Garner J B
Department of Medicine, University of Western Australia, Perth, Australia.
Stat Med. 1991 May;10(5):767-75. doi: 10.1002/sim.4780100512.
This paper gives a standard error for Cohen's Kappa, conditional on the margins of the observed r x r table. An explicit formula is given for the 2 x 2 table, and a procedure for the more general situation. A parsimonious log-linear model is suggested for the general case and an approximate confidence interval for kappa is based on that model. Numerical illustrations are given comparing the standard results with exact conditional results and those of the present paper. The conclusions are, first, that the standard error of kappa under the null hypothesis (that kappa is zero) should not be used except when the null is plausible; secondly, that the usual formula for the standard error appears appropriate except in the unusual circumstance of kappa taking large negative values; and, thirdly, in small samples the distribution of the estimate of kappa appears very non-symmetric, and it is preferable to base confidence intervals on transformations of kappa. A PC program with source code implementing the suggested procedures is available from the author.
本文给出了基于观测到的r×r表的边际条件下科恩kappa系数的标准误差。给出了2×2表的显式公式以及更一般情况的计算方法。针对一般情况提出了一个简约的对数线性模型，并基于该模型给出了kappa的近似置信区间。给出了数值示例，比较了标准结果与精确条件结果以及本文结果。结论如下：第一，除了在原假设合理的情况下，不应使用原假设（kappa为零）下kappa的标准误差；第二，标准误差的常用公式似乎是合适的，除非在kappa取大的负值这种不寻常的情况下；第三，在小样本中，kappa估计值的分布看起来非常不对称，最好基于kappa的变换来构建置信区间。作者可提供一个带有实现所建议程序的源代码的个人计算机程序。
