Robust multiple confidence intervals for contrasts

This paper shows that multiple confidence intervals for all pairwise differences of the effects according to Tukey can be calculated with robust M-estimators just as in the classical case using the quantiles of the studentized range distribution. It will be shown in the two-way analysis of variance without interaction that such multiple confidence intervals are asymptotically correct if the error distribution is symmetrical. For the interaction model we make a simple proposal how multiple confidence intervals for the difference of only the interesting cell effects (diagonal cell comparison is not interesting) of one factor can be built. Refering to Monte-Carlo results we compare average length and probability for the α-error of the robust confidence intervals with the classical ones for t-distributed and lognormal errors and show the great liberty of the robust confidence intervals in the presence of heterogeneous scale parameters.