平均數分析(Analysis of means, ANOM)的優點是可以藉由圖形的方式來呈現分析的結果，並能清楚看出k個母體平均數與整體平均數之間的差異情形。而傳統ANOM模型的基本假設為變異數必須同質，然而在實際案例中，k個母體的變異數不等且未知與每個母體所抽取的樣本數不相等是經常碰到的問題，Nelson and Dudewicz (2002)利用Stein (1945)所提出之二階段抽樣方法解決變異數異質性下的平均數分析問題。本研究採用一階段抽樣方法處理不平衡設計之下平均數異質分析，可以有效避免二階段抽樣方法因須加抽樣本數，導致成本增加，或是執行不易的問題。

The analysis of means (ANOM) compares the mean of each group to the overall mean and can be presented in a graphical form. From the graphical result, we can clearly indicate which one is different. The one of assumption of the classical ANOM model is that the variances are equal. However, the variances and the sample sizes are often not equal in the real cases. Nelson and Dudewicz (2002) developed two-stage sampling procedure which was proposed by Stein (1945) to deal with ANOM models under heteroscedasticity (HANOM). Two-stage sampling procedure must add samples, but it is not practical all the time. The single-stage sampling procedure can avoid the disadvantage of two-stage sampling procedure. In this study, we attack HANOM model in one-way layout and unbalanced design by single-stage sampling procedure.

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