基于距离协方差的二维列联表的独立性检验

A Test of Independence for Two Dimensional Contingency Tables Based on Distance Covariance

通过引入虚拟向量,将二维列联表的独立性检验转换为两个虚拟向量的独立性检验,文章基于这两个虚拟向量的距离协方差导出了一种新的独立性检验方法,相比传统的卡方检验,新方法不受列联表各单元格频数的影响,且在二维列联表退化为2×2四格表时新方法等价于卡方检验.数值模拟进一步说明了新方法克服了传统的列联表独立性卡方检验的局限性,实例验证了新方法的实用性.

By introducing two dummy vectors,the test of independence for the twoway contingency table is transformed into the test of independence for two dummy vectors.Based on the distance covariance of the two dummy vectors,a new test of independence is derived.Compared to the traditional chi-square test,the new method proposed in this paper is not affected by the frequency of each cell in the contingency table,and it is equivalent to the chi-square test when the two-way contingency table only has four cells.Numerical simulation further illustrates that the new method overcomes the limitations of the traditional chi-square test of independence in the contingency table.A real data analysis verifies the practicability of the new method.