On some single-stage, step-down and step-up procedures for comparing three normal means.


Liu, W. (1996) On some single-stage, step-down and step-up procedures for comparing three normal means. Computational Statistics & Data Analysis, 21, (2), 215-227. (doi:10.1016/0167-9473(95)00013-5).

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Description/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 δ-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.

Item Type: Article
ISSNs: 0167-9473 (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 30083
Date Deposited: 14 Mar 2007
Last Modified: 27 Mar 2014 18:18
URI: http://eprints.soton.ac.uk/id/eprint/30083

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