A Test of Homogeneity for Ordered Alternatives

D. J. Bartholomew

doi:10.1093/biomet/46.1-2.36

January 1, 1959Biometrika

A Test of Homogeneity for Ordered Alternatives

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Key Points

To develop a specialized statistical test for the equality of means across multiple populations when the alternative hypothesis specifies that the means follow a predetermined monotonic order.
Formulated a likelihood ratio test criterion to evaluate the null hypothesis of equal means against simple ordered alternatives assuming normally distributed populations.
Derived the exact and asymptotic null distributions of the test statistic using isotonic regression principles to handle order-restricted parameter spaces.
Demonstrated that incorporating directional ordering into the alternative hypothesis yields substantially greater statistical power than standard omnibus F-tests.
Tabulated exact critical values and distribution functions across varying sample sizes and group numbers to facilitate practical application.

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Implication

Methodological study demonstrates a likelihood ratio test for ordered alternatives across multiple normal populations, highlighting increased statistical power for detecting directional trends.

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D. J. Bartholomew (1959) studied this question.

synapsesocial.com/papers/6a0f25241cf410a932426873 https://doi.org/10.1093/biomet/46.1-2.36

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A Test of Homogeneity for Ordered Alternatives

Key Points

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Implication

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A Test of Homogeneity for Ordered Alternatives

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Implication

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