A New Confidence Interval Method Based on the Normal Approximation for the Difference of Two Binomial Probabilities
基于正态近似的两二项概率之差置信区间新方法AI 解读 ↓
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基于正态近似的两二项概率之差置信区间新方法
- 研究问题
- 如何构造两二项成功概率之差的简便置信区间，使其覆盖率更接近名义水平，并兼顾区间精度与小样本适用性？
- 方法与思路
- 作者由离散分布区间构造的一般方法提出新正态近似区间，与另外三种方法比较，并精确计算覆盖概率和精度指标。
- 材料陈述的贡献
- 摘要依据覆盖率、精度及适用样本规模的比较推荐新方法；四种方法均便于计算，另推导了部分“精确”区间端点。
- 阅读关注点
- 应核对连续性修正、标准误估计与精度指标的定义，以及覆盖率比较所用的概率和样本量范围及边界情形。
- 阅读边界
- 仅据稿件版本未注明的OpenAlex索引摘要；未给出区间公式、比较数值或适用阈值，作者的推荐不能视为所有配置下占优。
原文摘要
Using a general method for obtaining confidence intervals from samples from discrete distributions, this article introduces a new confidence interval method for estimating the difference of two binomial probabilities and compares it to three other confidence interval methods, one of which is the usual method with no continuity correction. Each of the other two confidence interval methods uses its own continuity correction; one combines it with an estimate of the standard error that is slightly different from that commonly used. Some values of the “exact” confidence interval limits are also derived. The four confidence interval methods, each of which is based on the normal approximation and can be carried out easily on a hand calculator, are compared in terms of their precision, the agreement of their coverage probabilities with nominal confidence level values, and the smallness of their sample sizes before the normal approximation can be considered appropriate. Coverage probabilities and measures of precision are computed exactly rather than estimated by simulation. On the basis of these comparisons, the new confidence interval method is recommended.