Multiple comparison for checking differences among normal variances

ABSTRACT

In this study, we discuss multiple comparisons for checking differences among normal variances. Specifically, we consider the multiple comparison with a control and the all-pairwise multiple comparison. For the multiple comparison with a control we determine the critical value for pairwise comparison satisfying a specified significance level exactly and formulate the power of the test under a specified alternative hypothesis. For the all-pairwise multiple comparison we determine two kinds of conservative critical values for pairwise comparison for a specified significance level and calculate the power of the test by Monte Carlo simulation. Finally, we give some numerical examples regarding critical values and power of the test.

KEYWORDS:

• All-pairwise multiple comparison
• multiple comparison with a control
• power comparison.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62H15

Acknowledgments

Special thanks are due to the reviewer and the editors for their helpful advices and comments in modifying the paper. I am deeply grateful to Dr. N. Tsuchiya and Dr. T. Nakamura in Tohoku University for their helpful comments and suggestions for the example given in Section 4.