如何正确运用方差分析——分式析因设计定量资料一元方差分析与SAS实现

How to use analysis of variance correctly——an analysis of variance for the univariate quantitative data collected from the fractional factorial design

本文目的是介绍分式析因设计及其定量资料的方差分析和SAS实现。分式析因设计与析因设计及正交设计很相似,但又有一些区别。分式析因设计比相同规模的析因设计所需要的水平组合数少,甚至比相同规模的正交设计所需的样本含量更少。一般来说,分式析因设计所得结果的精确度低于正交设计,也远低于析因设计。分式析因设计适用于试验因素非常多的预试验,其主要目的是探索对定量试验结果影响比较大的试验因素。在对分式析因设计定量资料进行方差分析和回归分析时,应明确哪些因素或交互作用项之间出现了效应混杂。

The purpose of this paper was to introduce the fractional factorial design and its quantitative data analysis of variance and the SAS implementation.The fractional factorial designs were very similar to the factorial designs and the orthogonal designs,but they had some differences.The fractional factorial design required significantly fewer combinations of levels than the factorial design of the same size,and even saved sample size than the orthogonal design of the same size.In general,the precision of the results obtained by a fractional factorial design was lower than an orthogonal design and much lower than a factorial design.The fractional factorial design was suitable for the trial tests with many experimental factors,and its main purpose was to explore experimental factors that had a greater impact on the quantitative experimental results.When performing ANOVA and regression analysis on quantitative data with a fractional factorial design,it should be clear which factors or interactions had confounded effects.