Generalized Maximum Range Tests for Pairwise Comparisons of Several Populations |
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Authors: | Prof. Dr. Th. Royen |
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Affiliation: | Fachhochschule Rheinland-Pfalz Abteilung Bingen D - 6530 Bingen Rochusallee 4 |
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Abstract: | A multiple comparison procedure (MCP) is proposed for the comparison of all pairs of several independent samples. This MCP is essentially the closed procedure with union-intersection tests based on given single tests Qij for the minimal hypotheses Hij. In such cases where the α-levels of the nominal tests associated with the MCP can be exhausted, this MCP has a uniformly higher all pair power than any refined Bonferroni test using the same Qij. Two different general algorithms are described in section 3. A probability inequality for ranges of i.i.d. random variables which is useful for some algorithms is proved in section 4. Section 5 contains the application to independent normally distributed estimates and section 6 the comparisons of polynomial distributions by multivariate ranges. Further applications are possible. Tables of the 0.05-bounds for the tests of section 5 and 6 are enclosed. |
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Keywords: | Closed test procedures Multiple comparison procedures Multivariate ranges Pairwise comparisons Polynomial distributions Probability inequalities |
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