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| 合理进行均值比较——单组和配对设计 定量资料多元方差分析 |
| Reasonably carry out mean value comparison: MANOVA of the quantitative data collected from the single group design and the paired design |
| 投稿时间：2023-05-09 修订日期：2023-05-09 |
| DOI：10.11886/scjsws20230509002 |
| 中文关键词: 单组设计 配对设计 均值向量 方差协方差矩阵 多元方差分析 |
| 英文关键词:Single group design Paired design Mean vector Variance-covariance matrix Multivariate analysis of variance |
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| 中文摘要: |
| 【摘要】 本文目的是介绍与单组设计和配对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。基本概念包括单组设计与配对设计、均值向量、多元方差分析和前提条件；计算方法涉及一般检验统计量和Hotelling’s T2检验统计量；两个医学实例分别为“结核病患者营养状况的调查资料”和“石杉碱甲治疗增龄相关记忆障碍效果的试验资料”。借助SAS对两个医学实例中的定量资料分别进行一元和多元差异性分析，并对这两类分析方法的区别进行讨论。 |
| 英文摘要: |
| 【Abstract】 The purpose of this article was to introduce the basic concepts, calculation methods, two medical examples and SAS implementation related to the multivariate analysis of variance (MANOVA) for quantitative data with the single group design and the paired design. Basic concepts included the single group design and the paired design, mean vector, MANOVA and preconditions, calculation methods involved the general test statistics and Hotellings T2 test statistics, two medical examples were survey data on nutritional status of tuberculosis patients and trial data on the efficacy of huperzine A in the treatment of age-related memory impairment. With the help of SAS software, the univariate and multivariate difference analysis of quantitative data in two medical cases were carried out, and the differences between these two types of analysis approaches were discussed.
【Keywords】 Single group design; Paired design; Mean vector; Variance-covariance matrix; Multivariate analysis of variance
在医学研究中，由于所研究问题的复杂性，研究者不仅要考虑多个影响因素，而且，还要观测多个定量指标的取值，并希望采用多元统计分析方法将多个定量指标同时纳入统计分析中。在多元统计分析中[1-2]，最简单的统计分析方法是多元方差分析，它是一元定量资料t检验或方差分析的推广。对于不同的设计类型下收集的多元定量资料，需要采用相应的多元方差分析方法。本文将介绍2种最简单的设计类型（即单组设计和配对设计）下，多元定量资料的实例、多元方差分析的计算方法以及SAS实现。 |
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