存在異質變異數的多組平均數比較，在統計學上是長期存在的問題。過去研究顯示，檢定統計量的分布受未知變異數的影響很大，並且在存在異質變異數時會不穩健。Bishop 和 Dudewicz (1978) 基於 Stein (1945) 的兩階段抽樣程序，提出了在變異數未知且不相等時的精確檢定量分配的方法，並在許多後續研究中用於解決各種多重比較問題。但是，兩階段抽樣程序是研究設計導向，需要在第二階段增加額外的樣本，缺乏實用性。在本論文中，我們分別應用了 Chen 和 Lam (1989)、Chen 和 Chen (1998) 以及 Chen (2001) 的單階段抽樣程序，來處理樣本數相等和不相等的兩種異質變異數下的平均數分析以及與單一控制組的多重比較問題。為了驗證此程序的品質，進行了整體型I誤差率的模擬，並提供了多個實例分析來說明程序如何使用。創建R Shiny的網路介面，供使用者可以更輕易的使用這些程序。

Comparison of several means in the presence of heteroscedasticity has been a long-standing problem in statistics. According to studies, the distribution of test statistics is highly influenced by unknown variances and is not robust in the presence of heteroscedastic variances. Bishop and Dudewicz (1978) proposed an exact analysis of variance when the variances are unknown and unequal, based on a two-stage sampling process described by Stein (1945). The approach has been used in a number of follow-up research to solve various multiple comparison problems. However, the two-stage sampling procedure is design-oriented which requires additional samples at the second stage, and it is inconvenient for the practice. In this thesis, we applied Chen and Lam's (1989), Chen and Chen's (1998) and Chen's (2001) single-stage sampling procedure, respectively, to analysis of means and multiple comparison with a control under heteroscedasticity with equal and unequal sample sizes. In order to validate the quality of the procedures, simulations of the family-wise error rate were undertaken, and various numerical examples were supplied to illustrate the procedures. R Shiny was utilized in the creation of an interface so that we can make the procedures more user-friendly.

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