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.
ABSTRACT
The purpose of this article was to introduce the likelihood ratio test and the SAS implementation. Specifically， three definitions of the likelihood ratio test statistics and six more commonly used likelihood ratio test statistics were introduced. The three definitions were called based on the spatial size of the parameter vector to construct the likelihood ratio test statistic， based on the two nested statistical models to construct the likelihood ratio test statistic and based on the full model and partial model to construct the likelihood ratio test statistic； the six commonly used likelihood ratio test statistics were the general likelihood ratio χ2 test statistic，the adjusted likelihood ratio χ2 test statistic，the profile likelihood ratio χ2 test statistic，the quasi-likelihood ratio χ2 test statistic，the pseudo-likelihood ratio χ2 test statistic，and the Rao-Scott likelihood ratio χ2 test statistic. In the paper， through two examples， and with the help of the SAS software， the likelihood ratio χ2 tests were realized， the SAS calculation results were output and explained， and statistical and professional conclusions were made.