This chapter introduces conventional and permutation methods for multiple independent variables, i.e., completely randomized designs. The chapter contains example analyses illustrating computation of exact permutation probability values for multi-sample tests, calculation of measures of effect size for multi-sample tests, exact and Monte Carlo permutation procedures for multi-sample tests, and applications of permutation methods to multi-sample rank-score data. Also included in the 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, and a permutation-based alternative for the four conventional measures of effect size for multi-sample tests: Cohen’s \(\hat{f}\) , Pearson’s \(\eta ^{2}\) , Kelley’s \(\hat{\eta}^{2}\) , and Hays’ \(\hat{\omega}^{2}\) .