4 - Statistical Tests Based on Ranks

Summary

The hypothesis tests discussed in the previous chapters are parametric. That is, the procedures assume samples come from a prescribed family of distributions, leaving only the parameters of the distribution open to question. For instance, a univariate Gaussian distribution is characterized by two parameters, the mean and variance, and hypotheses are expressed in terms of those parameters. This chapter discusses a class of procedures called nonparametric statistics, or distribution-free methods, that make fewer assumptions. For some hypotheses, nonparametric tests are almost as powerful as parametric tests, hence some statisticians recommend nonparametric methods as a first choice. This chapter discusses the following non-parametric tests: Wilcoxon rank-sum test, a non-parametric version of the t-test, Kruskal-Wallis test, a nonparametric version of Analysis of Variance, a nonparametric version of the F-test, based on medians, Spearman’s rank correlation, a non-parametric version of the correlation test. This chapter assumes familiarity with hypothesis tests, particularly the concepts of null hypothesis, decision rule, and significance level.