The means of quantitative measurements from two groups can be compared using Student’s t-test. To compare the means of measurements for more than two levels of a categorical variable, one-way ANOVA has to be used. Here, we’ll explore the parametric, one-way ANOVA test as well as the non-parametric version of the test, the Kruskal-Wallis test, which compares median values.
The benefit of non-parametric tests over parametric tests is that they not make any assumptions about the data. Thus, they are well-suited in situations where the assumptions of parametric tests are not met, which is typically the case for small sample sizes.
Popular non-parametric test
This table gives an overview over popular non-parametric tests:
|Test||Test for what?|
|Wilcoxon rank sum test||Difference in medians|
|Wilcoxon signed-rank test||Difference in paired means|
|Fisher’s exact test||Independence in contingency tables|
|Kruskal-Wallis test||Difference of multiple medians|
Posts about Non-Parametric Significance Testing
One of the most common areas of statistical testing is testing for independence in contingency tables. In this post, I will show how contingency tables can be computed and I will introduce two popular tests on contingency tables: the chi-squared test and Fisher’s exact test.
In this post, we will explore tests for comparing two groups of dependent (i.e. paired) quantitative data: the Wilcoxon signed rank test and the paired Student’s t-test. The critical difference between these tests is that the test from Wilcoxon is a non-parametric test, while the t-test is a parametric test. In the following, we will explore the ramifications of this difference.