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研究生:任海峽
研究生(外文):Hai-shia Ren
論文名稱:在有限區間上檢定兩迴歸直線是否相交
論文名稱(外文):Test Whether Two Regression Lines IntersectOver a Finite Interval
指導教授:吳榮彬吳榮彬引用關係林文欽林文欽引用關係
指導教授(外文):Jungpin WuWin-Chin Lin
學位類別:碩士
校院名稱:逢甲大學
系所名稱:統計與精算所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:33
中文關鍵詞:交叉點共變異數分析拔靴假設檢定程序蒙地卡羅模擬非顯著區域詹森-內曼技巧
外文關鍵詞:non-significant regionnon-significant regionJohnson-Neyman techniquenon-significant regionANCOVAMonte-Carlo simulation method
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面對需要考慮兩種處理和一種共變數的統計問題時,
若接受不同處理的反應變數與共變數之關係不違反迴歸假設,
詹森-內曼技巧和共變異數分析經常被考慮做為統計分析方法的選項。
對於這些不同組反應變數與共變數所形成之迴歸線,
彼此之間是否平行,
會影響到此兩種分析方法的適用性。
當它們的斜率未能通過同質性檢定時,
一般會採用詹森-內曼技巧進行分析。
但對於以『兩迴歸線是否平行』做為詹森-內曼技巧是否適用的檢驗標準,
其實有些不適當;
尤其是,
當共變數的範圍也在此問題的考慮條件之列時。
假定共變數有一個實務上限定的區間,
必須在此區間內判斷兩種處理效果是否有顯著差異時,
共變異數分析方法可以清楚的做出判斷;
但詹森-內曼技巧找出的非顯著區域卻未必會落入此區間內。
由於兩直線交叉點的存在對詹森-內曼方法有很大的影響,
當交叉點橫坐標遠離此一區間時,
詹森-內曼技巧得到的結論未必適用於此組共變數範圍。
因此,
以『兩直線在有限區間內相交』取代斜率的同質性檢定,
來檢驗詹森-內曼方法的適用性,
便是這篇文章所要探討的。
本文建議一種拔靴假設檢定程序,
並利用蒙地卡羅模擬方法討論其型I風險與檢定力。
While discussing the difference of two regression lines with one covariate,
two statistical tools, ANCOVA, and Johnson-Neyman Technique,
are often to be used.
Generally, the most important reason to decide which one would be chosen,
is whether two regression lines are parallel.
If these lines are not parallel, that is,
intersect at some point;
then, we would choose Johnson-Neyman technique to analyze data.
Existence of interection point somehow means two regression lines are not parallel;
however, if this point is far away from our research range for covariate,
JN tech''s non-significant region would be also away from the range.
JN tech''s non-significant region has strongly affected by interection point so it may cause some problem hard to explain.
In this situation,
the choice of JN tech should be discussed again.
If the interection point lies in research range,
we can definitely use JN tech to analyze data;
nevertheless, when interection point''s x-coordinate estimated value exceed our range and regression lines are not parallel,
use JN tech to solve question may be not appropriate.
For discussing if JN tech is appropriate over a finite interval,
this article suggests one hypothesis testing procedure to determine whether two regression lines intersect over a finite interval.
We use bootstrap hypothesis testing procedure to solve this question,
and use Monte-Carlo simulation method to discuss type I error and power in different sample, sigma, and slope of two regresiion lines.
1 緒論 p1
1.1研究動機與目的 p1
1.2 文獻回顧 p2
1.2.1 共變異數分析 p2
1.2.2 詹森-內曼技巧 p3
1.2.3 兩迴歸直線的關係 p4
1.2.4 拔靴假設檢定 p5
2 檢定兩迴歸直線是否在有限區間內相交p6
2.1 假設檢定程序 p6
2.2 拔靴假設檢定程序 p8
2.3 改進的拔靴假設檢定程序 p9
3 模擬研究 p12
3.1 ­控制變數與狀況設計 p12
3.2 模擬結果 p12
3.3 結果分析 p21
4 實例分析 p23
5 結論 p26
參考文獻 p28
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M.H.(1987). Blood Pressure and Metabolic E ects of Calcium Supplementation in
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