On step-up tests for comparing several treatments
On step-up tests for comparing several treatments
Consider a one-way layout in which independent observations Xi have distributions F(x-ui) with ui unknown, 1<=i<=k. The basic problem is to test the family of subset hypotheses about ui. The step-up test scheme of Welsch (1977) is studied in detail. A general result is given on how to determine the critical values so that the type I familywise error rate is strongly controlled at a preassigned level ?, and a particular set of critical values is recommended. The interrelationship between the step-up tests and the closed tests of Marcus, Peritz and Gabriel (1976) is illuminated. This enables us to construct a closed test which is uniformly more powerful than a step-up test. Monte Carlo simulation is carried out to compare the power of the two new tests with that of Welsch's (1977) test and several other multiple tests. The two new tests turn out to be preferable. The one-way ANOVA setting is given special attention, and the critical values of the new step-up test are tabulated.
957-972
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
1997
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Liu, W.
(1997)
On step-up tests for comparing several treatments.
Statistica Sinica, 7 (4), .
Abstract
Consider a one-way layout in which independent observations Xi have distributions F(x-ui) with ui unknown, 1<=i<=k. The basic problem is to test the family of subset hypotheses about ui. The step-up test scheme of Welsch (1977) is studied in detail. A general result is given on how to determine the critical values so that the type I familywise error rate is strongly controlled at a preassigned level ?, and a particular set of critical values is recommended. The interrelationship between the step-up tests and the closed tests of Marcus, Peritz and Gabriel (1976) is illuminated. This enables us to construct a closed test which is uniformly more powerful than a step-up test. Monte Carlo simulation is carried out to compare the power of the two new tests with that of Welsch's (1977) test and several other multiple tests. The two new tests turn out to be preferable. The one-way ANOVA setting is given special attention, and the critical values of the new step-up test are tabulated.
This record has no associated files available for download.
More information
Published date: 1997
Organisations:
Statistics, Mathematical Sciences
Identifiers
Local EPrints ID: 30086
URI: http://eprints.soton.ac.uk/id/eprint/30086
ISSN: 1017-0405
PURE UUID: efe5416c-374c-41e0-8311-4e3eb345ba99
Catalogue record
Date deposited: 13 Mar 2007
Last modified: 09 Jan 2022 02:41
Export record
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
