不等變異數時多種平均數相等檢定方法比較

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Title:	不等變異數時多種平均數相等檢定方法比較
Other Titles:	Comparison of several statistics testing the equality of means under heteroscedasticity
Authors:	吳冠逸;Wu, Kuan-Yi
Contributors:	淡江大學數學學系碩士班陳順益;Chen, Shun-Yi
Keywords:	二階段和一階段樣本;不等變異數;可控制的檢定力;t分配;Two-stage and one-stage sampling;Unequal variances;Controllable power;t-distribution
Date:	2013
Issue Date:	2013-04-13 11:05:44 (UTC+8)
Abstract:	在常態分佈母體下，一般常使用的變異數分析是Fisher的F統計量來檢定各組平均數是否相等。當變異數未知且不相等時，Brown和Forsythe (1974) 針對小樣本的情況下提出Welch，James，ANOVA F* 等單一樣本檢定統計方法來檢定母體平均數是否相等。Bishop和Dudewicz (1978)提出二階段抽樣程序，檢定常態分佈下不等變異數時是否有相同的平均數。而Chen(2001)提出一階段抽樣程序檢定當變異數未知且不相等時是否有相同的平均數。本論文利用電腦模擬計算，以型一誤差和檢定力來比較以上各種檢定統計方法的優劣。 The F-test of equality of normal means in the conventional analysis of variances (ANOVA) is based on the assumption of equal variances. When the variances are unknown and unequal, Brown and Forsythe (1974) compared four single-sample test statistics, Welch, James, ANOVA F and F*, for the equality of normal population means in the case of small sample. Bishop and Dudewicz (1978) proposed a two-stage sampling procedure to test the equality of means under heteroscedasticity. Chen (2001) derived an exact test using one-stage sampling procedure to test the equality of means when the variances are unknown and unequal. In this thesis we employ computer simulation to compare the level and power of the above-mentioned test statistic procedures.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Thesis

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