| 胡纯严,胡良平.如何正确运用方差分析——方差齐性检验与SAS实现[J].四川精神卫生杂志,2022,35(1):11-15.Hu Chunyan,Hu Liangping,How to use analysis of variance correctly——the tests of homogeneity of variance and SAS implementation[J].SICHUAN MENTAL HEALTH,2022,35(1):11-15 |
| 如何正确运用方差分析——方差齐性检验与SAS实现 |
| How to use analysis of variance correctly——the tests of homogeneity of variance and SAS implementation |
| 投稿时间：2022-01-10 |
| DOI：10.11886/scjsws20220110005 |
中文关键词: 方差齐性检验 方差分析 变量变换 正态分布 F![]() ![]() 分布 |
| 英文关键词:Test of homogeneity of variance Analysis of variance Variable transformation Normal distribution F distribution |
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| 中文摘要: |
| 本文目的是介绍方差齐性检验与SAS实现。方差齐性检验可分为以下三类：①直接基于方差比较的方差分析法；②对原始数据经过变量变换后的新数据采取基于均值比较的方差分析法；③对符合正态分布的定量原始数据采取χ2检验法。在第一类中，直接基于两样本方差比构造出服从F分布的检验统计量；在第二类中，对原始数据有多种不同的变量变换方法，对变换后的新数据进行单因素多水平设计一元定量资料方差分析；在第三类中，对服从正态分布的定量资料构造χ2检验统计量。本文基于SAS软件对三个实例进行方差齐性检验，并对输出结果作出解释。 |
| 英文摘要: |
| The purpose of the paper was to introduce the test for homoscedasticity and the SAS implementation. The test of homogeneity of variance could be divided into the following three categories， ①analysis of variance directly based on comparison of variances， ②analysis of variance based on mean comparison was adopted for the new data from the variable transformation of the original data， ③the method of the χ2 test was used to analyze the quantitative raw data which followed the normal distribution. In the first category， a test statistic that followed the F distribution was constructed directly based on the variance ratio of the two samples. In the second category， there were a variety of different variable transformation approaches for the original data， and the new data after the transformation， which was viewed as the univariate quantitative data collected from a single-factor with multi-level design， was analyzed by using one-way ANOVA. In the third category， the χ2 test statistic was constructed for quantitative data that followed the normal distribution. The paper was based on SAS software to test the homogeneity of variances of three examples， and explained the output results. |
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