兩獨立二項分布勝算筆的區間估計之研究

針對兩獨立二項母體的勝算比，我們通常會以區間估計的方式來探討勝算比。一般而言都是使用大樣本近似方法建構勝算比的信賴區間，但在中、小樣本時，此方法誤差會很大，故本文使用正確條件法及正確非條件法建構勝算比的信賴區間。由正確條件法所建構的信賴區間常具有保守性；由正確非條件法所建構的信賴區間會有最短的區間長度，其覆蓋機率會靠近名目水準 1-α 且不小於 1-α 。

關鍵字

區間估計；勝算比；正確條件方法；正確非條件方法；兩獨立二項分布

並列摘要

For the interval estimation of the odds ratio in two independent binomial samples, the usual method to construct confidence interval is the large-sample approximation method. But, such a method will produce a confidence interval which has the actual significant level much larger than or equal to the nominal lever if the sample sizes are small or moderate. In this paper, we use the exact conditional approach and the exact unconditional approach to obtain a modified interval. Numerical studies show that confidence intervals based on the exact conditional approach can be conservative with small to moderate sample sizes. The modified confidence intervals based on the exact unconditional approach has shorter length, and its coverage probability is closer to and at least the nominal level.

並列關鍵字

the Exact Unconditional Approach. ； Two Independent Binomial Samples ； the Exact Conditional Approach ； Odds Ratio ； Interval Estimation

參考文獻

1. Agresti, A. (2003). Dealing with discreteness:making ''exact'' confidence intervals for proportions, differences of proportions, and odds ratios more exact. Statistical Methods in Medical Research 2003 12, 3-21.

2. Agresti, A.(2007). An Introduction to Categorical Data Analysis, 2nd edition. John Wiley and Sons, INC., Publication.

3. Agresti, A. and Gottard, A. (2007). Nonconservative exact small-sample inference for discrete data. Computational Statistics and Data Analysis 51, 6447-6458.

4. Agresti, A. and Min, Y. (2001). On a small-sample confidence intervals for parameters in discrete distributions. Biometrics 57, 963-971.

5. Agresti, A. and Min, Y. (2002). Unconditional small-sample confidence intervals for the odds ratio. Biostatistics 3, 379-386.

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兩獨立二項分布勝算筆的區間估計之研究

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