Comparing Rank Tests for Ordered Alternatives in Randomized Blocks

Abstract

Two classes of rank tests are considered for ordered alternatives in a randomized block design with $k$ treatments and $n$ blocks: tests based on among-blocks rankings ($A$-tests) and tests based on within-blocks rankings ($W$-tests). Previous efficiency comparisons for fixed $k, n \rightarrow \infty$ under the normal distribution have indicated that $A$-tests are more sensitive. In the present paper it is shown that this behavior is not typical under other distributions. Further, analysis of efficiencies for fixed $n, k \rightarrow \infty$ indicates greater sensitivity for $W$-tests. Considering these results and certain other desirable properties of the $W$-tests, the latter are recommended for most applications.