Stepwise multiple tests for successive comparisons
Stepwise multiple tests for successive comparisons
Suppose that the k treatments under comparison are ordered in a certain way. For example, they may be a sequence of increasing dose levels of a drug. It is interesting to look directly at the successive differences between the treatment effects µi's, namely the set of differences µ2-µ1,µ3-µ2,…,µk-µk-1. Lee and Spurrier (J. Statist. Plann. Inference 43 (1995) 323) propose a one-sided and a two-sided simultaneous confidence interval procedures for making successive comparisons between treatments. In this paper we develop step-down and step-up tests for testing the families of hypotheses.
Hi0:µi+1-µi = 0 vs Hia:µi+1-µi > 0, i=1,...,k-1 (one-sided alternatives) Hi0:µi+1-µi = 0 vs Hia:µi+1-µi ≠ 0, i=1,...,k-1 (two-sided alternatives)
These stepwise tests are uniformly more powerful than the simultaneous confidence interval procedures in terms of rejection of the null hypotheses, though the simultaneous confidence interval procedures provide information on the magnitudes of the µi+1-µi's. The critical constants required for applying these multiple tests are provided, and the tests are illustrated with a numerical example.
critical constants, familywise error rate, multiple comparisons, multivariate-t distribution, simultaneous confidence intervals
189-199
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Somerville, P.
b459fa9a-b948-40cb-81ef-4076979b4946
2004
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Somerville, P.
b459fa9a-b948-40cb-81ef-4076979b4946
Liu, W. and Somerville, P.
(2004)
Stepwise multiple tests for successive comparisons.
Computational Statistics and Data Analysis, 46 (1), .
(doi:10.1016/S0167-9473(03)00137-3).
Abstract
Suppose that the k treatments under comparison are ordered in a certain way. For example, they may be a sequence of increasing dose levels of a drug. It is interesting to look directly at the successive differences between the treatment effects µi's, namely the set of differences µ2-µ1,µ3-µ2,…,µk-µk-1. Lee and Spurrier (J. Statist. Plann. Inference 43 (1995) 323) propose a one-sided and a two-sided simultaneous confidence interval procedures for making successive comparisons between treatments. In this paper we develop step-down and step-up tests for testing the families of hypotheses.
Hi0:µi+1-µi = 0 vs Hia:µi+1-µi > 0, i=1,...,k-1 (one-sided alternatives) Hi0:µi+1-µi = 0 vs Hia:µi+1-µi ≠ 0, i=1,...,k-1 (two-sided alternatives)
These stepwise tests are uniformly more powerful than the simultaneous confidence interval procedures in terms of rejection of the null hypotheses, though the simultaneous confidence interval procedures provide information on the magnitudes of the µi+1-µi's. The critical constants required for applying these multiple tests are provided, and the tests are illustrated with a numerical example.
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Published date: 2004
Keywords:
critical constants, familywise error rate, multiple comparisons, multivariate-t distribution, simultaneous confidence intervals
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Statistics
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Local EPrints ID: 30121
URI: http://eprints.soton.ac.uk/id/eprint/30121
ISSN: 0167-9473
PURE UUID: e43641cf-c468-4a2a-a958-cb39e1f02f43
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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 02:42
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Author:
P. Somerville
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