因子平方和的正交对照分解及其应用  

Orthogonal Contrasts Decomposition for Factor Sum of Squares and its Application

作　　者：孙法省[1] 刘民千[1] 

机构地区：[1]南开大学数学科学学院统计学系,天津300071

出　　处：《应用数学学报》2007年第4期757-765,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10671099号);高等学校博士学科点专项科研基金(20050055038号)资助项目.

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。In this paper, the sum of squares of an α-level factor is decomposed to α- 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 corresponding 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.

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 

分 类 号：O212.6[理学—概率论与数理统计]