如何正确运用方差分析——拉丁方设计定量资料一元方差分析

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

本文目的是介绍拉丁方设计定量资料一元方差分析的计算公式和SAS实现。拉丁方设计可分为一般拉丁方设计与希腊拉丁方设计两大类,前者可以用于一个试验因素和两个区组因素的试验场合;后者可用于两个试验因素和两个区组因素的试验场合。事实上,还可以按是否进行重复试验和区组因素是否为单个体型,对拉丁方设计做进一步细分。一般来说,在对拉丁方设计定量资料进行方差分析时,除了应满足“独立性、正态性和方差齐性”的要求外,还要求所有因素之间的交互作用不存在或可以忽略不计。当定量资料不满足前述提及的前提条件时,建议采用混合效应模型建模并求解,或者基于广义估计方程方法求解方差分析模型中参数的估计值。

The purpose of this paper was to introduce the calculation formulas and the SAS implementation of the analysis of variance of the univariate quantitative data with the Latin square design.The Latin square design could be divided into two categories:the general Latin square design and the Greek Latin square design.The former could be used for the experimental situation with one experimental factor and two block factors,the latter could be used for the experimental situation with two experimental factors and two block factors.In fact,Latin square designs could be further subdivided by whether or not the repeated experiments were performed and whether the block factor was a single individual type.Generally speaking,in addition to satisfying the requirements of"independence,normality and homogeneity of variance",the interaction between all factors was required to be non-existent or negligible when performing an analysis of variance on the quantitative data with Latin square design.When the quantitative data did not meet the preconditions mentioned above,it was recommended to use a mixed-effects model to build the model and solve it,or to solve the estimated values of the parameters in the ANOVA model based on the generalized estimating equation method.