| 胡纯严,胡良平.如何正确运用χ2检验——χ2分布及相关内容[J].四川精神卫生杂志,2021,34(1):39-43.Hu Chunyan,Hu Liangping,How to use χ2 test correctly——χ2 distribution and the related contents[J].SICHUAN MENTAL HEALTH,2021,34(1):39-43 |
| 如何正确运用χ2检验——χ2分布及相关内容 |
| How to use χ2 test correctly——χ2 distribution and the related contents |
| 投稿时间：2021-01-15 |
| DOI：10.11886/scjsws20210115002 |
| 中文关键词: χ2分布 正态分布 概率密度函数 自由度 χ2检验 拟合优度检验 |
| 英文关键词:χ2 distribution Normal distribution Probability density function Degrees of freedom χ2 test Goodness of fit test |
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| 中文摘要: |
本文目的是介绍χ2分布及相关内容，包括χ2分布和非中心χ2分布。着重展示了两种χ2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：①χ2分布的极限分布为正态分布；②n-1s2σ2![]() ![]() 服从自由度为n![]() ![]() -1的χ2分布。除此之外，还阐释了χ2分布与正态分布、χ2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χ２分布的计算方法。 |
| 英文摘要: |
The purpose of this article was to introduce the χ2 distribution and related contents， including χ2 distribution and non-central χ2 distribution. It focused on showing the definition of two χ2 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 the χ2 distribution was the normal distribution； second， n-1s2σ2![]() ![]() followed the χ2 distribution with n![]() ![]() -1 degrees of freedom.In addition， it also explained the relationship between the χ2 distribution and the normal distribution， the relationship between χ2 test statistic and Z test statistic. Finally， it illustrated the computational approaches of the χ2 distribution based on the two SAS functions in SAS software. |
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