平均數分析法(ANOM)是可以利用圖形的方法比較各組母體平均數是否有顯著差異於整體平均數的一種方法。但平均數分析法的假設需要變異數相等，Nelson和Dudewicz (2003)利用Stein(1945)的理論提出了二階段抽樣法的平均數分析，該方法又被稱作異質變異下的平均數分析(HANOM)。但由於二階段抽樣需要抽取額外的樣本，很多時候加抽樣本並不容易進行。本篇研究中，我們運用Efron所提出的拔薛法(Bootstrap Procedure)來應用在異質變異下的平均數分析中，我們僅需要原來一階段的樣本即可執行異質變異下的平均數分析方法。

The analysis of means (ANOM) compares the mean of each group with the overall mean and the comparison can be presented in a graphical form. One assumption of the classical ANOM model is that the variances must be equal. But, variances and the sample sizes are often not equal in the real cases. Nelson and Dudewicz (2003) developed two-stage sampling procedure based on Stein’s theory (1945) to deal with ANOM models on heteroscedastic data (HANOM). However, two-stage sampling procedure needs more samples to analyze the data. In this study, we use single-stage sampling procedure and bootstrapping procedure to handle HANOM problem, which do not require additional observations.

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