On some single-stage, step-down and step-up procedures for comparing three normal means.
On some single-stage, step-down and step-up procedures for comparing three normal means.
The problem of pairwise comparisons of three normal means in the balanced one-way fixed effects anova model is considered. In order to compare the performance of a single-stage procedure, a step-down procedure and a step-up procedure which all strongly control the type I familywise error at the same level, a method of power assessment is proposed. The power function is defined to be the probability of detecting, with correct directional decision, each pair of treatments with mean values at least ?-distance away from each other. The global minimum power is then used as a criterion for comparing the three procedures. Expressions are provided allowing simple computer evaluation of the global minimum power for each of the three procedures. The findings are that the step-down procedure performs better than the step-up procedure, and both step-down and step-up procedures perform substantially better than the single-stage procedure. A table of sample sizes necessary to guarantee certain power levels for each of the three procedures is also given.
215-227
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
1996
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Liu, W.
(1996)
On some single-stage, step-down and step-up procedures for comparing three normal means.
Computational Statistics and Data Analysis, 21 (2), .
(doi:10.1016/0167-9473(95)00013-5).
Abstract
The problem of pairwise comparisons of three normal means in the balanced one-way fixed effects anova model is considered. In order to compare the performance of a single-stage procedure, a step-down procedure and a step-up procedure which all strongly control the type I familywise error at the same level, a method of power assessment is proposed. The power function is defined to be the probability of detecting, with correct directional decision, each pair of treatments with mean values at least ?-distance away from each other. The global minimum power is then used as a criterion for comparing the three procedures. Expressions are provided allowing simple computer evaluation of the global minimum power for each of the three procedures. The findings are that the step-down procedure performs better than the step-up procedure, and both step-down and step-up procedures perform substantially better than the single-stage procedure. A table of sample sizes necessary to guarantee certain power levels for each of the three procedures is also given.
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Published date: 1996
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Statistics
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Local EPrints ID: 30083
URI: http://eprints.soton.ac.uk/id/eprint/30083
ISSN: 0167-9473
PURE UUID: d9115802-8403-4750-bd5e-40f8e5dcfd2d
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Date deposited: 14 Mar 2007
Last modified: 16 Mar 2024 02:42
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