Tests for the umbrella alternative under normality

Arthur Cohen, H. B. Sackrowitz

Research output: Contribution to journalArticle

3 Scopus citations


Consider a one-way layout of the analysis of variance assuming independence, normality, and homogeneity of variance. Test the null hypothesis H0 that the means, μi, of each of k 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 ≥ . . . ≥ μm ≤ μm+1 ≤ . . . ≤ μk, and m is known. We derive 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.

Original languageEnglish (US)
Pages (from-to)2807-2817
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Issue number11
StatePublished - Jan 1 1996


All Science Journal Classification (ASJC) codes

  • Statistics and Probability


  • Complete class
  • Cone order monotonicity
  • Dual cone
  • Generators of cones
  • Likelihood ratio test
  • Order restricted inference
  • Unbiased test

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