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Analysis of power functions of multiple comparisons tests

Analysis of power functions of multiple comparisons tests
Analysis of power functions of multiple comparisons tests
The power functions of the Studentized range test and the F-test for comparing the means of normal populations in the one-way fixed effects analysis of variance model is investigated. The least favourable configurations of population means under certain range restrictions of the population means are given. These results are important in the calculation of the sample sizes required to guarantee power level under the restrictions on the range of the population means. The optimal test procedures which maximise the least favourable power under the range restrictions of the population means are found for the known variance case. Then the relations between these optimal tests and the range type tests, sum of square tests are pointed out. The problem of comparing several treatment means with a control mean is also considered. Finally, these results are applied to the binary data, by using the arcsin-root transformation and the asymptotic distribution, for both comparison between k Bernoulli responses and comparison between k Bernoulli responses and a control Bernoulli response.
University of Bath
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, Anthony J.
0ac7de8f-0995-4766-afc0-c0c95313e94d

Liu, Wei (1990) Analysis of power functions of multiple comparisons tests. University of Bath, Doctoral Thesis, 128pp.

Record type: Thesis (Doctoral)

Abstract

The power functions of the Studentized range test and the F-test for comparing the means of normal populations in the one-way fixed effects analysis of variance model is investigated. The least favourable configurations of population means under certain range restrictions of the population means are given. These results are important in the calculation of the sample sizes required to guarantee power level under the restrictions on the range of the population means. The optimal test procedures which maximise the least favourable power under the range restrictions of the population means are found for the known variance case. Then the relations between these optimal tests and the range type tests, sum of square tests are pointed out. The problem of comparing several treatment means with a control mean is also considered. Finally, these results are applied to the binary data, by using the arcsin-root transformation and the asymptotic distribution, for both comparison between k Bernoulli responses and comparison between k Bernoulli responses and a control Bernoulli response.

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More information

Published date: July 1990

Identifiers

Local EPrints ID: 457940
URI: http://eprints.soton.ac.uk/id/eprint/457940
PURE UUID: 9052f6ca-4d96-4231-83e3-e4d042cc6bc6
ORCID for Wei Liu: ORCID iD orcid.org/0000-0002-4719-0345

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Date deposited: 23 Jun 2022 16:49
Last modified: 24 Jun 2022 01:33

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Contributors

Author: Wei Liu ORCID iD
Thesis advisor: Anthony J. Hayter

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