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.
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Analogy
Instead of measuring each runner's time, you only record who finished first, second and third.
Example
A: 3, 5, 8 B: 4, 9, 12All sorted: 3,4,5,8,9,12Ranks of A: 1, 3, 4, sum = 8Ranks of B: 2, 5, 6, sum = 13U 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.