An empirical study of the durbin and ANOVA F tests and their contrasts

The Durbin and ANOVA F test on the ranks are competing tests for equality of treatment mean ranks. When the levels of the treatments are ordered, both tests have informative decompositions into orthonormal contrasts that detect linear, quadratic, etc. effects. It is known that the ANOVA F test on the ranks better adheres to the nominal significance level than the Durbin test. Here we investigate whether the same is true for their orthonormal contrasts.