Journal of Applied Science and Engineering

Published by Tamkang University Press


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Shun-Yi Chen This email address is being protected from spambots. You need JavaScript enabled to view it.1 and Su-Hao Lee1

1Department of Mathematics, Tamkang University, Tamsui, Taiwan 251, R.O.C.


Received: October 21, 2010
Accepted: February 22, 2011
Publication Date: December 1, 2011

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When the homogeneity hypothesis of treatment means under heteroscedasticity is rejected, one may be interested in comparing each treatment with all other treatments. The objective of this paper is to derive two multiple range test procedures, the Newman-Keuls type and Duncan type, for multiple comparisons of treatment means with unknown and unequal variances. We investigate these pairwise comparison procedures with the Tukey type simultaneous confidence intervals approach with respect to comparisonwise and experimentwise error rates, as well as correct decision rates. The tables for applying the new multiple range test procedures are provided, along with a numerical example to demonstrate the methods.

Keywords: Pairwise Comparisons, One-Stage and Two-Stage Sampling Procedures, Significance Level, Protection Level, Correct Decision Rate


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