Non-Parametric Tests

This chapter discusses a large number of non-parametric tests. These tests are used when data are not normally distributed. We begin the chapter with a discussion on the runs test to check for random sampling in both categorical and continuous data. The chapter then discusses non-parametric alternatives to t-tests, along with the hypotheses: One-sample Wilcoxon signed-rank test (one-sample t-test), Wilcoxon rank sum test (independent samples t-test) and Wilcoxon matched-pair test (paired samples t-test), with relevant examples. These tests use ranks to compare medians. We then discuss the non-parametric alternatives to ANOVA: Kruskal-Wallis test (one-way ANOVA), Two-way Friedman's test (two-way ANOVA), and Friedman's repeated measures test (repeated measures ANOVA). Since these tests involve multiple groups, we also explain the post-hoc analyses using Dunn's test and pairwise Wilcoxon tests to examine the groupwise differences. The chapter ends with a discussion on Chi-square goodness-of-fit test, Chi-square test of association and Fisher's exact test. We explain when to use each, and that Fisher's exact test is preferred for small samples or when Chi-square assumptions are violated due to low expected counts. The chapter also discusses how to handle missing values, where required.