What are Non-Parametric Tests in Statistics?

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

Common non-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.

Categories of Non-Parametric Tests

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

Table 1.0: Summary of Non-Parametric Tests