Interval estimation for the odds ratio of a 2 × 2 contingency table from multinomial distribution

• Main Authors: CHEN-HSUAN WU, 吳晨瑄
• Other Authors: Ming-Chung Yang
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/32n7je

碩士 === 國立中央大學 === 統計研究所 === 96 === For a 2 × 2 contingency table sampled from multinomial distribution, we are interested in measuring strength of association between two variables by the odds ratio. Also constructing a confidence interval for the odds ratio is primarily of concerned in practice. For the multinomial sampling, there are two nuisance parameters except for the odds ratio. Hence we usually take the exact conditional approach to obtain a confidence interval for the odds. However, the exact conditional confidence interval can be very conservative because the exact conditional approach may use a high discrete conditional distribution when the sample size is small. On the other hand, the exact unconditional approach eliminates the nuisance parameters by taking the maximal p-value over all possible values of the nuisance parameters. In this paper, we take the unconditional approach to obtain a modified confidence interval. For small to moderate sample sizes, numerical studies show that comparing to other interval the modified confidence interval usually has shorter length, and its actual confidence coefficient is closer to and at least the nominal confidence coefficient.