How to use analysis of variance correctly——an analysis of variance for the univariate quantitative data collected from the design of a single factor with multi-level

Abstract

The purpose of this paper was to introduce the prerequisites， basic ideas， calculation formulas and the SAS implementation of a single-factor multi-level design quantitative data univariate analysis of variance. The prerequisites included the independence， normality and homogeneity of variance. The core of the basic idea was the decomposition of the sum of squares of the total deviations for the mean. The test statistic F was constructed through the between-group mean square divided by the within-group （or called error） mean square. The result of analysis of variance was a general evaluation of the difference among all means of a factor with the whole levels. When it was found that the difference among all means of the factor was statistically significant， a specific approach needed to be adopted for the multiple comparisons about the multiple means of the factor. With the help of the SAS software， the paper performed the analysis of variances for two examples， and used three approaches to make the multiple comparisons among all means of a factor in one of the examples.

Keywords

• prerequisites
• sum of squared deviations from the mean
• analysis of variance
• multiple comparisons
• f distribution