A one-sided studentized range test for testing against a simple ordered alternative

Abstract Consider the usual balanced one-way fixed effects analysis of variance (ANOVA) model X ij = μ i + e ij (1 ≤ j ≤ n; 1 ≤ i ≤ k), where the e ij are independent N(0, [sgrave]2) random variables and μ i is the mean of the ith treatment (1 ≤ i ≤ k). The μ i and [sgrave] 2 are unknown parameters. Let X i be the sample mean of the ith treatment based on n observations (1 ≤ i ≤ k), and let S 2 be an unbiased estimate of [sgrave]2, which is distributed independently of the X i as a σ2 χ 2 v /v random variable. Usually, the ANOVA mean squared error with v = k(n − 1) df is used as the estimate S 2. A problem that has received considerable attention is that of testing the null hypothesis H 0 : μ 1, = … = μ k against the simple ordered alternative hypothesis H A : μ 1 ≤ … ≤ μ k with at least one strict inequality [see, e.g., Barlow, Bartholomew, Bremner, and Brunk (1972) and Robertson, Wright, and Dykstra (1988)]. Various test procedures have been proposed for this problem, such as the likelihood ratio test (...

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