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

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 ra-tio is proportional to the square root of this quantity.This article demonstrates that a misspecication of the ratio of the popula-tion variances can cause a substantial loss in power of the cor-responding tests. As a robust alternative, a maximin approach is used to construct designs, which are efcient, whenever the experimenter is able to specify a specic 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