Completely-Randomized Designs

This chapter introduces permutation methods for multiple independent variables; that is, completely-randomized designs. Included in this chapter are six example analyses illustrating computation of exact permutation probability values for multi-sample tests, calculation of measures of effect size for multi-sample tests, the effect of extreme values on conventional and permutation multi-sample tests, exact and Monte Carlo permutation procedures for multi-sample tests, application of permutation methods to multi-sample rank-score data, and analysis of multi-sample multivariate data. Included in this chapter are permutation versions of Fisher’s F test for one-way, completely-randomized analysis of variance, the Kruskal–Wallis one-way analysis of variance for ranks, the Bartlett–Nanda–Pillai trace test for multivariate analysis of variance, and a permutation-based alternative for the four conventional measures of effect size for multi-sample tests: Cohen’s d ̂ $$\hat {d}$$ , Pearson’s η 2, Kelley’s η ̂ 2 $$\hat {\eta }^{2}$$ , and Hays’ ω ̂ 2 $$\hat {\omega }^{2}$$ .