Dealing with discreteness: making 'exact' confidence intervals for proportions, differences of proportions, and odds ratios more exact
Dealing with discreteness: making 'exact' confidence intervals for proportions, differences of proportions, and odds ratios more exact
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DOI：
10.1191/0962280203sm311ra
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发表时间：
2003-01-01
影响因子：
2.3
通讯作者：
Agresti, A
中科院分区：
文献类型：
--
作者：
Agresti, A
分类数据的“精确”方法在使用不依赖于未知参数的概率分布方面是精确的。然而，他们是保守的推论。测试和置信区间的实际误差概率以标称水平为界。本文研究了区间估计的保守性，并描述了降低保守性的方法；我们举例说明了几个基本参数的置信区间，包括二项参数，独立样本中两个二项参数之间的差异，以及比值比和相对风险。以下设备的保守性较低：(1)使用“离散性较低”的统计量进行反向检验，(2)对单个双侧检验进行反向检验，而不是两个单独的单侧检验，每个检验的大小至少为标称水平的一半，(3)使用无条件方法而不是条件方法（适当时），以及(4)使用替代p值进行反向检验。文章最后给出了在三种情况下选择区间的建议：当需要保证覆盖概率的下界时，当实际覆盖概率接近名义水平时，以及在课堂或咨询环境中教学时。
'Exact' methods for categorical data are exact in terms of using probability distributions that do not depend on unknown parameters. However, they are conservative inferentially. The actual error probabilities for tests and confidence intervals are bounded above by the nominal level. This article examines the conservatism for interval estimation and describes ways of reducing it; We illustrate for confidence intervals for several basic parameters, including the binomial parameter, the difference between two binomial parameters for independent samples, and the odds ratio and relative risk. Less conservative behavior results from devices such as (1) inverting tests using statistics that are 'less discrete', (2) inverting a single two-sided test rather than two separate one-sided tests each having size at least half the nominal level, (3) using unconditional rather than conditional methods (where appropriate) and (4) inverting tests using alternative p-values. The article concludes with recommendations for selecting an interval in three situations-when one needs to guarantee a lower bound on a coverage probability, when it is sufficient to have actual coverage probability near the nominal level, and when teaching in a classroom or consulting environment.