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.
Tamkang Journal of Science and Engineering=淡江理工學刊 14(4), pp.293-302