无重复因析试验中多个散度效应检验的一种改进方法

A Modified Method for Testing Multiple Dispersion Effects in Unreplicated Factorial Experiments

在无重复因析试验的多个散度效应分析中,常常出现错误识别的现象,即两个显著的散度效应可能在它们的交互列上产生一个错误的散度效应,并且现有的许多方法都存在这样的问题.为了解决这种模棱两可性,McGrath和Lin(2001)提出了一种基于残差样本方差几何平均的检验方法(ML方法),但是这个方法不能应用于零残差样本方差的情形.鉴于此,提出了一种基于修改残差的改进方法,适用于零残差样本方差的情形,并且通过实例验证了方法的合理性.最后,通过模拟和ML方法做了比较.

In the analysis of multiple dispersion effects from unreplicated factorial experiments, there often exists the phenomenon for picking up factors spuriously, that is, two active dispersion effects may create a spurious dispersion effect in their interaction column, and most existing methods are subject to these spurious effects. To resolve the ambiguousness, McGrath and Lin （2001）[9] proposed a testing method based on geometric means of residual sample variances（ML method）. But the method cannot be suitable in situations with zero residual sample variances. We propose a modified method based on modified residuals and illustrate the rationality of proposed test through examples from the literature. Finally, a comparison is given between the method of ours and the ML method by simulations.