Tests for the umbrella alternative under normality
- 1 January 1996
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 25 (11) , 2807-2817
- https://doi.org/10.1080/03610929608831870
Abstract
Consider a one-way layout of the analysis of variance assuming independence, normality, and homogeneity of variance. Test the null hypothesis Ho that the means, j., of each of Amp; columns, i = 1,…, k are equal versus the alternative that they follow an umbrella pattern. That is, the alternative is H1-H0 where H1: μ1> μ2>… > μk, and m is known. We derive a class of tests which are unbiased and lie in a nontrivial complete class. We recommend specific tests within the class. A simulation of the power functions of some tests is contrasted with the simulated power function of the likelihood ratio test.Keywords
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