OPTIMAL DESIGNS FOR COMPARING THE VARIANCES OF SEVERAL TREATMENTS WITH THAT OF A STANDARD TREATMENT

Optimal designs and associated tables of probability points for comparing the variances of p experimental treatments with that of a standard treatment under the assumption of normality are presented. One-sided and two-sided alternatives are considered. The optimality criteria are those of maximizing the probability of declaring an experimental treatment variance to be smaller than, larger than, or different from that of the standard for a fixed total sample size and a fixed experimentwise error rate. Both small-sample and asymptotic results are given. It is shown that the proportion of observations assigned to the standard treatment for comparing variances in the limiting case is the same as that for comparing means. These optimal proportions are in some cases quite different for small samples.