Paired Samples t-test

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T-Tests

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

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Compares two measurements taken on the SAME people (or matched pairs) — like before vs after — to see whether the average change is real.

It tests whether the mean within-pair difference on a continuous outcome is zero. By working with each person's own change it cancels out between-person variation, which is why a paired design is far more powerful than comparing two separate groups at the same sample size.

Worked example

Does an 8-week yoga programme improve hamstring flexibility?

32 adults did a sit-and-reach test (in cm) before the programme and again after. Same people, two time points → the measurements are paired.

Result

Flexibility rose from M = 19.4 cm (SD 5.9) to M = 24.0 cm (SD 6.9) — an average within-person gain of 4.66 cm, t(31) = 7.43, p < .001, 95% CI [3.38, 5.94], a large effect (Cohen's d_z ≈ 1.3). The differences were normal (Shapiro-Wilk W = .98, p = .83), so the test is valid.

How you'd report it (APA)

A paired-samples t-test showed hamstring flexibility increased significantly from pre-programme (M = 19.4, SD = 5.9) to post-programme (M = 24.0, SD = 6.9), t(31) = 7.43, p < .001, d_z = 1.31, 95% CI [3.38, 5.94].

Try it yourself: Load this ready-made sample and follow the exact run above.

When to use it

  • Pre-test / post-test (change over time)
    The same participants are measured twice. e.g. 30 smokers' daily cigarettes measured before a programme and 6 months after.
  • Two conditions on the same people (crossover)
    Each person is exposed to both conditions. e.g. 100 employees' output measured in a week with music vs a week without.
  • Two measurements on one unit
    Two comparable readings on the same subject. e.g. Gene A vs Gene B expression in the same 50 tissue samples.
  • Matched pairs
    Naturally paired units. e.g. left-leg vs right-leg kicking distance in 40 athletes.

When NOT to — use instead

Hypotheses

H₀: μ_D = 0 — the mean difference between the paired measurements is zero.
Hₐ: μ_D ≠ 0 — the mean difference is not zero (two-tailed; can be one-tailed if you predict a direction in advance).

Parameter tested: μ_D — the mean of the difference scores

Assumptions (and what to do if they fail)

The difference scores are approximately normalmedium

Check: Q-Q plot and histogram of the differences; StatMinds runs Shapiro-Wilk automatically.

If violated: With n ≥ 30 pairs the Central Limit Theorem protects you — proceed. Below that, use the Wilcoxon signed-rank test or a permutation/bootstrap version. (It's the DIFFERENCES that must be normal, not the original scores.)

No influential outliers in the differencesmedium

Check: Boxplot of the difference scores; values beyond 1.5×IQR are flagged.

If violated: Check for data-entry errors, report results with and without the outlier (sensitivity), or switch to Wilcoxon / a trimmed or bootstrapped test.

Ready to run a Paired Samples t-test on your own data?

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