Introduction to Non-parametric Tests

Non-parametric tests, also known as distribution-free tests, do not make assumptions about the specific parameters of the population from which the samples were drawn.
They only assume that the data are measureable at least at the ordinal level.
Examples of non-parametric tests include the sign test, Mann-Whitney U test, Wilcoxon signed-rank test, Kruskal-Wallis test, and Spearman rank correlation test.

The Sign Test

This is the simplest non-parametric test for paired data.
It analyses the differences between paired samples by recording only the signs of the differences, not their magnitudes.
It is an alternative to the paired t-test when the assumptions of this test, such as normality, are violated.

It tests whether two independent samples have been drawn from the same population.
The hypothesis being tested is that Samples A and B are different.
It is similar to the independent samples t-test but does not require the assumption of normally distributed data.

This is a non-parametric test for paired data which takes both the direction and the magnitude of differences into account.
It is an alternative to the paired t-test when the assumptions of this test, such as normality, are violated.

This is a non-parametric substitute for a one-way ANOVA, and it is used to test the difference between two or more independent groups.
Unlike the ANOVA, the Kruskal-Wallis test does not require the assumption of normally distributed data.

In contrast to Pearson’s correlation, Spearman’s correlation is a non-parametric measure of statistical dependence between two variables.
It assesses how well an arbitrary monotonic function can describe the relationship between two variables, without making assumptions about the frequency distribution of the variables.

Data used in non-parametric tests should be at least ordinal, i.e., they can be ranked.
The tests are more applicable when the data shows skewness or when outliers are present in the data.
While they don’t assume normality in the data, they do have other assumptions which must be met for the test results to be valid. These include assumptions of independence, symmetry, or randomness, depending on the particular test.
Importantly, if data meet the assumptions for a parametric test, the parametric test will generally have more power to detect a given effect than will a non-parametric test.