A note on comparing several variances with a control variance

Abstract

Consider the problem of comparing variances of k populations with the variance of a control population. When the experimenter has a prior expectation that the variances of k populations are not less than the variance of a control population, one-sided simultaneous confidence intervals provide more inferential sensitivity than two-sided simultaneous confidence intervals. But the two-sided simultaneous confidence intervals have advantages over the one-sided simultaneous confidence intervals as they provide both lower and upper bounds for the parameters of interest. In this article, a new multiple comparison procedure is developed for comparing several variances with a control variance, which provides two-sided simultaneous confidence intervals for the ratios of variances with the control variance and maintains the inferential sensitivity of one-sided simultaneous confidence intervals. Computation of the critical constants for the implementation of the proposed procedure is discussed and the selected critical constants are tabulated.