Paired T-Test Calculator
The paired t-test is the right tool for "before vs after." Because each subject serves as their own control, it strips out the noise between people and asks one clean question: did the changes consistently point the same way? Paste your pairs (or the summary numbers) and get the t statistic, the p-value, and an effect size.
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Paired vs Independent vs Wilcoxon
Three tests look similar but answer different questions. Using the wrong one either wastes your data's power or breaks its assumptions.
Choosing the right test for two measurements
| Paired t-testBest | Independent t-test | Wilcoxon signed-rank |
|---|
If your data are paired, the paired t-test is almost always the most powerful correct choice.
Worked Example: Blood Pressure Before vs After a Drug
Ten patients are measured before treatment and four weeks after. The drops (after − before) are consistently around −5 mmHg: mean difference −5.4, SD of differences 1.07, n = 10. The t statistic is −5.4 / (1.07 / √10) = −15.9 with df = 9. The two-tailed p-value is vanishingly small (< 0.0001), and Cohen's d = 5.0 — an enormous effect. Pairing is what makes this so decisive: the between-patient variation (some at 115, some at 130) cancels out once you look at each person's own change.
How to Interpret the p-Value (Without Overselling It)
The p-value answers a narrow question: if the treatment did absolutely nothing, how often would random pairing produce a difference this extreme? Below your α (usually 0.05) you conclude the change is real. But p is not the probability the drug works, and a tiny p on a tiny effect is still a tiny effect. That's why this calculator reports Cohen's d alongside p — d tells you whether the change is big enough to matter, independent of how many subjects you recruited.
Frequently Asked Questions
When should I use a paired vs independent t-test?
Paired when the two measurements are the same subjects (before/after, left/right, matched). Independent when they're different, unrelated people. Pairing removes between-subject noise and is more powerful.
What does the p-value tell me?
It's the chance of a difference at least this extreme if the true effect were zero. Below α you reject "no effect." It is not the probability the treatment works.
What are the assumptions of the paired t-test?
Independent pairs and approximately normal differences. Normality matters for small n; above ~30 it's robust. For skewed differences, use Wilcoxon signed-rank.
What is Cohen's d for a paired test?
Mean difference ÷ SD of differences. It's the effect in standard-deviation units (0.2 small, 0.5 medium, 0.8 large), independent of sample size.