如何正确运用χ^(2)检验——χ^(2)分布及相关内容

How to use χ^(2) test correctly——χ^(2) distribution and the related contents

本文目的是介绍χ^(2)分布及相关内容,包括χ^(2)分布和非中心χ^(2)分布。着重展示了两种χ^(2)分布的定义、概率密度函数的图形和主要性质,其中,两个最重要的性质分别是:①χ^(2)分布的极限分布为正态分布;②(n-1)s^(2)σ^(2)服从自由度为n-1的χ^(2)分布。除此之外,还阐释了χ^(2)分布与正态分布、χ^(2)检验统计量与Z检验统计量之间的关系。最后,基于SAS软件中的两个SAS函数呈现了χ^(2)分布的计算方法。

The purpose of this article was to introduce theχ^(2)distribution and related contents,includingχ^(2)distribution and non-centralχ^(2)distribution.It focused on showing the definition of twoχ^(2)distributions,the graph and the main properties of the probability density function.Among them,the two most important properties were:first,the limiting distribution of theχ^(2)distribution was the normal distribution;second,(n-1)s^(2)σ^(2)followed theχ^(2)distribution with n-1 degrees of freedom.In addition,it also explained the relationship between theχ^(2)distribution and the normal distribution,the relationship betweenχ^(2)test statistic and Z test statistic.Finally,it illustrated the computational approaches of theχ^(2)distribution based on the two SAS functions in SAS software.