The Scheffe test procedure in comparison with multiple contrast tests

The global ANOVA F-test based on the quadratic test statistics using the sum of squares in the nominator. An alternative to the quadratic test statistic are linear multiple contrast tests, i.e. the multiple contrast for comparing the treatment means with the overall mean (MCT). A certain alternative to the ANOVA F-test is the Scheffe test, however considering any contrasts instead of just pairwise contrasts. Size and power of theses three global tests are compared for finite sample sizes by means of a simulation study. Unbalanced designs and heteroscedasticity are considered. Moreover, the quantiles of Scheffe test is compared with Bonferroni, Tukey and Grand Mean type MCT's.