【作者】 孙法省； 刘民千；

【Author】 SUN FA-SHENG,Liu MIN-QIAN(Department of Statistics,School of Mathematical Sciences,Nankai University,Tianjin 300071)

【机构】 南开大学数学科学学院统计学系；

【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,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。更多还原

【Abstract】 In this paper,the sum of squares of an a-level factor is decomposed toa-1 sums of squares of mutually orthogonal contrasts,such that the total variationsum of squares is decomposed to a parts including the residual sum of squares.Thenthis decomposition method is generalized to the multi-factor case,and theorthogonal contrast vectors corresponding to multi-factor interactions are obtainedvia this decomposition,which makes the computation and explanation of theinteractions between multi-level factors easier,and also brings more convenienceto the analysis of variance.Some application examples are provided at last.更多还原