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系統識別號 U0026-0812200915081464
論文名稱(中文) 異質變異下的聯合信賴區間
論文名稱(英文) Simultaneous Confidence Intervals 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 97
學期 2
出版年 98
研究生(中文) 沈宗毅
研究生(英文) Tsung-Yi Shen
學號 r2696108
學位類別 碩士
語文別 英文
論文頁數 42頁
口試委員 指導教授-溫敏杰
口試委員-陳占平
口試委員-吳宗正
中文關鍵字 不等變異  不等樣本  多重比較 
英文關鍵字 Unequal variances  Unequal sample sizes  Multiple comparisons 
學科別分類
中文摘要 在給定k (>= 2)個獨立母體π1, π2, . . . , πk下,假定Xij (j = 1, . . . , ni)為從平均數為μi且變異數為σi2的常態母體πi中所抽取之觀測值,其中σi2 (i = 1, . . . , k)為未知或不等變異數。一般來說,變異數分析 (ANOVA) 是用來檢定母體平均數是否相等的方法,而其前提假設為常態性、獨立性與同質變異,由於資料並非皆符合前提假設,因此 Dudewicz 與 van der Meulen (1983) 提出若資料不服從常態性的假設時,ANOVA 的 F 檢定仍會有相當穩健的檢定結果,然而,Bishop (1976) 則提出當變異數不相等時則會對檢定結果帶來相當大的影響,尤其是連樣本數也不相等的情況影響更甚。因此,一階段抽樣法被用來解決不等變異數的問題,本研究除了介紹一階段抽樣法之外,運用一階段抽樣法建立多重比較方法,並應用在實際資料上。
英文摘要 Given that k (>= 2) independent populations π1, π2, . . . , πk such that observations Xij (j = 1, . . . , ni) taken from population πi are normally distributed with mean μi and unknown (and possibly unequal) variance σi2 (i = 1, . . . , k). Analysis of variance (ANOVA) test procedures are generally used to test the equality of population means, where the procedures depend on the assumptions of normality, independence, and homogeneity of variance. Dudewicz and van der Meulen (1983) has shown that violation of normality doesn’t bring much effects on the ANOVA F test. However, Bishop (1976) presented that violation of homogeneity can give serious consequences in the ANOVA F test, especially under unequal sample sizes. Therefore, a single-stage sampling procedure is used to deal with such unequal variances cases. In addition, single-stage sampling procedure is introduced and applied to multiple comparisons, and numerical examples to apply the procedure is also given.
論文目次 1 Introduction...................................................1
2 Single-Stage Sampling Procedure................................3
3 Multiple Comparisons With Each Other...........................7
3.1 All Pairwise Comparisons.....................................7
3.2 All Linear Combinations of α′is............................8
3.3 All Contrasts of μ′is......................................10
4 Multiple Comparisons With The Best Population..................11
5 Multiple Comparisons With A Control Population.................15
6 Numerical Examples.............................................20
7 Study of Single-Stage Sampling Procedure Properties............24
7.1 Initial Sample Size..........................................24
7.2 Weights......................................................25
7.3 Random Times.................................................26
8 The Two-Way Model..............................................27
9 Conclusion and Discussion......................................30
References.......................................................31
Appendix A: Tables and Figure....................................33
Appendix B: R Programs...........................................40
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