统计指数体系内在矛盾的破解

Solution of Inner Contradictions of the Statistical Index System

统计指数分析法是社会经济统计学的一种重要分析方法。但是,指数体系分析中可能出现的绝对数分析和相对数分析之间的矛盾问题,一直未能从理论上真正得到解决。本文从指数体系分析中矛盾现象的剖析入手,在回顾西方指数的偏误和检验理论的基础上,通过对相对数和绝对数关系的数学分析,得出了指数权偏误是指数体系矛盾现象的根源以及马埃指数近似地满足因子互换测验等重要结论。由此构建了基于马埃指数的"均值加权指数体系",并通过理论证明和实证分析,论证了"均值加权指数体系"的科学性。

Statistical index analysis is one of the most important methods in social and economic statistics. However,the great progress has not been made in statistical index theory for a long time because of the unsolved contradictions between absolute and relative measurements. This paper,starting from the paradox,reviews the bias and test theories of Statistical index in the West and concludes that the index weight bias is the cause of the problem through the mathematical analysis on the relation between the relative and absolute number. Meanwhile,it is found that Marshall-Edgenorth Index can approximately pass the factor reversal test. Then an ＂average weighted index system＂is created based on MarshallEdgenorth Index,and theoretical proof and empirical analysis shows that this system is scientific.