非正交试验的平方和分解及其应用

在方差分析中,平方和分解占有很重要的地位.在正交试验里,可以将平方和分解为各效应平方和和误差平方和之和,且使各效应平方和相互独立,从而对各效应假设分别作F 检验.但在实际中,我们经常碰到的数据并不是正交的,此时用最小二乘法得到的估计,其总平方和不再等于各效应平方和与误差平方和之和,而且计算复杂,应用起来极不

THE DECOMPOSITION OF THE SUM OF SQUARE IN UNBALANCED EXPERIMENTAL DESIGN AND ITS APPLICATION

In the unbalanced two-way model,the total sum of squares can not be decomposed be-cause the unbalance of design.In this paper,in terms of design matrix,we view the balance ofexperiment as the independence of design distribution,and then introduce the design weightto obtain the weighted least square estimation so that the total sum of squares can be decompo-sed.The distributions of the various sums of squares are derived and the associated F tests arestudied.The simulation and comparison indicate that this method is valuable under the permit-ted significance of the independence of design distribution.Finally,we discuss its applicationin the selection of regression terms in regression model.