2 × 2列聯表邊際同質性之改良概似比檢定 ;Improved likelihood ratio tests for testing marginal homogeneity in 2 × 2 contingency tables

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题名:	2 × 2列聯表邊際同質性之改良概似比檢定;Improved likelihood ratio tests for testing marginal homogeneity in 2 × 2 contingency tables
作者:	林峻陞;Jyun-Sheng Lin
贡献者:	統計研究所
关键词:	多項分佈;概似比檢定;型一誤差;正確非條件法;二元配對資料;likelihood ratio test;multinomial distribution;binary matched-pairs data;exact unconditional test;exact size
日期:	2009-05-27
上传时间:	2009-09-22 11:03:21 (UTC+8)
出版者:	國立中央大學圖書館
摘要:	本文考慮二元反應配對資料的邊際機率單尾檢定問題，使用正確非條件檢定方法與概似比檢定統計量建構出概似比p-值，由於概似比p-值檢定在中小樣本下具有保守性，所以考慮在給定信賴係數為1- 的概似比信賴區間p-值，但是選擇最佳的並無一個準則，且在概似比p-值及概似比信賴區間p-值互有優劣的的狀況下，我們進而嘗試再一次極大化求取修正信賴區間p-值並經由數值計算比較此三種檢定方法的真正型一誤差，探討其改良狀況。數值分析顯示，修正的信賴區間 p-值與三種的選擇無關，且除了在某些樣本點的真正型一誤差跟概似比p-值或概似比信賴區間p-值相同外，在某些中大樣本數之下亦能有效的改善真正型一誤差，即更靠近指定的名目水準。 This paper considers one-sided hypotheses for testing the marginal homogeneity in a binary matched-pairs design. First we use the exact unconditional tests based on the likelihood ratio statistic to obtain the p-value. The likelihood ratio p-value may be very conservative if the sample sizes are small or moderate. Alternatively, we consider the confidence interval p-value with the specified confidence coefficient, which was derived by Berger and Sidik (2003). But numerical calculations are not give a strong evidence to show that the confidence interval p-value is better than the likelihood ratio p-value for any case. On the other hand, the performance of confidence interval p-value is highly dependent on the choice of confidence coefficient, and hence such the p-value can be improved by using the unconditional approach again. Our numerical studies show that the improved confidence interval p-value is closer to and at least the nominal level than likelihood ratio p-value and confidence interval p-value in all sample sizes.
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