The Dunnett procedure with possibly heterogeneous variances

Most comparisons of treatments or doses against a control are performed by the original Dunnett single step procedure \cite{Dunnett1955} providing both adjusted p-values and simultaneous confidence intervals for differences to the control. Motivated by power arguments, unbalanced designs with higher sample size in the control are recommended. When higher variance occur in the treatment of interest or in the control, the related per-pairs power is reduced, as expected. However, if the variance is increased in a non-affected treatment group, e.g. in the highest dose (which is highly significant), the per-pairs power is also reduced in the remaining treatment groups of interest. I.e., decisions about the significance of certain comparisons may be seriously distorted. To avoid this nasty property, three modifications for heterogeneous variances are compared by a simulation study with the original Dunnett procedure. For small and medium sample sizes, a Welch-type modification can be recommended. For medium to high sample sizes, the use of a sandwich estimator instead of the common mean square estimator is useful. Related CRAN packages are provided. Summarizing we recommend not to use the original Dunnett procedure in routine and replace it by a robust modification. Particular care is needed in small sample size studies.