平均數分析是藉由圖形的方式來比較所蒐集到的k(>=3)個處理平均數是否與整體平均數間有顯著差異的分析方法。當k個母體的變異數不等且未知時，
Nelson和Dudewicz(2002)利用Stein(1945)所提出之二階段抽樣方法進行異質變異下的平均數分析。二階段抽樣方法，顧名思義，就是樣本抽取分兩個階段，亦即在第二階段時需要加抽樣本，但有時加抽樣本不易執行，故本研究採用一階段抽樣方法解決平均數分析於變異數不等且未知的情況，同時可避免二階段抽樣加抽樣本不易執行的問題。

The analysis of means (ANOM) is a graphical procedure which compares k (>3) treatment means to see if any of them has signi cant diifference from the overall mean. For unknown and unequal variances, Nelson and Dudewicz (2002) developed a two-stage sampling procedure which was proposed by Stein (1945) to deal with ANOM under heteroscedasticity (HANOM). However, additional samples must be taken at the second stage, which is not practical or feasible all the time. Thus, in this thesis, we discuss HANOM in one-way layout with balanced design under the heteroscedastic situation by single-stage sampling procedure which could avoid disadvantages of two-stage sampling procedure.

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