On Association Coefficients for 2×2 Tables and Properties That Do Not Depend on the Marginal Distributions
On Association Coefficients for 2×2 Tables and Properties That Do Not Depend on the Marginal Distributions
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关于2×2表的关联系数和不依赖于边际分布的性质
作者：
M. Warrens
我们讨论关联系数通常可能具有的性质，例如，在统计独立性下的零值，并且我们检查2×2表的系数与这些性质有关。此外，我们研究了一组系数，它们是给定边际概率的观察到的一致性比例的线性变换。这个家族包括phi系数和科恩kappa。主要的结果是线性变换将独立性的值设为零，最大值设为单位，将这个族中的所有系数都转化为相同的底层系数。这个系数恰好是Loevinger的H。
We discuss properties that association coefficients may have in general, e.g., zero value under statistical independence, and we examine coefficients for 2×2 tables with respect to these properties. Furthermore, we study a family of coefficients that are linear transformations of the observed proportion of agreement given the marginal probabilities. This family includes the phi coefficient and Cohen’s kappa. The main result is that the linear transformations that set the value under independence at zero and the maximum value at unity, transform all coefficients in this family into the same underlying coefficient. This coefficient happens to be Loevinger’s H.