Multiple Contrast Tests in the Presence of Partial Heteroskedasticity

Abstract

This paper proposes a general approach for handling multiple contrast tests for normally distributed data in the presence of partial heteroskedasticity. In contrast to the usual case of complete heteroskedasticity, the treatments belong to subgroups according to their variances. Treatments within these subgroups are homoskedastic, whereas treatments of different subgroups are heteroskedastic. New candidate as well as already existing approaches are described and compared by $\alpha$-simulations. Power simulations show that a gain in power is achieved when the partial heteroskedasticity is taken into account compared to procedures which wrongly assume complete heteroskedasticity. The new approaches will be applied to a phytopathological experiment.