# Paired t test

A paired t test compares two measurements on the same subjects, such as before and after. Work out each person's difference, then run a one-sample t test on the differences against 0.

Statistics (university) · Part 06: Hypothesis testing · Card 8 of 9 · Last updated 2026-10-19

## Analogy

Weighing the same people before and after a diet removes differences in body size from the comparison.

## Example

**Before and after**

Differences: 4, 6, 2, 5, 3
Mean = 4, s = 1.58
SE = 1.58 / square root of 5 = 0.707
t = 4 / 0.707 = 5.66, df = 4
p about 0.005: significant

## In practice

Used for before and after studies, matched twins and left versus right comparisons.

## Practice

### Flashcards

- **When is a paired t test used?** When two measurements come from the same subjects or matched pairs.

## Questions people ask

### Why is a paired test more powerful than an unpaired one?

Pairing removes the variation between people, because each person acts as their own control. Only the change matters. When people differ a lot from each other but respond similarly to the treatment, the paired test spots the effect more easily.

### How do I decide between paired and two-sample tests?

Ask whether each value in one group is naturally linked to one value in the other. Same person before and after, or matched pairs, means paired. Two separate groups of different people means two-sample. The design decides, not the numbers.

## Related concepts

- [One-sample t test](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-6/statistics-university-part-6-concept-6)
- [Two-sample t test](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-6/statistics-university-part-6-concept-7)

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