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Completely Randomized Designs

In: Statistical Methods: Connections, Equivalencies, and Relationships

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  • Kenneth J. Berry
  • Janis E. Johnston

Abstract

Chapter 6 describes connections, equivalencies, and relationships relating to multi-sample tests of null hypotheses. First, Fisher’s conventional one-way completely randomized analysis of variance is described. Second, a multi-sample permutation test is presented and the connection linking the two tests is established. An example analysis illustrates the differences in the two approaches and the connection linking the two tests. Third, measures of effect size for multiple independent samples are described and the interconnections among the measures of effect size are detailed. Fourth, the connection linking the analysis of variance and the intraclass correlation coefficient is described. Fifth, the Kruskal–Wallis g-sample rank-sum test is described and illustrated with a small rank-score dataset. A permutation alternative multi-sample rank-sum test is introduced and the connection linking the Kruskal–Wallis H test statistic and the permutation multi-sample test statistic is described and illustrated with an example analysis.

Suggested Citation

  • Kenneth J. Berry & Janis E. Johnston, 2023. "Completely Randomized Designs," Springer Books, in: Statistical Methods: Connections, Equivalencies, and Relationships, chapter 0, pages 217-289, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-41896-9_6
    DOI: 10.1007/978-3-031-41896-9_6
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