Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures
Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures
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DOI：
10.2307/2685779
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发表时间：
2000-11-01
影响因子：
1.8
通讯作者：
Caffo, B
中科院分区：
文献类型：
--
作者：
Agresti, A;Caffo, B
在统计学入门课程中使用的比例及其差异的标准置信区间的性能很差，实际覆盖概率往往比预期的要低得多。然而，基于添加四个伪观测值（每种类型各一半）对这些间隔进行简单调整，即使对于小样本也表现得令人惊讶。为了说明，对于每个样本中具有10个观测值的各种参数设置，比例差异的标称95%区间在88%的情况下具有低于0.93的实际覆盖概率，而在标准区间中只有1%;对于标准间隔，标称和实际覆盖概率之间的平均距离为0.06，但是对于调整后的间隔，为0.01。在使用这些调整后的间隔进行教学时，可以绕过尴尬的样本量指南，并使用相同的公式处理小样本和大样本。
The standard confidence intervals for proportions and their differences used in introductory statistics courses have poor performance, the actual coverage probability often being much lower than intended. However, simple adjustments of these intervals based on adding four pseudo observations, half of each type, perform surprisingly well even for small samples. To illustrate, for a broad variety of parameter settings with 10 observations in each sample, a nominal 95% interval for the difference of proportions has actual coverage probability below .93 in 88% of the cases with the standard interval but in only 1% with the adjusted interval; the mean distance between the nominal and actual coverage probabilities is .06 for the standard interval, but .01 for the adjusted one. In teaching with these adjusted intervals, one can bypass awkward sample size guidelines and use the same formulas with small and large samples.