Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions
Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions
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DOI：
10.1080/00031305.1998.10480550
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发表时间：
1998-05
期刊：
影响因子：
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通讯作者：
A. Agresti;B. Coull
中科院分区：
文献类型：
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作者：
A. Agresti;B. Coull
摘要对于比例的区间估计，覆盖概率往往对于基于反演二项式检验的“精确”置信区间太大，而对于基于反演Wald大样本正态检验的区间太小（即，样本比例± z分数×估计标准误差）。威尔逊的建议，反转相关分数测试与零，而不是估计的标准误差产生的覆盖概率接近名义上的置信水平，即使是非常小的样本量。95%评分区间与在样本中添加两个“成功”和两个“失败”后获得的调整Wald区间具有相似的行为。在基础课程中，使用分数和调整的Wald方法，不需要为学生提供尴尬的样本量指南。
Abstract For interval estimation of a proportion, coverage probabilities tend to be too large for “exact” confidence intervals based on inverting the binomial test and too small for the interval based on inverting the Wald large-sample normal test (i.e., sample proportion ± z-score × estimated standard error). Wilson's suggestion of inverting the related score test with null rather than estimated standard error yields coverage probabilities close to nominal confidence levels, even for very small sample sizes. The 95% score interval has similar behavior as the adjusted Wald interval obtained after adding two “successes” and two “failures” to the sample. In elementary courses, with the score and adjusted Wald methods it is unnecessary to provide students with awkward sample size guidelines.