An empirical study of nonparametric multiple comparison procedures in randomized blocks

In this article, nonparametric procedures for multiple comparison in the randomized block design are studied. Procedures based on separate rankings are shown to have extremely conservative Type I family-wise error rates indicating slow convergence to the limiting distribution. Procedures based on joint ranking are seen to be superior even though they do not have the joint testing family property. The empirical studies in this article show that the aligned rank transform tests have stable Type I family-wise error rates. More importantly, aligned rank transform is shown to be generally the most powerful method even outperforming Tukey's parametric method with normal error terms. Although the aligned rank transform multiple comparison procedures can be applied in more general designs, the simulation studies in this article are carried out for randomized blocks with one observation per cell since all of the existing techniques are developed for this particular design.