Did students score higher after the training program than before it? Did anxiety fall between the first and the last session? When the same people are measured twice, the paired t-test is the standard tool for answering the question. It looks simple, yet results chapters often confuse it with the independent samples test, check normality on the wrong variable or report an effect size that does not match the design.
This article is part of our guide How to Write a Master’s Thesis by the Mastermind PhD team and relates to our Statistical Analysis service. Sources last checked: November 2026.
This guide covers when the test applies, its five assumptions, the SPSS steps, how to read the three output tables, how to compute Cohen’s dz, and how to write the result in APA style, ending with the mistakes examiners notice first.
What is the paired samples t-test? It is a parametric test that compares two means obtained from the same participants (or from matched pairs) on a continuous variable. It works on the difference score of each person and asks whether the mean of those differences is larger than chance would produce. It is also called the dependent t-test, the repeated measures t-test or the matched pairs t-test.
When should you use the paired t-test?
Use the paired t-test when each score in the first column has a natural partner in the second column. Typical designs in a thesis:
- Pre-test and post-test on the same group, with no control group, or within one arm of an experiment.
- Two conditions experienced by the same participants, such as reading speed on paper and on screen.
- Matched pairs, where each participant is deliberately paired with another on age or ability, and the two members receive different conditions.
- Two related ratings of the same people, such as a self-rating and a supervisor rating of the same employee.
Do not use it when the two groups contain different people (use the independent samples t-test), when there are three or more time points (use repeated measures ANOVA), or when the difference scores are clearly non-normal in a small sample (use the Wilcoxon signed-rank test).
What are the five assumptions and how do you check them?
| Assumption | How to check it | If it fails |
|---|---|---|
| Continuous dependent variable | Nature of the measure; scale scores averaged from items are treated as interval | Wilcoxon signed-rank test |
| Related pairs | Study design: the same person, or a matched partner, in both columns | Independent samples t-test |
| Independence between pairs | Each pair is unrelated to the other pairs | A different design (for example multilevel models) |
| No extreme outliers in the differences | Boxplot of the difference variable | Check entry errors; report any exclusion |
| Approximate normality of the differences | Shapiro-Wilk, skewness and kurtosis of the difference variable | Rely on robustness above about 30 pairs, or use Wilcoxon |
The key point is that normality concerns the difference scores, not the pre-test and post-test separately. Create the difference with Transform, then Compute Variable (post minus pre), and run Analyze, then Descriptive Statistics, then Explore on that new variable.
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How do you run the paired t-test in SPSS?
- Enter the data in wide format: one row per participant, one column for each measurement (for example
pre_scoreandpost_score). - Choose Analyze, then Compare Means, then Paired-Samples T Test.
- Move the first measurement to Variable1 and the second to Variable2 in the same row. Several pairs can be entered at once.
- In SPSS 27 and later, tick Estimate effect sizes. Leave the default 95% confidence interval under Options.
- Click OK. SPSS prints Paired Samples Statistics, Paired Samples Correlations and Paired Samples Test, and an effect size table if you requested it.
The order of the two variables matters only for the sign: SPSS subtracts Variable2 from Variable1, so a post-test that is higher than the pre-test gives a negative mean difference when the pre-test is entered first.
How do you read the three output tables?
Paired Samples Statistics gives the mean, N, standard deviation and standard error of each measurement. These values go into your descriptive table.
Paired Samples Correlations shows how strongly the two measurements are related. A high correlation is expected and is the reason the paired t-test is more powerful than an independent comparison of the same means; it is not a test of your hypothesis and is usually not reported as a finding.
Paired Samples Test is the main result. Read the mean of the differences, its standard deviation, the 95% confidence interval of the difference, t, df (number of pairs minus one) and the two-sided p value. A confidence interval that excludes zero corresponds to a significant difference at the .05 level.
How do you compute the effect size for a paired t-test?
The most common choice is Cohen’s dz: the mean difference divided by the standard deviation of the differences. SPSS reports it as Cohen’s d in the Paired Samples Effect Sizes table, with the standardizer named in a footnote. Lakens (2013) explains that dz is not directly comparable with the d of an independent design, because it depends on the correlation between the two measurements; some authors therefore also report d computed from the average of the two standard deviations. State which one you used.
| Value | Common interpretation (Cohen, 1988) |
|---|---|
| About 0.20 | Small |
| About 0.50 | Medium |
| 0.80 and above | Large |
These benchmarks are conventions. Compare your effect with effects reported for similar interventions in your field where possible.
Worked example: from output to APA sentence
The numbers below are an illustrative scenario, not data from a real study. Forty students take an achievement test before and after a six-week program.
- Pre-test: M = 62.4, SD = 10.2. Post-test: M = 68.9, SD = 9.7.
- Mean difference (post minus pre) = 6.5, SD of differences = 8.1.
- Standard error = 8.1 ÷ √40 = 1.28; t = 6.5 ÷ 1.28 = 5.08; df = 39; p < .001.
- 95% CI of the difference: 6.5 ± 2.02 × 1.28, that is [3.91, 9.09].
- Cohen’s dz = 6.5 ÷ 8.1 = 0.80.
APA sentence: “A paired t-test showed that achievement scores were higher after the program (M = 68.9, SD = 9.7) than before it (M = 62.4, SD = 10.2), t(39) = 5.08, p < .001, dz = 0.80, 95% CI of the mean difference [3.91, 9.09].” The sentence contains both means and standard deviations, the direction, t, df, p, the effect size and the interval.
How do you present the result in a table?
Give one row per outcome, with columns for the pre-test mean and SD, the post-test mean and SD, the mean difference, t, df, p and dz. Place the bold table number above an italic title, for example “Table 6, Paired t-Test Results for Achievement Before and After the Program“. When you test several outcomes on the same participants, add a note stating whether you corrected the alpha level, for example with the Bonferroni method.
APA number rules apply: two decimals for means, standard deviations, t and effect sizes; exact p values to two or three decimals unless p < .001; no leading zero before p; statistical symbols in italics.
Which mistakes weaken a paired t-test result?
- Running an independent samples t-test on pre and post scores of the same people, which ignores the pairing and wastes power.
- Testing normality of the pre-test and post-test instead of the difference scores.
- Writing p = .000 instead of p < .001.
- Claiming that the program caused the change when there is no control group. A one-group pre-post design shows change, not cause; maturation, practice and testing effects are alternative explanations.
- Reporting the Paired Samples Correlations table as if it answered the research question.
- Running several paired t-tests across three or more time points instead of one repeated measures ANOVA.
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Frequently asked questions
What is the difference between the paired and the independent samples t-test?
The paired t-test compares two measurements of the same people, so it analyzes difference scores. The independent samples test compares two separate groups of people. Choosing the wrong one changes the degrees of freedom, the standard error and often the conclusion.
When should I use the Wilcoxon signed-rank test instead?
Use Wilcoxon when the difference scores are clearly non-normal and the number of pairs is small (roughly under 30), when outliers cannot be justified for removal, or when the outcome is ordinal, such as a single Likert item. Report medians with it.
How many pairs do I need for a paired t-test?
It depends on the effect you expect. A power analysis in G*Power for a medium effect (dz = 0.50), alpha .05 and power .80 gives about 34 pairs for a two-tailed test. Larger samples also make the normality assumption less critical.
Can I use the paired t-test with a control group?
Within each group, yes, but the stronger analysis compares the change between groups, for example an independent samples t-test on gain scores or an ANCOVA with the pre-test as a covariate. Your supervisor and field conventions will guide the choice.
Why is my mean difference negative?
Because SPSS subtracts the second variable from the first. If you enter the pre-test first and scores rose, the difference is negative. Report the direction in words and, if you prefer, present the difference as post minus pre.
Sources
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
- American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.). APA.
- Laerd Statistics. Dependent t-test using SPSS Statistics. https://statistics.laerd.com/spss-tutorials/dependent-t-test-using-spss-statistics.php
- Pallant, J. (2020). SPSS Survival Manual (7th ed.). Open University Press / Routledge.
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.