Paired Samples t-test
Also known as: dependent t-test, matched pairs t-test, repeated measures t-test, within-subjects t-test
The paired samples t-test is a parametric hypothesis test that compares the means of two related measurements from the same subjects or matched pairs to determine whether the average difference is significantly different from zero. It leverages the dependency between observations to produce a more powerful test than its independent-samples counterpart.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use the paired t-test when you have two measurements that are naturally linked — the same subjects measured twice (pre-test / post-test), two conditions administered to each participant, or matched pairs such as twins or left-versus-right limb. The difference scores should be approximately normally distributed; check this with a Shapiro-Wilk test on the differences rather than on the raw scores. Do not use this test when observations are truly independent — that case calls for the independent samples t-test. With clear non-normality or small n, prefer the Wilcoxon signed-rank test.
Strengths & limitations
- Increases statistical power by eliminating between-subject variability from the error term.
- Requires fewer participants than an independent design to detect the same effect size.
- Conceptually simple: reduces a paired problem to a one-sample test on difference scores.
- Reports Cohen's d_z as a natural, interpretable effect size within the paired context.
- Available in every major statistical software package with consistent output.
- Requires that each unit appear in both conditions; if pairing breaks, the design collapses.
- Sensitive to outlying difference scores, especially in small samples.
- Assumes the difference scores are approximately normally distributed, not the raw scores.
- Limited to exactly two time points or conditions; more conditions require repeated measures ANOVA.
Frequently asked
How is the paired t-test different from the independent samples t-test?
The paired test exploits the correlation between two measurements on the same unit, reducing error variance and increasing power. The independent test treats the two groups as unrelated and pools variance across them. Using an independent test on paired data wastes the pairing, inflates the error term, and reduces power.
What if the difference scores are not normally distributed?
With larger samples (roughly n > 30) the central limit theorem makes the test robust to moderate non-normality. For small samples with clearly skewed or heavy-tailed differences, use the Wilcoxon signed-rank test, which ranks the absolute differences and does not assume normality.
Should I report Cohen's d_z or Cohen's d_av?
Cohen's d_z (mean difference divided by the SD of differences) is the natural effect size for the paired t-test and is directly linked to the t statistic and power calculations. Cohen's d_av (mean difference divided by the average of the two SDs) is more comparable to effect sizes from independent designs but requires separate reporting of both SDs. Choose d_z for power analysis and d_av when comparing effect magnitudes across study designs.
Can I use the paired t-test with more than two time points?
No. For three or more repeated measurements use one-way repeated measures ANOVA, or a mixed model. Running multiple paired t-tests inflates the family-wise error rate unless a correction such as Bonferroni is applied.
Does sample size refer to the number of individuals or the number of observations?
In a paired design, n is the number of pairs (i.e., the number of individuals or matched pairs), not the total number of observations. Degrees of freedom equal n minus one.
Sources
- Student (1908). The probable error of a mean. Biometrika, 6(1), 1–25. DOI: 10.1093/biomet/6.1.1 ↗
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE. ISBN: 978-1446249185
How to cite this page
ScholarGate. (2026, June 3). Paired Samples t-test. ScholarGate. https://scholargate.app/en/statistics/paired-samples-t-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Independent samples t-testStatistics↔ compare
- One-sample t-testStatistics↔ compare
- Repeated-measures ANOVAStatistics↔ compare