = 4.08.
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