Comparison of Unweighted and Weighted Rank Based Tests for an Ordered Alternative in Randomized Complete Block Designs

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In randomized complete block designs, a monotonic relationship among treatment groups may already be established from prior information, e.g., a study with different dose levels of a drug. The test statistic developed by Page (1963) and another from Jonckheere (1954) and Terpstra (1952) are two unweighted rank based tests used to detect ordered alternatives when the assumptions in the traditional two-way analysis of variance are not satisfied. We consider a new weighted rank based test by utilizing a weight for each subject based on the sample variance in computing the new test statistic. The new weighted rank based test is compared with the two commonly used unweighted tests with regard to power under various conditions. The weighted test is generally more powerful than the two unweighted tests when the number of treatment groups is small to moderate.