On Some Multiple Decision Procedures for Normal Variances

In this article, we propose a multiple decision procedure to test the homogeneity of normal variances. If the null-hypothesis is rejected, our goal is to select a subset containing the population associated with the largest variance. An approximation for the critical value is obtained by deriving an approximate distribution for a linear combination of independent log-gamma distributed random variables. A lower bound for the probability of correct decision is obtained. We also study the determination of the common sample size in order to satisfy a given probability of correct decision when the largest variance is “sufficiently” larger than the rest.