| 胡纯严,胡良平.如何正确运用方差分析——方差分析概述[J].四川精神卫生杂志,2022,35(1):6-10.Hu Chunyan,Hu Liangping,How to use analysis of variance correctly——an overview of analysis of variance[J].SICHUAN MENTAL HEALTH,2022,35(1):6-10 |
| 如何正确运用方差分析——方差分析概述 |
| How to use analysis of variance correctly——an overview of analysis of variance |
| 投稿时间：2022-01-10 |
| DOI：10.11886/scjsws20220110004 |
| 中文关键词: 方差 离均差平方和 全模型 部分模型 F分布 |
| 英文关键词:Variance Sum of squared deviations from the mean Full model Partial model F distribution |
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| 中文摘要: |
本文目的是概述方差分析。方差分析是统计学中一个非常重要的分支，其内容丰富、适用面宽。本文将从以下四个方面对方差分析进行概述：①与方差分析有关的基本概念；②方差分析的数学基础——F分布；③方差分析在差异性检验中的应用场合；④基于均值比较的方差分析基本思想。在第一方面内容中，重点介绍方差的定义、性质、意义和内容；在第二方面内容中，重点介绍F分布的定义与性质；在第三方面内容中，重点介绍三种应用场合下的方差分析，即均值比较、方差比较和线性回归模型评价；在第四方面内容中，重点阐释方差分析的核心内容，即总离均差平方和的分解以及检验统计量F![]() ![]() 的构造。 |
| 英文摘要: |
| The purpose of this paper was to outline the analysis of variance. Analysis of variance was a very important branch of statistics with rich contents and wide applicability. This paper summarized the analysis of variance from the following four aspects. Firstly， the basic concepts related to the analysis of variance. Secondly， the mathematical fundamentals of the analysis of variance， the F distribution. Thirdly， the application of the analysis of variance in the difference tests. Fourthly， the basic idea of the analysis of variance based on the comparison of means. In the first aspect， the definition， nature， meaning and contents of variance were mainly introduced. In the second aspect， the definition and nature of the F distribution were mainly introduced. In the third aspect， the analysis of variance in three kinds of application， namely the mean comparisons， the variance comparisons and the linear regression model evaluation were mainly introduced. In the fourth aspect， the core contents of the analysis of variance was the decomposition of the sum of squares of the total deviation from the mean and the construction of the test statistic F. |
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