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.
ABSTRACT
The purpose of this paper was to outline the analysis of variance. Analysis of variance was a very important branch of statistics with rich contents and wide applicability. This paper summarized the analysis of variance from the following four aspects. Firstly， the basic concepts related to the analysis of variance. Secondly， the mathematical fundamentals of the analysis of variance， the F distribution. Thirdly， the application of the analysis of variance in the difference tests. Fourthly， the basic idea of the analysis of variance based on the comparison of means. In the first aspect， the definition， nature， meaning and contents of variance were mainly introduced. In the second aspect， the definition and nature of the F distribution were mainly introduced. In the third aspect， the analysis of variance in three kinds of application， namely the mean comparisons， the variance comparisons and the linear regression model evaluation were mainly introduced. In the fourth aspect， the core contents of the analysis of variance was the decomposition of the sum of squares of the total deviation from the mean and the construction of the test statistic F.