Tables for testing ordered alternatives in an analysis of variance without replications

Abstract

Given a series of k normal populations with a common but unknown variance, and supposing that an observation is drawn from each one of them, then a likelihood ratio test of homogeneity of the means against the simple order alternative is possible when the significance level α is less than 1/ k !. For these possible combinations of α and k tables for testing the hypothesis are provided where α = 0.10, 0.05, 0.025, 0.01, 0.005, 0.0025, 0.001 and k = 4(1)20.