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 , , or (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 with a non-parametric test, you can be more confident in your decision.