在給定k (>= 2)個獨立母體π1, π2, . . . , πk下，假定Xij (j = 1, . . . , ni)為從平均數為μi且變異數為σi2的常態母體πi中所抽取之觀測值，其中σi2 (i = 1, . . . , k)為未知或不等變異數。一般來說，變異數分析 (ANOVA) 是用來檢定母體平均數是否相等的方法，而其前提假設為常態性、獨立性與同質變異，由於資料並非皆符合前提假設，因此 Dudewicz 與 van der Meulen (1983) 提出若資料不服從常態性的假設時，ANOVA 的 F 檢定仍會有相當穩健的檢定結果，然而，Bishop (1976) 則提出當變異數不相等時則會對檢定結果帶來相當大的影響，尤其是連樣本數也不相等的情況影響更甚。因此，一階段抽樣法被用來解決不等變異數的問題，本研究除了介紹一階段抽樣法之外，運用一階段抽樣法建立多重比較方法，並應用在實際資料上。

Given that k (>= 2) independent populations π1, π2, . . . , πk such that observations Xij (j = 1, . . . , ni) taken from population πi are normally distributed with mean μi and unknown (and possibly unequal) variance σi2 (i = 1, . . . , k). Analysis of variance (ANOVA) test procedures are generally used to test the equality of population means, where the procedures depend on the assumptions of normality, independence, and homogeneity of variance. Dudewicz and van der Meulen (1983) has shown that violation of normality doesn’t bring much effects on the ANOVA F test. However, Bishop (1976) presented that violation of homogeneity can give serious consequences in the ANOVA F test, especially under unequal sample sizes. Therefore, a single-stage sampling procedure is used to deal with such unequal variances cases. In addition, single-stage sampling procedure is introduced and applied to multiple comparisons, and numerical examples to apply the procedure is also given.

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