RESUMO
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.
RESUMO
The purpose of the paper was to introduce the test for homoscedasticity and the SAS implementation. The test of homogeneity of variance could be divided into the following three categories， ①analysis of variance directly based on comparison of variances， ②analysis of variance based on mean comparison was adopted for the new data from the variable transformation of the original data， ③the method of the χ2 test was used to analyze the quantitative raw data which followed the normal distribution. In the first category， a test statistic that followed the F distribution was constructed directly based on the variance ratio of the two samples. In the second category， there were a variety of different variable transformation approaches for the original data， and the new data after the transformation， which was viewed as the univariate quantitative data collected from a single-factor with multi-level design， was analyzed by using one-way ANOVA. In the third category， the χ2 test statistic was constructed for quantitative data that followed the normal distribution. The paper was based on SAS software to test the homogeneity of variances of three examples， and explained the output results.
RESUMO
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.
RESUMO
The purpose of this paper was to introduce the factorial design and its quantitative data analysis of variance and the SAS implementation. Factorial design could not only present the main effect magnitude of all experimental factors， but also comprehensively reflected the size of each-order interaction effect among multiple factors. However， this design required a large sample size. This paper introduced the calculation formulas of the analysis of variance for quantitative data with two-factor factorial design， and realized the analysis of variance for quantitative data with two-factor and three-factor factorial design through two examples with the help of SAS software， and multiple comparisons of interaction effects were also performed.
RESUMO
The purpose of this paper was to introduce the orthogonal design and its quantitative data analysis of variance and the SAS implementation. From the perspective of degrees of freedom， the orthogonal design could be divided into the saturated orthogonal design and the unsaturated orthogonal design. From the perspective of the number of factor levels， the orthogonal design could be divided into the same level orthogonal design and the mixed level orthogonal design. From the perspective of normalization， the orthogonal design could also be divided into the standard orthogonal design and the non-standard orthogonal design. Quantitative data from the standard orthogonal designs could be analyzed by the conventional methods， while quantitative data from the non-standard orthogonal designs needed to be improved. Based on three examples， this paper realized the quantitative data analysis of variance with the standard orthogonal design without repeated experiments and with repeated experiments by means of the SAS software.