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系統識別號 U0026-0507201011284900
論文名稱(中文) 異質變異下的平均數分析
論文名稱(英文) Analysis of Means under Heteroscedasticity
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 98
學期 2
出版年 99
研究生(中文) 洪采襄
研究生(英文) Tsai-Hsiang Hung
學號 r2697409
學位類別 碩士
語文別 英文
論文頁數 39頁
口試委員 指導教授-溫敏杰
口試委員-呂金河
口試委員-杜宜軒
中文關鍵字 一階段抽樣方法  二階段抽樣方法  單因子設計  平衡設計 
英文關鍵字 Single-stage sampling procedure  Two-stage sampling procedure  One-way layout  Balanced design 
學科別分類
中文摘要 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。
英文摘要 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.
論文目次 1 Introduction 1
2 Single-Stage Sampling Procedure 3
3 Analysis of Means with Unequal Variances 5
3.1 The One-Way Layout 5
3.2 Computing the Critical Value 6
3.3 Computing the p-Value 8
4 Analysis of Means for Variances and Its Critical Value 10
5 Examples 13
5.1 Loan to Value Data 13
5.2 Target Power Data 15
5.3 Fasting Plasma Glucose Data 17
5.4 Comparing with Analysis of Means 18
6 Conclusion and Discussion 25
References 26
Appendix A: R Programs 27
Appendix B: Raw Data 32
Appendix C: Critical Values for ANOMV 34
Appendix D: Critical Values of HANOM 38
參考文獻 Chen, H. J. and Lam, K. (1989). Single-stage interval estimation of the largest normal mean under heteroscedasticity. Communications in Statistics - Theory
and methods, 18(10), 3703-3718.
Chang, C. J., Wu, J. S., Lu, F. H., Lee, H. L., Yang, Y. C., and Wen, M. J. (1998). Fasting plasma glucose in screening for diabetes in the Taiwanese population. Diabetes Care, 21(11), 1856-1860.
Cheng, H. J. (2007). A study of two-stage rike early warning models of mortgage in Tainan city. Unpublished master thesis, National Cheng Kung University, Taiwan.
Nelson, P. R. and Dudewicz, E. J. (2002). Exact analysis of means with unequal variances. Technometrics, 44(2), 152-160.
Stein, C. (1945). A two-sample test for a linear hypothesis whose power is independent of the variance. The Annals of Mathematical Statistics, 16(3), 243-258.
Wen, M. J. and Chen, H. J. (1994). Single-stage multiple comparison procedures under heteroscedasticity. American Journal of Mathematical and Management Sciences, 14, 1-48.
Wludyka, P. S. and Nelson, P. R. (1997). An analysis-of-means-type test for variances from normal populations. Technometrics, 39(3), 274-285.
Wu, S. F. and Chen, H. J. (1998). Multiple comparisons with the average for normal distributions. American Journal of Mathematical and Management Sciences, 18(1), 193-218.
Wu, S. F. and Liao, B. X. (2004). A simulation study of multiple comparisons with the average under heteroscedasticity. Communications in Statistics - Simulation and Computation, 33(3), 639-659.
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