Written by Dackohn; last reviewed November 2026.
Samples are paired when each value in one group is linked to one value in the other, such as the same person measured twice. They are independent when the groups contain unrelated individuals. Using the wrong test can change your conclusion: the same data below gives p = .004 when paired and p = .076 when treated as independent.
How to tell
Ask: does each value in one group have a specific partner in the other?
| Paired | Independent |
|---|---|
| Same people before and after | Different people in each group |
| Left and right eye of each patient | Patients randomised to two treatments |
| Twins, or matched pairs by age and sex | Men vs women in a survey |
| Two raters scoring the same essays | Two classes taking one test |
Worked example
Ten people rate their sleep before and after a routine change. Before: 62, 70, 55, 68, 74, 59, 66, 71, 60, 65 (mean 65.0). After: 65, 69, 60, 74, 72, 67, 70, 80, 67, 75 (mean 69.9).
- Correct, paired t-test: the mean change is 4.9 with an SD of differences of 4.01, so t(9) = 3.86, p = .004.
- Wrong, independent t-test: t(18) = 1.88, p = .076, not significant.
Why pairing helps
People differ a lot from each other: some sleep well, some badly. That spread (SDs of about 6) swamps the change in an independent test. Pairing removes it, because each person acts as their own control. Only the changes matter, and they vary much less. The two measurements here correlate at r = .76, which is what makes pairing pay off. The stronger the correlation, the bigger the gain.
Which test to use
| Design | Roughly normal | Skewed or ordinal |
|---|---|---|
| Independent, 2 groups | Independent t-test | Mann–Whitney U |
| Paired, 2 conditions | Paired t-test | Wilcoxon signed-rank |
| Independent, 3+ groups | One-way ANOVA | Kruskal–Wallis |
| Repeated, 3+ conditions | Repeated-measures ANOVA | Friedman |
Downsides of paired designs
- Order effects: practice or fatigue can affect the second measurement. Randomise the order where possible.
- No control group: a before-and-after change may reflect time passing or regression to the mean, not the treatment.
Common mistakes
- Dropping unmatched values without saying so. Report how many pairs were complete.
- Reporting only the two means. For paired data, report the mean change and its confidence interval.
Try it yourself
T-Test Calculator →Paired, independent and one-sample tests. Wilcoxon Signed-Rank Test →For paired data that are not normal.Frequently asked questions
How do I know if my samples are paired?
If each value in one group is linked to one specific value in the other, such as the same person measured twice, they are paired.
What happens if I use an independent test on paired data?
You usually lose power, because differences between subjects stay in the error term, and you may miss a real effect.
Can groups of different sizes be paired?
No. Pairs need one value from each condition. Any unmatched values have to be handled separately.
Related reading: Welch vs Student t-test · Sign test vs Wilcoxon · Choosing a statistical test
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.