Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

8Designed Experiments

Luck is the residue of design.

Branch Rickey,¹ former owner of the Brooklyn Dodgers (1881–1965)

This chapter deals with the nonparametric statistical analysis of designed experiments. The classical parametric methods in analysis of variance (ANOVA), from one‐way to multi‐way tables, often suffer from a sensitivity to the effects of non‐normal data. The nonparametric methods discussed here are much more robust. In most cases, they mimic their parametric counterparts but focus on analyzing ranks instead of response measurements in the experimental outcome. In this way, the chapter represents a continuation of the rank tests presented in Chapter 7.

We cover the Kruskal–Wallis (KW) test to compare three or more samples in an ANOVA, the Friedman test to analyze two‐way ANOVA in a “randomized block” design (RBD), and nonparametric tests of variances for three or more samples.

8.1 Kruskal–Wallis Test

The Kruskal–Wallis (KW) test (Kruskal (1952)) is a logical extension of the Wilcoxon–Mann–Whitney test. It is a nonparametric test used to compare three or more samples. It is used to test the null hypothesis that all populations have identical distribution functions against the alternative hypothesis that at least two of the samples differ only with respect to location (median), if at all.

The KW test is the analogue to the ‐test used in the one‐way ANOVA. While ...