中文摘要：

本文把α水平因子的平方和分解成相互正交的α-1个对照的平方和，这样总变差平方和就可以分解成α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．

英文摘要：

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.