Quant #27: Non-parametric Test Examples

Non-parametric tests are statistical tests that are conducted when certain statistical assumptions are not sustained. For example, when the data do not follow a normal distribution, it is suitable to use nonparametric tests as opposed to parametric tests that assume a normal distribution. Non-parametric tests are also called distribution-free tests. Non-parametric serve as alternative statistical tests to tests (such as T-tests, ANOVA, etc) that require that certain assumptions be made.

In addition to data not following a normal distribution, other reasons that warrant the use of non-parametric tests include situations where population size is small or when data are ordinal or nominal. When the sample size is too small, it becomes difficult to validate the distribution of the data, and the most appropriate and suitable option is to conduct non-parametric tests. As for data types, unlike the case of parametric tests that work with continuous data, non-parametric tests are most suitable for ordinal and nominal data types.

Examples of non-parametric tests include Mann-Whithney U test, Wilcoxon Signed Rank Test, Krustal-Wallis test, and Chi-squared test of independence.

1. Mann-Whitney U Test: this is a nonparametric version of the independent samples t-test that works with two independent samples that have ordinal data.
2. Wilcoxon Signed Rank Test: this is a nonparametric version of the paired samples t-test that draws a comparison between two dependent samples with ordinal data.
3. The Kruskal-Wallis Test: this is a nonparametric version of the one-way ANOVA employed to make a comparison between more than two independent groups with ordinal data.
4. Chi-squared Test of Independence: this is a non-parametric version of the Spearman’s r used to assess whether two categorical or nominal variables are likely to be related or not.