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Closed testing procedures for all pairwise comparisons in a randomized block design

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  • Taka-Aki Shiraishi
  • Shin-Ichi Matsuda

Abstract

We consider multiple comparison test procedures among treatment effects in a randomized block design. We propose closed testing procedures based on maximum values of some two-sample t test statistics and based on F test statistics. It is shown that the proposed procedures are more powerful than single-step procedures and the REGW (Ryan/Einot–Gabriel/Welsch)-type tests. Next, we consider the randomized block design under simple ordered restrictions of treatment effects. We propose closed testing procedures based on maximum values of two-sample one-sided t test statistics and based on Batholomew’s statistics for all pairwise comparisons of treatment effects. Although single-step multiple comparison procedures are utilized in general, the power of these procedures is low for a large number of groups. The closed testing procedures stated in the present article are more powerful than the single-step procedures. Simulation studies are performed under the null hypothesis and some alternative hypotheses. In this studies, the proposed procedures show a good performance.

Suggested Citation

  • Taka-Aki Shiraishi & Shin-Ichi Matsuda, 2018. "Closed testing procedures for all pairwise comparisons in a randomized block design," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(15), pages 3571-3587, August.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:15:p:3571-3587
    DOI: 10.1080/03610926.2017.1359302
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