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Paired samples t-test

5 min

The paired t-test compares two measurements taken on the same people (or matched pairs), such as before and after treatment.

Why it matters

Using each person as their own control removes person-to-person differences and gives a sharper test.

Key ideas

  • Outcome: numeric
  • Two measurements linked by person or pair
  • Analyses the differences d = after − before
  • t = mean(d) ÷ (SD(d) ÷ √n), df = n − 1
  • Assumes differences are roughly normal
  • Effect size: dz = mean(d) ÷ SD(d)

Real-life research example

Systolic BP of 8 patients before and after a 4-week diet.

When to use

  • Same participants measured twice
  • Matched pairs (twins, case–control matched)

When NOT to use

  • Don't use for two different groups of people
  • Don't use if the differences are strongly skewed (use Wilcoxon)

Mini example

Before: 150, 142, 160, 155, 148, 152
After: 140, 138, 150, 149, 141, 146

Quick takeaway

Same people twice? Analyse the differences, not the two groups separately.

Try it yourself

Run the paired t-test on the example. Then swap the two lists. What changes and what stays the same?

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