Nonparametric Tests Based on Rank

Rank‐based nonparametric tests are versatile in application and simple in calculation. They enable simple hypothesis testing on data of various design types and have good approximate properties for large samples. In this chapter, the authors introduce rank‐based tests for different designs. When distributions are not normal, these tests have greater statistical efficacy than their parametric counterparts. Wilcoxon's signed‐rank test is a signed rank test of paired samples that is analogous to the paired samples t‐test. A powerful nonparametric test, also developed by F. Wilcoxon, compares entire probability distributions and not just the medians. This test, called Wilcoxon's rank‐sum test, tests whether the probability distributions associated with the two populations are identical. The nonparametric test analogous to one‐way ANOVA is called the Kruskal–Wallis test. The test is also called nonparametric ANOVA. The authors also introduce the nonparametric Friedman's test corresponding to ANOVA for the randomized block design.