SAMPLE SIZE DETERMINATION FOR MULTIPLE COMPARISONS WITH COMPONENTS OF A LINEAR FUNCTION OF MEAN VECTORS

Abstract

This article considers sample size determination for designing multiple comparisons with respect to components of a linear function of mean vectors from N_p . We propose a two-stage procedure to determine the sample size so that multiple comparisons confidence intervals will cover the true parameters and be sufficiently narrow with a guaranteed high accuracy. Appropriate formulas of design constant involved in the two-stage procedure are provided and tabulated for Tukey's method of all pairwise multiple comparisons, Hsu's method of multiple comparisons with the best, and Dunnett's method of multiple comparisons with a control. An advantage of the proposed procedure is to guarantee a high probability of simultaneous confidence intervals for treatment contrasts as well as maintaining a prespecified width when 's are unknown but spherical models.

Keywords:

• Multiple comparisons
• Sample size
• Sphericity
• Tukey conjecture
• Two-stage procedure

ACKNOWLEDGMENTS

The author would like to thank a referee for making encouraging remarks. This research was supported by Grant-in-Aid for Encouragement of Young Scientists, the Ministry of Education, Science, Sports and Culture, Japan, under Contract Number 721-7027-11780167.