A Distribution-Free Rank Test for Ordered Alternatives in Randomized Complete Block Designs

Abstract

A distribution-free rank test for detecting ordered alternatives in randomized complete block designs and repeated measures designs is proposed for four or fewer treatments. The null hypothesis distribution of the statistic is well-known and readily available to the user. The article establishes the asymptotic normality of an appropriately standardized form of the statistic and the consistency of the test. Asymptotic relative efficiency comparisons are made with Jonckheere's test, Page's L, Hollander's test, and a normal theory competitor. The authors illustrate the good intermediate sample size characteristics of the test via a Monte Carlo study.

Key Words:

• Distribution-free
• Nonparametric
• Jonckheere's test
• Page's L
• Hollander's test
• Wilcoxon signed rank statistic
• Joint symmetry