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

ABSTRACT

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.