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

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.

KEYWORDS:

• All pairwise comparisons
• Closed testing procedures
• Multiple comparison procedure
• Multistep procedures
• Simple ordered restrictions.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F03
• Secondary 62K10

Acknowledgments

The authors would like to thank the referees for some valuable comments.

Funding

This research was supported in part by Nanzan University Pache Research Subsidy I-A-2 for 2017 academic year.