Combining one-sided and two-sided confidence interval procedures for successive comparisons of ordered treatment effects
Combining one-sided and two-sided confidence interval procedures for successive comparisons of ordered treatment effects
Lee and Spurrier (1995) present one-sided and two-sided confidence interval procedures for making successive comparisons between ordered treatments. Their procedures have important applications for problems where the treatments can be assumed to satisfy a simple ordering, such as for a sequence of increasing dose-levels of a drug. The two-sided procedure provides both upper and lower bounds on the differences between successive treatments, whereas the one-sided procedure only provides lower bounds on these differences. However, the one-sided procedure allows sharper inferences regarding which treatments can be declared to be better than their previous ones. In this paper we apply the results obtained in Hayter, Miwa, and Liu (2000) to develop a new procedure which combines the good aspects of both the one-sided and the two-sided procedures. This new procedure maintains the inferential sensitivity of the one-sided procedure while also providing both upper and lower bounds on the differences between successive treatments. Some new critical points are needed which are tabulated for the balanced case where the sample sizes are all equal. The application of the new procedure is illustrated with an example.
critical points, directional decisions, multivariate-t distribution, ordered inference, pairwise comparisons, simultaneous confidence intervals
533-542
Somerville, Paul
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Miwa, Tetsuhisa
cb4e7293-e076-437a-b31c-b5dd6c6a3b4a
Liu, Wei
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Hayter, Anthony J.
0ac7de8f-0995-4766-afc0-c0c95313e94d
2001
Somerville, Paul
ead2ab60-85dd-4e10-bce1-aa71b7c2dc4e
Miwa, Tetsuhisa
cb4e7293-e076-437a-b31c-b5dd6c6a3b4a
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, Anthony J.
0ac7de8f-0995-4766-afc0-c0c95313e94d
Abstract
Lee and Spurrier (1995) present one-sided and two-sided confidence interval procedures for making successive comparisons between ordered treatments. Their procedures have important applications for problems where the treatments can be assumed to satisfy a simple ordering, such as for a sequence of increasing dose-levels of a drug. The two-sided procedure provides both upper and lower bounds on the differences between successive treatments, whereas the one-sided procedure only provides lower bounds on these differences. However, the one-sided procedure allows sharper inferences regarding which treatments can be declared to be better than their previous ones. In this paper we apply the results obtained in Hayter, Miwa, and Liu (2000) to develop a new procedure which combines the good aspects of both the one-sided and the two-sided procedures. This new procedure maintains the inferential sensitivity of the one-sided procedure while also providing both upper and lower bounds on the differences between successive treatments. Some new critical points are needed which are tabulated for the balanced case where the sample sizes are all equal. The application of the new procedure is illustrated with an example.
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Published date: 2001
Keywords:
critical points, directional decisions, multivariate-t distribution, ordered inference, pairwise comparisons, simultaneous confidence intervals
Organisations:
Statistics
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Local EPrints ID: 30105
URI: http://eprints.soton.ac.uk/id/eprint/30105
ISSN: 0323-3847
PURE UUID: b431c051-bdab-410a-9031-1d22c39a7798
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 02:42
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Author:
Paul Somerville
Author:
Tetsuhisa Miwa
Author:
Anthony J. Hayter
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