列联表分析中的Simpson悖论问题

The Problem of Simpson Paradox in Contingency Table

对于分类数据,列联表无疑是最好的统计工具之一,但列联表分析也会带来Simpson悖论问题。从理论上来说,可以通过改变试验结构来消解Simpson悖论,但社会研究数据大多是观测数据,是无法通过试验来控制的,因此Simpson悖论与其说是"悖论",不如说是反映了分类数据的非线性特征,是"不可压缩"而压缩的结果,反映了列联表从高维压缩至低维时的统计信息差异,实质上是欧氏空间的降维问题。

Contingency table is a good statistical tool to categorical data.It is an important applicative problem in social statistic analysis that how to explain Simpson Paradox in contingency table.Theoretically,we can change experiment structure to eliminate the paradox,but most of the data in social research is observational data.It can＇t be controlled by experiment.So Simpson Paradox is not a paradox but unique nonlinearity character reflection of categorical data.It is a compressible result under incompressible condition.It is different reflection of statistic information from the upper dimensions to low dimension.It is essentially a problem of reducing dimensions in Euclidean space.