16. Non-parametric Tests

The definition of what a non-parametric test is best understood by comparing parametric tests to non-parametric tests.

Parametric Tests Non-parametric Tests
Estimate a parameter like \mu, \sigma, or p (proportion) prior to hypothesis testing. Hypothesis testing without parameter estimation. Involves counting or ranking.
Generally require a population to be normally distributed. “Distribution-free statistics”.
Only works for quantitative data. Works for both qualitative and quantitative data.
More power. Less power.
Need more detailed data (more information). Work with less detailed data (less information).
Work with smaller sample sizes. Need large sample sizes.

If you have a choice, generally a parametric test is preferred to a non-parametric one because it has more power. On the other had, if you reject H_{0} with a non-parametric test, you can be more confident in your decision.