Nonparametric methods for pairwise comparisons in the randomized complete block design

Abstract

The main focus of this investigation is to verify the robustness of validity of these tests. By robustness of validity, it is meant the stability of the Type I error rate for small designs as well as conditions under which some of the underlying assumptions are violated. For methods that produce valid tests, further investigations with respect to power are meaningful. Since many nonparametric methods use large sample approximation theory, it may be expected that these methods will perform better as n, the number of blocks, increases. As the number of treatments, p, gets larger, it becomes harder to reject the null hypothesis since this increases the critical value. As we will see, some design structures make rejection of the null hypothesis impossible for certain methods. The methods of interest include the sign statistic, signed rank statistic, rank sum statistic (Aligned Rank statistic using separated rankings and uniform scores). Aligned-Rank Transform, Within-Block ranking, and least squares.