| 因子平方和的正交对照分解及其应用 |
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| 引用本文： | 孙法省,刘民千.因子平方和的正交对照分解及其应用[J].应用数学学报,2007,30(4):757-765. |
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| 作者姓名： | 孙法省 刘民千 |
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| 作者单位： | 南开大学数学科学学院统计学系,天津,300071 |
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| 基金项目： | 国家自然科学基金;教育部高等学校博士学科点专项科研基金 |
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| 摘 要： | 本文把a水平因子的平方和分解成相互正交的a-1个对照的平方和,这样总变差平方和就可以分解成a个部分(包括残差项),然后又将该分解方法推广到了多因子的情形,并通过因子平方和的分解找到了多因子交互效应对应的对照向量,这使得多水平因子交互效应的计算和解释更加容易,也为方差分析带来了更多的方便,最后给出了几个应用示例。
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| 关 键 词： | 正交对照 因子平方和 总变差平方和 方差分析 正交表 |
| 修稿时间： | 2007-04-06 |
Orthogonal Contrasts Decomposition for Factor Sum of Squares and its Application |
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| SUN FASHENG,LIU MINQIAN.Orthogonal Contrasts Decomposition for Factor Sum of Squares and its Application[J].Acta Mathematicae Applicatae Sinica,2007,30(4):757-765. |
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| Authors: | SUN FASHENG LIU MINQIAN |
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| Institution: | Department of Statistics, School of Mathematical Sciences, Nankai University, Tianjin 300071 |
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| Abstract: | In this paper,the sum of squares of an a-level factor is decomposed to a-1 sums of squares of mutually orthogonal contrasts,such that the total variation sum of squares is decomposed to a parts including the residual sum of squares.Then this decomposition method is generalized to the multi-factor case,and the orthogonal contrast vectors corre- sponding to multi-factor interactions are obtained via this decomposition,which makes the computation and explanation of the interactions between multi-level factors easier,and also brings more convenience to the analysis of variance.Some application examples are provided at last. |
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| Keywords: | orthogonal contrast factor sum of squares total variation sum of squares analysis of variance orthogonal array |
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