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檢定兩獨立母體比例前進選擇法 = Forward selection t...

國立高雄大學統計學研究所

檢定兩獨立母體比例前進選擇法 = Forward selection two sample binomial test

紀錄類型:	書目-語言資料,印刷品 : 單行本
並列題名:	Forward selection two sample binomial test
作者:	林妙珊,
其他團體作者:	國立高雄大學
出版地:	[高雄市]
出版者:	撰者;
出版年:	民99[2010]
面頁冊數:	38面圖，表 : 30公分;
標題:	2x2列聯表
標題:	2x2 table
電子資源:	http://handle.ncl.edu.tw/11296/ndltd/29198524528792563864
摘要註:	來自兩獨立二項分佈的數據，在實務上是廣泛存在的，例如臨床試驗。傳統上，欲比較兩獨立二項分佈母體比例，當遇到小樣本時，一般建議使用費雪精確檢定法。2008年Gerald G. Crans和Jonathan J. Shuster證實如果將費雪精確檢定法運用在檢定兩獨立二項分佈母體比例是否相同的問題上，則會造成型I錯誤的機率遠低於所設定的顯著水準，即使兩組樣本的樣本數都達到125，依舊遠低於所給定的顯著水準。更進一步的，他們針對費雪精確檢定法提出一個修正方法，他們定義出新的顯著水準，α=α+ε，α代表欲設定之顯著水準，ε代表一特定的正數。為了方便使用，他們提供在不同樣本數時的新顯著水準和預期之顯著水準的對照表，此修正方法除了提升型I錯誤機率問題外，也有效的提昇檢定力；事實上從另一個觀點來看，此修正方法雖然使用兩獨立二項分佈計算真實型I錯誤的發生機率，但是實際上可能結果進入拒絕域的順序依然採用超幾何分布做決定，因此，相對於修正費雪精確檢定的方法，在本篇論文中我們給出另一方法來決定可能結果進入拒絕域的順序，在此不使用超幾何分布決定順序，取而代之的是使用兩獨立二項分佈來決定進入拒絕域的順序。最後，我們會將所提出的新方法和一些已經被提出的方法作比較，藉由有限樣本下的數值結果說明這個新的方法的特性和優點，且同時經由檢定力函數圖形看各個方法的曲線變化。 The data which come from two-sample comparative binomial trial is one of the most widely applied statistical data structure in practice such as in clinical trial. In the comparison of two independent binomial proportions for small sample sizes, one of the commonly used technique is Fisher's exact test. Fisher's exact test is a conditional method which considers the hypergeometric distribution as null distribution. In year 2008, Gerald G. Crans and Jonathan J. Shuster verify that applying Fisher's exact test to this type of comparison will give a lower probability of type I error than that we expected even for sample sizes up to 125 subjects per group. Additionally, they propose an adjusted method that defines new significance levels α=α+ε, where α is pre-specified and ε is a small positive number, and gives a cross-reference table which contains all new significance levels links for various sample sizes and target α. The adjustment uniformly improves the test size, rasing the actual probability of type I error and hence more powerful. From another pointof view, their proposed method applies two independent binomial distribution to calculate the actual probability of type I error, where the sequence of the possible outcomes for the rejection region is based on hypergeometric distribution. In this paper, we give another sequence to involve the possible outcomes into the rejection region. Instead of using hypergeometric distribution, we are strictly forward to consider two independent binomial distribution to as the reference. Lastly, we through comparing with some proposed methods, then, the properties and advantages of this method are demonstrated by numerical results. Some figures are presented to show the pattern changes of the power functions for these methods.

檢定兩獨立母體比例前進選擇法 = Forward selection two sample binomial test
林, 妙珊

檢定兩獨立母體比例前進選擇法 = Forward selection two sample binomial test / 林妙珊撰 - [高雄市] : 撰者, 民99[2010]. - 38面 ; 圖，表 ; 30公分.
參考書目：面.
2x2列聯表2x2 table

檢定兩獨立母體比例前進選擇法 = Forward selection two sample binomial test
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330 $a 來自兩獨立二項分佈的數據，在實務上是廣泛存在的，例如臨床試驗。傳統上，欲比較兩獨立二項分佈母體比例，當遇到小樣本時，一般建議使用費雪精確檢定法。2008年Gerald G. Crans和Jonathan J. Shuster證實如果將費雪精確檢定法運用在檢定兩獨立二項分佈母體比例是否相同的問題上，則會造成型I錯誤的機率遠低於所設定的顯著水準，即使兩組樣本的樣本數都達到125，依舊遠低於所給定的顯著水準。更進一步的，他們針對費雪精確檢定法提出一個修正方法，他們定義出新的顯著水準，α*=α+ε，α代表欲設定之顯著水準，ε代表一特定的正數。為了方便使用，他們提供在不同樣本數時的新顯著水準和預期之顯著水準的對照表，此修正方法除了提升型I錯誤機率問題外，也有效的提昇檢定力；事實上從另一個觀點來看，此修正方法雖然使用兩獨立二項分佈計算真實型I錯誤的發生機率，但是實際上可能結果進入拒絕域的順序依然採用超幾何分布做決定，因此，相對於修正費雪精確檢定的方法，在本篇論文中我們給出另一方法來決定可能結果進入拒絕域的順序，在此不使用超幾何分布決定順序，取而代之的是使用兩獨立二項分佈來決定進入拒絕域的順序。最後，我們會將所提出的新方法和一些已經被提出的方法作比較，藉由有限樣本下的數值結果說明這個新的方法的特性和優點，且同時經由檢定力函數圖形看各個方法的曲線變化。 The data which come from two-sample comparative binomial trial is one of the most widely applied statistical data structure in practice such as in clinical trial. In the comparison of two independent binomial proportions for small sample sizes, one of the commonly used technique is Fisher's exact test. Fisher's exact test is a conditional method which considers the hypergeometric distribution as null distribution. In year 2008, Gerald G. Crans and Jonathan J. Shuster verify that applying Fisher's exact test to this type of comparison will give a lower probability of type I error than that we expected even for sample sizes up to 125 subjects per group. Additionally, they propose an adjusted method that defines new significance levels α*=α+ε, where α is pre-specified and ε is a small positive number, and gives a cross-reference table which contains all new significance levels links for various sample sizes and target α. The adjustment uniformly improves the test size, rasing the actual probability of type I error and hence more powerful. From another pointof view, their proposed method applies two independent binomial distribution to calculate the actual probability of type I error, where the sequence of the possible outcomes for the rejection region is based on hypergeometric distribution. In this paper, we give another sequence to involve the possible outcomes into the rejection region. Instead of using hypergeometric distribution, we are strictly forward to consider two independent binomial distribution to as the reference. Lastly, we through comparing with some proposed methods, then, the properties and advantages of this method are demonstrated by numerical results. Some figures are presented to show the pattern changes of the power functions for these methods.
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