| 胡纯严,胡良平.如何正确运用方差分析——单因素多水平设计定量资料一元方差分析[J].四川精神卫生杂志,2022,35(1):16-20.Hu Chunyan,Hu Liangping,How to use analysis of variance correctly——an analysis of variance for the univariate quantitative data collected from the design of a single factor with multi-level[J].SICHUAN MENTAL HEALTH,2022,35(1):16-20 |
| 如何正确运用方差分析——单因素多水平设计定量资料一元方差分析 |
| How to use analysis of variance correctly——an analysis of variance for the univariate quantitative data collected from the design of a single factor with multi-level |
| 投稿时间：2022-01-10 |
| DOI：10.11886/scjsws20220110006 |
| 中文关键词: 前提条件 离均差平方和 方差分析 多重比较 F分布 |
| 英文关键词:Prerequisites Sum of squared deviations from the mean Analysis of variance Multiple comparisons F distribution |
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| 中文摘要: |
| 本文目的是介绍单因素多水平设计定量资料一元方差分析的前提条件、基本思想、计算公式和SAS实现。前提条件包括独立性、正态性和方差齐性；基本思想的核心是对总离均差平方和的分解；检验统计量F由组间均方除以组内（或称为误差）均方构造而成。方差分析结果是关于某因素全部水平下均值之间差异情况的一个概括性评价，当得出该因素全部均值之间的差异有统计学意义时，需要采取特定的方法对该因素的多个均值进行多重比较。本文借助SAS软件，对两个实例进行方差分析，并采用三种方法对其中一个实例的多个均值之间进行多重比较。 |
| 英文摘要: |
| The purpose of this paper was to introduce the prerequisites， basic ideas， calculation formulas and the SAS implementation of a single-factor multi-level design quantitative data univariate analysis of variance. The prerequisites included the independence， normality and homogeneity of variance. The core of the basic idea was the decomposition of the sum of squares of the total deviations for the mean. The test statistic F was constructed through the between-group mean square divided by the within-group （or called error） mean square. The result of analysis of variance was a general evaluation of the difference among all means of a factor with the whole levels. When it was found that the difference among all means of the factor was statistically significant， a specific approach needed to be adopted for the multiple comparisons about the multiple means of the factor. With the help of the SAS software， the paper performed the analysis of variances for two examples， and used three approaches to make the multiple comparisons among all means of a factor in one of the examples. |
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