A nonparametric test is a hypothesis test that does not require the population's distribution to be characterized by certain parameters. For example, many hypothesis tests rely on the assumption that the population follows a normal distribution with parameters μ and σ. Nonparametric tests do not have this assumption, so they are useful when your data are strongly nonnormal and resistant to transformation.
However, nonparametric tests are not completely free of assumptions about your data. For instance, nonparametric tests require the data to be an independent random sample.
When a choice exists between using a parametric or a nonparametric procedure, and you are relatively certain that the assumptions for the parametric procedure are satisfied, then use the parametric procedure.
The following is a list of the nonparametric tests, and their parametric alternatives.
|Nonparametric test||Alternative parametric test|
|1-sample sign test||1-sample Z-test, 1-sample t-test|
|1-sample Wilcoxon test||1-sample Z-test, 1-sample t-test|
|Mann-Whitney test||2-sample t-test|
|Kruskal-Wallis test||One-way ANOVA|
|Mood's Median test||One-way ANOVA|
|Friedman test||Two-way ANOVA|