Non-parametric tests which are also called distribution-free tests are applied when the distribution of the population is not known. In other words, non-parametric tests makes no assumption about the probability distributions of the observations.
See also What are Parametric Tests
Kolmogorov-Smirnov Test: This test is used to examine wether a sample is taken from a given distribution. In case of two samples, it tests if the two samples are taken from the same distribution.
Mann-Withney U (also called Wilcoxon rank sum test): Just like the Kolmogorov-Smirnov test, this is used to test wether two samples are drawn from the same distribution.
Wilcoxon signed-rank test: This is used to test wether matched pair samples are drawn from populations with different mean ranks.
Sign Test: Used to test whether matched pair samples are taken from populations with equal medians.
Kruskal-Wallis one-way ANOVA on ranks test: This is used to test if two samples are taken from the same distribution. It compares two samples which could be of equal or different sample sizes.
Chi-Square Tests:This test is used to determine whether there is significant difference in between the expected frequencies and the observed frequencies in one or more categories.
Non-Parametric tests could be categorized into three different categories as shown below:
- Goodness of Fit Tests: In this categories, the distribution of the variable being analyzed is the same as hypothetical
- Tests for Independence: Here, the claim is that the rows and columns of variables being tested are independent.
- Tests for Homogeneity: In tests for homogeneity, the variables being analyzed are distributed equally
Table 1.0 summarized the three categories of non-parametric tests