Distribution-Free Tests for Ordered Alternatives in a Randomized Block Design

Abstract

In this article we consider a class of test statistics that are useful for testing against ordered alternatives in balanced or unbalanced block designs. The approach consists of forming a statistic on each block and then combining the block statistics as a weighted sum to obtain one overall test statistic. Large-sample properties such as asymptotic normality and asymptotic relative efficiency as the number of blocks tends to infinity are considered. Throughout the article special attention is given to a Jonckheere-type statistic. Some consideration is given to the selection of the optimal weighting constants for the Jonckheere statistic.

Key Words:

• Ordered alternatives
• Distribution-free tests
• Asymptotic relative efficiency
• Block design
• Jonckheere test