| 正交平衡区组设计统计模型中的方差分析 |
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| 引用本文： | 田萍,廖靖宇,张应山,吴亚桢.正交平衡区组设计统计模型中的方差分析[J].数学的实践与认识,2013,43(10). |
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| 作者姓名： | 田萍 廖靖宇 张应山 吴亚桢 |
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| 作者单位： | 1. 许昌学院 数学与统计学院,河南 许昌,461000
2. 华东师范大学 金融与统计学院,上海,200241 |
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| 摘 要： | 正交平衡区组设计(或广义正交表)的数据分析类似于正交拉丁方(或正交表)的数据分析.利用类似于正交表数据分析中的投影矩阵的正交分解技术,研究正交平衡区组设计的统计分析模型,给出了方差分析中的二次型以及各因子的二次型的分布性质,从而给出正交平衡区组设计统计模型中的方差分析方法.
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| 关 键 词： | 正交表 区组设计 方差分析 |
Analysis of Variance for a Statistical Analysis Model of Orthogonal Balanced Block Designs |
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| TIAN Ping
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LIAO Jing-yu
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ZHANG Ying-shan
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WU Ya-zhen.Analysis of Variance for a Statistical Analysis Model of Orthogonal Balanced Block Designs[J].Mathematics in Practice and Theory,2013,43(10). |
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| Authors: | TIAN Ping LIAO Jing-yu ZHANG Ying-shan WU Ya-zhen |
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| Abstract: | Data analysis of orthogonal balanced block designs(or generalized orthogonal arrays) can be done similar to that of the orthogonal Latin squares(or orthogonal arrays) since the orthogonality of orthogonal balanced block designs(or generalized orthogonal arrays) is equivalent to that of projection matrices(or their matrix images).By using the orthogonal decomposition of projection matrices,the sum of square of the factors,the distributions of all quadratic form statistics in a statistical model of orthogonal balanced block designs,are discussed,the method of analysis of variance is given. |
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| Keywords: | orthogonal arrays block designs analysis of variance |
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