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- W2090865137 abstract "Tests of homogeneity of normal means with the alternative restricted by an ordering on the means are considered. The simply ordered case, μ1 ≤ μ2 ≤ ··· ≤ μk, and the simple tree ordering, μ1 ≤ μj, for; j= 2, 3,…, k, are emphasized. A modification of the likelihood-ratio test is proposed which is asymptotically equivalent to it but is more robust to violations of the hypothesized orderings. The new test has power at the points satisfying the hypothesized ordering which is similar to that of the likelihood-ratio test provided the degrees of freedom are not too small. The modified test is shown to be unbiased and consistent. Nous considérons les tests d'homogénéité des moyennes de populations normales lorsque les contre-hypothèses stipulent une relation d'ordre entre celles-ci. Nous insistons davantage sur le cas d'un ordre total, μ1 ≤ μ2 ≤ ··· ≤ μk et sur le cas d'un ordre arborescent, μ1 ≤ μj j = 2, 3, …, k. Nous proposons une modification au test du rapport de vraisemblance qui le rend plus robuste quant aux écarts à l'ordre spécifié par la contre-hypothèse. Le nouveau test, qui est asymptotiquement équivalent au test du rapport de vraisemblance, admet aux points qui satisfont à l'ordre spécifié une puissance similaire à celle du test du rapport de vraisemblance à condition que les degrés de liberté ne soient pas trop faibles. Nous démontrons que le test modifié est sans biais et convergent." @default.
- W2090865137 created "2016-06-24" @default.
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- W2090865137 date "1988-03-01" @default.
- W2090865137 modified "2023-10-14" @default.
- W2090865137 title "The one-way analysis of variance with ordered alternatives: A modification of bartholomew's Ē2Test" @default.
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- W2090865137 doi "https://doi.org/10.2307/3315065" @default.
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