# Rank-based tests

Rank-based (nonparametric) tests replace the data with ranks, so they do not need a normal shape. The Mann-Whitney test is the rank version of the two-sample t test.

Statistics (university) · Part 07: Comparing categories and many groups · Card 7 of 8 · Last updated 2026-10-19

## Analogy

Instead of measuring each runner's time, you only record who finished first, second and third.

## Example

**Ranking two groups**

A: 3, 5, 8   B: 4, 9, 12
All sorted: 3,4,5,8,9,12
Ranks of A: 1, 3, 4, sum = 8
Ranks of B: 2, 5, 6, sum = 13
U for A = 8 - 6 = 2

## In practice

Useful for small samples, skewed data, outliers and ordinal ratings.

## Practice

### Flashcards

- **What does a rank-based test use instead of raw values?** The ranks of the values.

## Questions people ask

### When should I use a nonparametric test?

Use one when your data is badly skewed, has strong outliers, is ordinal, or the sample is too small to trust normality. They make fewer assumptions. The price is slightly lower power than a t test when the data really is normal.

### Why does ranking make a test less sensitive to outliers?

A ranking records only order, not size. An extreme value gets the same top rank whether it is slightly or enormously above the rest. So one wild observation cannot dominate the result the way it can with a mean, which is why rank tests stay stable on messy data.

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