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系統識別號 U0026-0812200913455086
論文名稱(中文) 成對資料相關係數相等性檢定
論文名稱(英文) Tests for Equivalence Based on Correlation Coefficient for Matched-pair Design
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 95
學期 2
出版年 96
研究生(中文) 顏欣怡
研究生(英文) Shin-Yi Yen
學號 r2694402
學位類別 碩士
語文別 英文
論文頁數 89頁
口試委員 口試委員-鄭順林
指導教授-馬瀰嘉
口試委員-趙昌泰
口試委員-陳俞成
中文關鍵字 相等性  相關係數  拔靴法  Fisher-transformation  成對設計  檢定力  型I誤差 
英文關鍵字 Fisher-transformation  Type I error  Bootstrap procedure  Equivalence  Correlation coefficient  Power  Match-paired design 
學科別分類
中文摘要 近年來針對成對設計的相等性評估,多應用在反應比率的差異、反應比率的比值、以及勝算比上。然而,這些相關係的量測只針對離散型的資料,無法解決連續型的資料所面臨的相同問題。因此在這篇論文中針對成對的連續型資料討論其相關係數的相等性。首先,會先回顧一些用來比較兩組相關係數是否相等的方法,並且利用近似的信賴區間方式來計算兩組相關係數的相等性。在過去的研究中提到如果將相關係數做Fisher-transformation後,相關係數的分配會更近似常態分配。利用前面建議的方法計算型I誤差發生的機率和檢定力,且也利用拔靴法做計算,並比較兩種方法的結果。我們也比較在相等性的檢定時,相關係數做Fisher-transformation後的常態近似檢定是會比較好的。最後,給一個實際的例子,利用這個論文提出的方法,來做相等性的檢定。
英文摘要 Current methods for evaluation of equivalence under a matched-pair design employ either difference in proportions, relative risk or odds ratio as measures of risk association. However, these measures of association are only for discrete data and they can not be applied to continuous data. In this paper, under a matched-pair design, the correlation coefficient is proposed to assess the equivalence for continuous data. We review the methods to test two different correlation coefficient equal or not, and suggest the use of the asymptotic confidence interval of the difference of two correlation coefficients for evaluation of equivalence. In the past research, the correlation coefficients that take Fisher-transformation are more asymptotic normal distribution. A simulation study was conducted to empirically investigate the size and power of the proposed procedures. A bootstrap-based approach is proposed and compared to the empirically investigate the size and power. We compare the correlation coefficient that take Fisher-transformation are more powerful than they are not in equivalence. Finally, a numerical example is used to illustrate the application of the proposed procedure.
論文目次 Chapter 1 Introduction……………………………………………………..1
Chapter 2 Literature Review…………………………………………….....5
2.1 Test for Elements of a Correlation Matrix………………………....5
2.2 Hypotheses Testing for Equivalence………………………………9
Chapter3 Proposed Methods……………………………………………....11
3.1 Two Dependent Correlation Coefficients for Four Treatments ......11
3.2 Two Dependent Correlation Coefficients for Three Treatments…..15
3.3 The Property of the Power Function………………………………19
3.4 Bootstrap Confidence Interval…………………………………….19
Chapter 4 Simulation Study……………………………………..................21
4.1 The Simulation Results in Four Treatments……………………….22
4.2 The Simulation Results in Three Treatments……………………...26
Chapter 5 Real Example………………………………………………........30
5.1 Magnetic Resonance Angiography (MRA)………………………..30
5.2 Dual-energy X-ray Absorptiometry (DXA)……………………….32
Chapter 6 Conclusion………………………………………………….......34
Reference…………………………………………………………..............36
Appendix A………………………………………………………………...38
Appendix B………………………………………………………………...42
Appendix C………………………………………………………………...85
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