You measured the same participants twice. Anxiety before and after an intervention, weight at baseline and at three months, reading speed pre- and post-training. The question is whether the average changed, and the tool is the paired samples t-test. It is the standard analysis for pre-post thesis designs, and SPSS runs it in about four clicks. Here is the complete procedure, including the assumption check that most students get wrong.
When to Use the Paired Samples T-Test
Use it when every score at time 1 has a natural partner at time 2. The most common case is repeated measures: the same person measured before and after something happened. The test also fits matched-pairs designs, where each participant in one condition is deliberately matched to a specific participant in the other, twins assigned to different treatments, for instance, or patients paired by age and disease severity. Either way, the analysis is identical because SPSS works with the difference within each pair.
That within-pair structure is the whole point. People differ from each other far more than they differ from themselves, so subtracting each person's own baseline removes the between-person noise. With the same effect and the same sample size, a paired design usually needs far fewer participants than a two-group design to reach significance. If your two measurements come from different people, stop here and use the independent samples t-test instead; the two tests are not interchangeable.
Our running example: 25 psychology students complete a statistics anxiety questionnaire (scored 20 to 100) before and after an 8-week statistics course. One group, two time points, continuous outcome.
Setting Up Your Data in SPSS
The layout rule is the opposite of the independent t-test. There is no grouping variable. Each participant gets one row, and the two measurements sit side by side in two columns:
| Participant | Pre_Score | Post_Score |
|---|---|---|
| 1 | 58 | 49 |
| 2 | 44 | 41 |
| 3 | 61 | 50 |
| 4 | 52 | 48 |
| 5 | 47 | 45 |
If your data arrived in "long" format, two rows per participant with a Time column, restructure it first via Data > Restructure > Cases to Variables. The paired t-test dialog cannot read long format. Also check that the pairing is intact: row 7's Pre_Score and Post_Score must belong to the same person. A sorting accident that scrambles one column destroys the analysis silently, and the output will look perfectly normal.
Running the Test
The menu path is Analyze > Compare Means > Paired-Samples T Test.
- Click Pre_Score, then move it into the Paired Variables box. It lands in the Variable1 slot of Pair 1.
- Click Post_Score and move it across. It fills the Variable2 slot of the same pair.
- Click OK.
The order matters for interpretation, not for the p-value. SPSS computes Variable1 minus Variable2, so with Pre in slot 1 a positive mean difference means scores dropped after the course. Put them in the other order and every sign flips. Pick a convention, remember it, and read the output accordingly. You can add several pairs in the same dialog (Pair 2, Pair 3, and so on), and each produces its own t-test.
Checking Assumptions
Here is the mistake we see constantly in draft theses: running Shapiro-Wilk on Pre_Score, then on Post_Score, and declaring the assumption met. The paired t-test says nothing about the distribution of either variable. Its normality assumption applies to the difference scores, one number per participant, post minus pre. Both raw variables can be skewed while the differences are beautifully normal, and the reverse can happen too.
Test it directly. Create the difference variable through Transform > Compute Variable: name it Diff, set the numeric expression to Post_Score - Pre_Score, and click OK. Then run Analyze > Descriptive Statistics > Explore with Diff in the Dependent List, click Plots, and check "Normality plots with tests." In our example the difference scores gave Shapiro-Wilk W = .97, p = .62, so the assumption holds. What counts as holding, and what the Q-Q plot should look like, is covered in our normality testing guide.
While you are in Explore, glance at the boxplot of Diff for outliers. A single participant whose score moved 40 points when everyone else moved 5 can drag the mean difference around badly in a sample of 25.
Reading the Output
SPSS prints three tables. Paired Samples Statistics comes first: the mean, n, standard deviation, and standard error for each measurement. Our example shows Pre_Score M = 52.40, SD = 9.60 and Post_Score M = 46.10, SD = 10.20, both with n = 25. If n is less than your sample size, some participants are missing one of the two scores; SPSS drops incomplete pairs without comment.
The second table, Paired Samples Correlations, reports the correlation between the two measurements, here r = .72, p < .001. Students often ask whether this is the result. It is not. It only tells you how strongly people kept their rank order from pre to post, which is typical of stable traits measured twice. A high correlation is good news for power, but the hypothesis test lives in the third table.
That third table, Paired Samples Test, holds everything you report:
| Statistic | Value | What It Means |
|---|---|---|
| Mean | 6.30 | Average difference (Pre minus Post): anxiety fell by 6.30 points |
| Std. Deviation | 7.50 | SD of the difference scores |
| 95% CI of the Difference | [3.20, 9.40] | Plausible range for the true change |
| t | 4.20 | Mean difference divided by its standard error |
| df | 24 | Number of pairs minus 1 |
| Sig. (2-tailed) | < .001 | Probability of a difference this large if the true change were zero |
The confidence interval excludes zero, which agrees with the significant p-value: the plausible drop in anxiety runs from about 3 points to about 9 points. Note the degrees of freedom. With 25 participants measured twice you have 50 data points but only 24 df, because the test operates on the 25 difference scores.
Reporting in APA Format
The template:
A paired-samples t-test showed that statistics anxiety decreased significantly from before the course (M = 52.40, SD = 9.60) to after the course (M = 46.10, SD = 10.20), t(24) = 4.20, p < .001, d = 0.84.
Cohen's d for a paired design is the mean difference divided by the standard deviation of the differences: 6.30 / 7.50 = 0.84. SPSS 27 and later print this automatically (labeled Cohen's d in the Effect Sizes block); in older versions the division above is all you need. One caveat worth knowing: because the SD of differences shrinks when pre and post are highly correlated, paired-design d values run larger than their independent-design cousins and are not directly comparable across the two designs. Say which formula you used in a footnote and nobody can object.
Report the exact p-value when SPSS gives one (p = .003, not p < .05), drop the leading zero per APA style, and write p < .001 whenever the output shows .000.
What If Normality Fails?
When the difference scores are clearly non-normal and the sample is small, under about 25 to 30 pairs, switch to the Wilcoxon signed-rank test. The menu path: Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples. Move Pre_Score and Post_Score in as a pair, make sure Wilcoxon is checked under Test Type, and click OK. The output reports a Z statistic and a p-value; the effect size r is Z divided by the square root of n, computed by hand.
With larger samples, mild non-normality of the differences matters much less, and the t-test's result will barely move. If you want the assumption checks and the parametric-or-not decision handled for you, Academic Stats Agent tests the difference scores and selects between the paired t-test and Wilcoxon automatically.
Key takeaway: Lay out one row per participant with the two measurements in separate columns, run Analyze > Compare Means > Paired-Samples T Test, and read the third output table. Check normality on the difference scores, never on the two variables separately. Report both means with SDs, t(df), the exact p-value, and Cohen's d (mean difference divided by the SD of the differences). If the differences are non-normal in a small sample, use the Wilcoxon signed-rank test.
Frequently Asked Questions
What is the difference between a paired and an independent samples t-test?
A paired samples t-test compares two measurements taken on the same participants (or matched pairs), such as scores before and after an intervention. An independent samples t-test compares two separate groups of different people. Using the wrong one either wastes statistical power or violates the independence assumption.
Do both variables need to be normally distributed for a paired t-test?
No. The normality assumption applies to the difference scores (post minus pre), not to each variable separately. Compute a difference variable and run Shapiro-Wilk on it. The pre and post scores can each be skewed while the differences are still approximately normal.
What if I measured participants at three or more time points?
Use repeated-measures ANOVA instead of running multiple paired t-tests. Each additional t-test at α = .05 inflates the overall Type I error rate, so with three time points and three pairwise tests, the chance of at least one false positive rises to about 14%.