2 × 2列聯表邊際同質性之改良概似比檢定

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林峻陞(Jyun-Sheng Lin) 查詢紙本館藏

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論文名稱

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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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 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

關鍵字(英)

★ likelihood ratio test
★ multinomial distribution
★ binary matched-pairs data
★ exact unconditional test
★ exact size

論文目次

Abstract . .. . . . . . . . . . . . . . . . . . . . . . . i
摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . ii
致謝辭 . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄 . . . . . . . . . . . . . . . . . . . . . . . . . .iv
圖目次. . . . . . . . . . . . . . . . . . . . . . . . . vi
表目次 . . . . . . . . . . . . . . . . . . . . . . . . vii
第一章緒論 . . . . . . . . . . . . . . . . . . . . . . . 1
第二章研究方法 . . . . . . . . . . . . . . .. . . . . . 5
2.1 概似比p-值檢定 . . . . . . . . . . . . . . .. . . . . 7
2.2 概似比信賴區間p-值檢定 . . . . . . . . . . . . . . . 11
2.3 修正信賴區間p-值檢定 . . . . . . . . . . . . . . .. .16
第三章數值分析. . . . . . . . . . . .. . . . . . . . . 18
3.1 真正型一誤差的計算 . . . . . . . . . . . . . . . . . 18
3.1.1 概似比信賴區間p-值檢定的真正型一誤差.. . . . . . . 20
3.1.2 概似比p-值檢定的真正型一誤差 . . . . . . . . . . . 22
3.1.3 修正信賴區間p-值檢定的真正型一誤差 . . . . . . . . 23
3.2 p-值檢定真正型一誤差的比較. . . . . . . . . . . . . 24
第四章結論與未來研究 . . . . . . . . . . . . . . . . .35
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . .37
附錄A . . .. . . . . . . . . . . . . . . . . . . . . . .39

參考文獻

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[10] Hsueh, H. M., Liu, J. P., and Chen, J. J. (2001). "Unconditional exact tests for equivalence or noninferiority for paired binary endpoints". Biometrics, 57, 478–483.
[11] Lin, C. Y. and Yang, M. C. (2005). "Improved p-value tests for comparing two independent binomial proportions". Graduate Institute of Statistics National Central University Technical Report.
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指導教授

楊明宗(Ming-Chung Yang)

審核日期

2009-6-19

推文