Efficient Experimental Design for the Behrens-Fisher Problem With Application to Bioassay

Abstract

A common experimental design for the problem of comparing two means from a normal distribution assumes knowledge of the ratio of the population variances. The optimal sampling ratio is proportional to the square root of this quantity. This article demonstrates that a misspecification of the ratio of the population variances can cause a substantial loss in power of the corresponding tests. As a robust alternative, a maximin approach is used to construct designs, which are efficient, whenever the experimenter is able to specify a specific region for the ratio of the population variances. The advantages of the robust designs for inference in the Behrens-Fisher problem are illustrated in a simulation study and an application to the design of experiment for bioassay is presented.