How to use analysis of variance correctly——an analysis of variance for the univariate quantitative data collected from the Latin square design / 四川精神卫生

ABSTRACT

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.