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系統識別號 U0026-1906201215234800
論文名稱(中文) Bootstrap法在一階段異質性下平均數分析模型的應用
論文名稱(英文) Bootstrap Procedure in Single-Stage HANOM Model
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 100
學期 2
出版年 101
研究生(中文) 陳致甫
研究生(英文) Chih-Fu Chen
學號 r26994078
學位類別 碩士
語文別 英文
論文頁數 36頁
口試委員 指導教授-溫敏杰
口試委員-高正雄
口試委員-連哲輝
口試委員-鄭文英
中文關鍵字 未知變異數和不等變異數  t 分配  異質變異下的平均數分析  拔靴法(Bootstrap procedure) 
英文關鍵字 Unknown and unequal variances  t distribution  HANOM  Bootstrapping procedure 
學科別分類
中文摘要 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。
英文摘要 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.
論文目次 1 Introduction...........................................1

2 Single-Stage Sampling Procedure (Sample-Splitting).....5

2.1 The One-Way Layout (Sample-Splitting)................7

3 Detail in Problem of Single-Stage Sampling Procedure...9

4 Introduction of Bootstrapping Procedure and Its Appliance into HANOM Models........................................15

4.1 Computing the Critical Value (With Bootstrap Procedure)...............................................17

5 Examples...............................................23

5.1 Example 1: Penicillium Expansum Data.................23

5.2 Example 2: Japanese Language Listening Test..........31

6 Conclusion and Future Studies..........................34

7 References.............................................35



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