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| 合理进行均值比较——单因素两水平 和多水平设计定量资料多元方差分析 |
| Reasonably carry out mean value comparison: MANOVA of the quantitative data collected from single factor two-level and multi-level design |
| 投稿时间：2023-05-09 修订日期：2023-05-09 |
| DOI：10.11886/scjsws20230509003 |
| 中文关键词: 单因素多水平设计 协变量 多元方差分析 多元协方差分析 两两比较 |
| 英文关键词:Single factor multilevel design Covariate Multivariate analysis of variance Multivariate analysis of covariance Pairwise comparison |
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| 中文摘要: |
| 【摘要】 本文目的是介绍与单因素两水平和多水平设计定量资料多元方差分析有关的基本概念、计算方法、两个医学实例以及SAS实现。基本概念包括试验因素与属性因素、方差分析与协方差分析、自变量与协变量、矩阵与行列式；计算方法涉及一般统计量、4个多元方差分析检验统计量和多个均值向量的两两比较；两个医学实例分别为“2种脱机方式下患者脱机前有关定量指标的测定结果”和“3种不同类型地区8岁男童的生长发育调查数据”。借助SAS对两个实例中的定量资料分别进行多元方差分析和协方差分析，并对如何合理选取协变量进行阐释和讨论。 |
| 英文摘要: |
| 【Abstract】 The purpose of the paper was to introduce the basic concepts, calculation methods, two medical examples and SAS implementation related to the multivariate analysis of variance (MANOVA) for the quantitative data with single factor two-level and multi-level design. Basic concepts included experimental factors and attribute factors, analysis of variance and covariance, independent variables and covariates, matrix and determinant. Calculation methods involved the general statistics, 4 MANOVA test statistics and pairwise comparison of multiple mean vectors. The two medical examples were measurement results of quantitative indicators related to patients before taking offline under two types of offline modes and investigation data on growth and development of 8-year-old boys in three different types of areas. With the help of SAS software, the multivariate analysis of variance and covariance were carried out on the quantitative data in the two cases, and how to reasonably select covariates was explained and discussed. |
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