Non-parametric tests
Non-parametric tests
- A non-parametric test makes no assumption that the data is normal — useful when that assumption fails.
- The basic ones:
- the sign test — count values above/below a proposed median, test with a binomial model,
- the Wilcoxon signed-rank test — also uses the sizes of differences,
- the Wilcoxon rank-sum test — compares two separate samples.
Practice
A non-parametric test is useful because it:
Non-parametric tests avoid the normality assumption, so they work when it fails.
Practice
The sign test works by counting values above and below a proposed median, then testing with a:
The number above the median follows a binomial model under the null hypothesis.
Practice
The Wilcoxon signed-rank test uses the sizes of the differences, not just their signs.
Unlike the sign test, the signed-rank test ranks the magnitudes of the differences.
You've got it
Key idea
- non-parametric tests need no normality assumption
- the sign test uses only above/below a median (binomial)
- Wilcoxon signed-rank (one sample, uses sizes) and rank-sum (two samples)