Technical Report // Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2003,21
A common approach in the design of experiment for the problem of comparing two means from a normal distribution is to assume knowledge of the ratio of the population variances. The optimal sampling ratio is proportional to the square root of this quantity. In this paper it is demonstrated that a misspecification of this ratio 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 by means of a simulation study and an application to the design of experiment for bioassay is presented.
Behrens-Fisher problem bioassay design of experiment local optimal design robust designs