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The purpose of this paper was to introduce how to reasonably analyze the multiple Logistic regression models in combination with the multilevel model analysis. Firstly， four basic concepts related to the multilevel model analysis were introduced. Secondly， three steps for building a multilevel model were given. Thirdly， through an example of a multicenter drug clinical trial， the whole process of how to use SAS software for the analysis was presented. The contests were as follows： ① testing whether the odds ratios of each center were homogenous； ② building the multiple Logistic regression model after generating dummy variables for the trial center； ③ constructing a multiple Logistic regression model with the trial center as a stratified variable； ④ building a random intercept multilevel multiple Logistic regression model； ⑤ constructing a random intercept and random slope multilevel multiple Logistic regression model. The conclusion was that when there were differences among the data at different hierarchies with binary outcome variables， the most appropriate approach was to build a multilevel multiple Logistic regression model.

The purpose of the paper was to introduce how to reasonably carry out multiple Logistic regression analysis combined with the average treatment effect analysis. Firstly， it introduced 4 basic concepts related to the average treatment effect analysis. Secondly， it presented the core contents in the average treatment effect analysis， that was， six estimation methods. Thirdly， through a hypothetical drug clinical trial example， it gave the whole process of how to use SAS software for the analysis. The contests were as follows： ① the traditional multiple Logistic regression model was used for the analysis； ② the propensity score model was used to calculate the inverse probability weights； ③ six estimation methods were used to estimate the potential outcome mean and the average treatment effect.

The purpose of this paper was to introduce how to combine the propensity score analysis to reasonably carry out multiple linear regression analysis. Firstly， it introduced 3 basic concepts related to the propensity score analysis. Secondly， it presented the core contents of the propensity score analysis， that was， three matching methods. Thirdly， through an epidemiological survey example， it gave the whole process of how to use SAS software for the analysis. The contents were as follows： ① for the original data set， test whether the difference of covariates between the treatment group and the control group was statistically significant； ② directly implement the multiple linear regression analysis for the original data set； ③ the propensity score analysis was used to generate the matched data set； ④ for the matched data set， test whether the difference of covariates between the treatment group and the control group was statistically significant； ⑤ a reasonable multiple linear regression analysis was used for the matched data set.

The purpose of this paper was to introduce how to reasonably carry out the method of the multiple Logistic regression analysis by combining the ROC curve analysis. Firstly， it introduced two groups of the basic concepts related to the ROC curve analysis， that was， the statistical description of common diagnostic indicators and the ROC curve analysis method of the diagnostic data. Secondly， it introduced the core contents of the ROC curve analysis， that was， the calculation of the area under the ROC curve and the comparison of the area under multiple ROC curves. Thirdly， through an example of a diagnostic test， the whole process of how to use SAS software for the analysis was introduced， the contents were as follows： ① the analysis using only multiple Logistic regression analysis； ② the multiple Logistic regression analysis combined with the ROC curve analysis. The conclusion was that， for the diagnostic test data， combining the multiple Logistic regression analysis with the ROC curve analysis could obtain richer and more reasonable statistical analysis results.

The purpose of this paper was to introduce the theoretical basis of the causal mediation effect analysis and the specific method to realize an example by the causal mediation effect analysis with SAS. The theoretical basis of the causal mediation effect analysis included the following two aspects， the basic concept and defining the counterfactual framework of the causal mediation effect. The example was about whether the encouraging environment provided by parents would affect the cognitive development of children. The traditional multiple linear regression analysis， the causal mediation effect analysis without considering covariates and with considering covariates were used， respectively. By comparing the results obtained by the three analysis methods， the following conclusions were drawn： ① when there were the mediation variables in the data， it was not suitable to use traditional multiple linear regression analysis to replace the causal mediation effect analysis； ② when there were covariates in the data， it was not suitable to conduct causal mediation analysis under the condition of ignoring covariates.

The purpose of this paper was to introduce how to set the options of variable levels and multimodal covariates， and to demonstrate the causal mediation effect analysis method with odds ratio （OR） and excess relative risk （ERR） as evaluation indicators through examples. For treatment variables， mediator variables and covariates， the variable-level options of them could be set through the evaluate statement. For categorical variables and their interaction terms， they could be treated as multimodal covariates， and the variable levels could also be set for them by using the evaluate statement. Through an example， this paper used SAS to realize the causal mediation effect analysis and the decomposition of effect components with OR and ERR as the evaluation indicators.

The purpose of this paper was to introduce five key techniques and the multi-directional decomposition methods of effect components in the analysis of causal mediation effects. The contents of the five key technologies were as follows： ① identification of causal mediation effect； ② regression method of causal mediation effect analysis； ③ maximum likelihood estimation； ④ estimation of total effect and various component effects； ⑤ estimation by bootstrap method. The multi-directional decomposition methods included 3 bidirectional decompositions， 2 three-directional decompositions and 1 four-directional decomposition. Through an example， a causal mediation effect analysis model including covariates and interaction terms was constructed with the help of SAS， bidirectional decomposition， three-directional decomposition and four-directional decomposition were carried out for the total effect in the causal mediation effect analysis， and the output results were explained.

The purpose of this paper was to introduce the setting method of the three types of variable levels in the causal mediation effect analysis and the implementing calculation method under the condition of stratification by using SAS. The setting of the three types of variable levels referred to the setting of the levels of treatment variable， the mediator variable and the covariate. Besides， a specific level combination could also be set for two variables. Through an example， with the help of the enveluate statement in proc causualmed procedure， this paper used an example to conduct the causal mediation effect based on different variable stratification， and gave the output results and explanations.

The purpose of this paper was to introduce the five limitations of the PROC CAUSALGRAPH procedure and estimate the causal effect of the data by using the adjustment set based on the causal graph model. The five limitations were as follows： ①the PROC CAUSALGRAPH procedure could not deal with the causal graph model of directed circles； ② the PROC CAUSALGRAPH procedure could not evaluate dynamic processing scheme； ③ causal effect identification was a population concept； ④ causal effect identification was a nonparametric concept； ⑤ the PROC CAUSALGRAPH procedure could not identify the causal effect in some causal graph models. The example was for a simulated data set， using the conventional multiple Logistic regression model analysis and the causal graph model analysis， respectively. By comparing the analysis results of the two， the following conclusions were drawn： ① causal graph theory was useful in identifying causal effects in confounding situations； ② by implementing hierarchical estimation of causal effects， a good statistical estimation of causal effects could be achieved based on the identification results of the PROC CAUSALGRAPH procedure.

The purpose of this paper was to introduce the method of checking adjustment sets based on a causal graph model， finding common adjustment sets and implementing the statistical calculation with SAS software. Firstly， the basic concepts related to the causal graph model were introduced.Secondly， the primary contents of the causal graph theory were given， including the composition and terminology of the causality diagram. Finally， for the two instances and with the help of the CAUSALGRAPH procedure in SAS/STAT， the following two tasks were completed： the first task was to examine the adjustment set and enumerate paths； the second task was to find the adjustment set common to the multiple causal graph models.

The purpose of this paper was to introduce the basic knowledge of the causal graph model， the contents of the CAUSALGRAPH procedure and the method of constructing and searching adjustment sets based on the CAUSALGRAPH procedure in SAS/STAT. The causal graph model was the product of the combination of graph theory and probability theory. It could find all possible adjustment sets including the minimum adjustment set based on the action relationship between the variables set by the user. The contents of the CAUSALGRAPH procedure mainly included three identification criteria， two operating modes and one verification checking method. This paper analyzed the causal effect of two instances based on the CAUSALGRAPH procedure in SAS， and explained the output results.

The purpose of this paper was to introduce the methods of identifying causal effects based on instrumental variables， distinguishing different models with data， and using SAS software to realize calculation. Firstly， the four main contents of causal graph theory were introduced， including sources of association， statistical properties of causal models， identification and adjustment， and instrumental variables. Secondly， for two examples and with the help of the CAUSALGRAPH procedure in SAS/STAT， the following two tasks were completed： the first task was to identify causal effects using instrumental variables； the second task was to use data to distinguish different models.

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.

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.

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.

The purpose of this paper was to introduce the nested design and its quantitative data analysis of variance and the SAS implementation. If one of the following two characteristics existed in a specific experimental study， a nested design could be considered to arrange the experiment. Firstly， there was a nested relationship between factors in natural attributes. Secondly， with professional knowledge as the basis， the impact of each factor on the quantitative observation results was divided into primary and secondary. The first feature mentioned above meant that the factors related to the subjects had the conditions for grouping and regrouping. The second feature mentioned above meant that the status of each factor was unequal. In the variance analysis of quantitative data， the calculation formulas of variable error mean square was required to use. Based on four examples and with the help of the SAS software， this paper implemented the univariate analysis of variance for the quantitative data of the nested design， and gave the detailed explanations for the output results of SAS software.

The purpose of the paper was to introduce the calculation formulas and the SAS implementation of the analysis of variance for the quantitative data of the crossover design. In the calculation， three test statistics were involved， namely Ftreatment， Fstage and Findividual. They were three test statistics used to evaluate the statistical significance of the effect of the treatment factor， the stage factor， and the individual factor on the quantitative outcome variable， respectively. In general， it was assumed that there was no or negligible interaction among the three factors in a crossover design， so there was no need to evaluate whether the interaction term was statistically significant. With the help of SAS software， this paper conducted the univariate analysis of variance for the quantitative data of crossover designs for three examples of 2×2 crossover design， 3×3 crossover design and three-stage crossover design， and presented the calculation results and drew the statistical and professional conclusions.

The purpose of this paper was to introduce the model， calculation formulas and the SAS implementation of the univariate analysis of variance for the quantitative data with randomized complete block design. In the calculation， two test statistics were involved， namely FA and FB. Among them， the subscript "A" represented the experimental factor， and the subscript "B" represented the block factor （i.e.， the important non-experimental factor）. In general， it was assumed that there was no or negligible interaction between the two factors in a randomized block design， so there was no need to assess whether the interaction term was statistically significant. Therefore， it was not necessary to do repeated experiments under each combination of two factors. With the help of SAS software， this paper conducted the analysis of variance for the quantitative data with randomized complete block design for two instances without and with repeated experiments， gave the calculation results， and made the statistical and professional conclusions.

The purpose of this paper was to introduce the model， calculation formulas and the SAS implementation of the analysis of variance for the quantitative data with balanced incomplete block design. In the calculation， two test statistics were involved， namely FA and FB. Among them， the subscript "A" represented the experimental factor， and the subscript "B" represented the block factor B （i.e.， the important non-experimental factor）. In general， it was assumed that there was no or negligible interaction between the two factors in a balanced incomplete block design， so there was no need to evaluate whether the interaction term was statistically significant. Therefore， it was not necessary to do repeated experiments under each combination of two factors. With the help of SAS software， this paper conducted the analysis of variance for the quantitative data with balanced incomplete block design on two examples， and presented the calculation results and made the statistical and professional conclusions.

The purpose of this paper was to introduce the calculation formulas and the SAS implementation of the analysis of variance of the univariate quantitative data with the Latin square design. The Latin square design could be divided into two categories： the general Latin square design and the Greek Latin square design. The former could be used for the experimental situation with one experimental factor and two block factors， the latter could be used for the experimental situation with two experimental factors and two block factors. In fact， Latin square designs could be further subdivided by whether or not the repeated experiments were performed and whether the block factor was a single individual type. Generally speaking， in addition to satisfying the requirements of "independence， normality and homogeneity of variance"， the interaction between all factors was required to be non-existent or negligible when performing an analysis of variance on the quantitative data with Latin square design. When the quantitative data did not meet the preconditions mentioned above， it was recommended to use a mixed-effects model to build the model and solve it， or to solve the estimated values of the parameters in the ANOVA model based on the generalized estimating equation method.

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.

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.

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.

The purpose of the paper was to introduce the multiple comparison method among multiple means and the SAS implementation. The multiple comparison approaches could be subdivided into the pairwise comparisons， the comparisons of all treatment groups with a control group， the comparisons of the mean of each treatment group with the average of all groups， the approximate and simulation-based approach， the multi-stage testing and Bayesian method. Except for the Bayesian approach， the difference between other multiple comparison methods lied in the types of error that were controlled. Error types could be roughly divided into the following three categories， the comparisonwise error rate， the experimentwise error rate and the maximum experimentwise error rate. The multiple comparison methods constructed based on the control of different error rates were not all the same in the strength of inference to draw conclusions. This paper used the SAS software to analyze the examples and explained the output results.

The purpose of this article was to introduce the Wald΄s test and the SAS implementation. The specific contents involved the following nine aspects， namely the general Wald΄s test，the robust Wald΄s test，the constrained Wald΄s χ2 test，the generalized Wald΄s test，the generalized Wald΄s log-linear test，the Wald΄s F test，the Wald΄s adjusted F test，the Wald΄s log-linear F test and the adjusted Wald΄s log-linear F test. The paper used two examples and the SAS software to achieve most of the Wald΄s tests mentioned above.

The purpose of this article was to introduce the score test and the SAS implementation. Concretely， there were five common forms of the score test statistics， namely the general score test statistic，the robust score test statistic，the residual score test statistic，the generalized score test statistic，and the Lagrange multiplier test statistic. The score test was mainly used in the following three situations， namely， testing whether part or all of the regression coefficients were 0， testing whether a single effect was not in the regression model，and testing whether the parallel line hypothesis was established. The paper used two examples and the SAS software to realize the various score tests mentioned above， and focused on explaining the output results related to the score tests.

The purpose of this article was to introduce the log-rank test and the SAS implementation. There were many different expression forms for the test statistics of the log-rank tests. Among them， there were two most common expression forms： the first was similar to "Pearson΄s goodness-of-fit χ2 test statistic"； the second was similar to "the test statistic of the odds ratio of high-dimensional table data， that was， the Breslow-Day΄s χ2 test statistic". The log-rank test statistic had two distribution types， one was the χ2 distribution， the other was the standard normal distribution. In the process of constructing log-rank test statistics， there were four contents that needed to be paid attention to： ① the sequential multiple four-fold tables formed by stratification or partition after sorting according to the individual "survival time"； ② it was necessary to distinguish whether the "survival time of each individual" was the complete data or the censored data； ③ only the calculation of the "theoretical or expected frequency" on a specific grid ［for example， （1，1） grid］ in each four-fold table data； ④ the method of calculating the theoretical frequency was different from the one in the independent test of the data of the four-fold table. Based on two examples with the different data structures， the paper realized the log-rank tests with the help of the SAS software.

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.

The purpose of this article was to introduce the rank sum test and its SAS implementation. The concrete contents included the following three aspects： ①the simple linear rank test of two-sample data， ②the one-way ANOVA rank sum test of the multi-sample data， ③the "scoring methods" in the aforementioned two situations. In the third aspect above， there were 10 concrete scoring approaches. Based on an example and with the aid of the SAS software， the paper implemented the first-type rank sum test previously， explained the output results， and made statistical and professional conclusions.

The purpose of this article was to introduce the likelihood ratio test， six nonparametric tests， and the SAS implementation of the survival data. Based on the assumption that the survival data had the exponential distribution， the likelihood ratio test method was derived， the main difference between six nonparametric test methods was that they had different weight functions. Under the conditions of non-stratification and stratification， the seven survival data hypothesis testing methods mentioned above could be used， and their common point was that their test statistics all followed the χ2 distribution. Through two examples and by means of the SAS software， the article realized the various hypothesis tests for two or more groups of survival data， outputed and explained SAS calculation results， and made statistical and professional conclusions.

The purpose of this article was to introduce the goodness of fit test and its SAS implementation. The main contents included the following four aspects： ① Pearson΄s goodness of fit test； ② deviance or likelihood ratio goodness of fit test； ③ Hosmer-Lemeshow goodness of fit test； ④ goodness of fit test for the sparse data. In the aforementioned “fourth aspect”， there were six specific test approaches， namely “information matrix test” “information matrix diagonal test” “Osius-Rojek test” “unweighted residual sum of squares test” “Spiegelhalter test” and “Stukel test”. The paper implemented the four types of the goodness of fit tests mentioned above with the help of the SAS software through an example， explained the output results， and made statistical and professional conclusions.

The purpose of the paper was to introduce the three special tests of the survival data and the SAS implementation. Specifically， it was the multiple comparisons， the trend test and the covariate test of the survival data. The multiple comparisons involved two situations： "the pairwise comparison" and "the comparison with control group". In the trend test， it involved two algorithms： "the log-rank test" and "the Wilcoxon test". In the covariate test， it involved "the single covariate test method" and "the multi-covariate test method of adding one covariate step by step". With the help of the SAS software and based on an example， this article implemented the three special tests mentioned above， explained the output results， and made statistical and professional conclusions.

The purpose of this article was to introduce the risk rate difference analysis method of the g×2×2 table data and the calculation method based on the SAS software. The tasks that needed to be completed included the following two terms： first， the point estimation of the common risk rate difference and its confidence interval estimation； second， the test "whether the common risk rate difference was equal to 0". Among them， there were a total of 6 approaches for achieving the aforementioned first task； and three approaches for achieving the aforementioned second task. Based on the SAS software and an example， the article realized the point estimation， the confidence interval estimation and the hypothesis test of the common risk rate difference， respectively. Next， the SAS output results were explained and the statistical and professional conclusions were made.

The purpose of this paper was to introduce the methods of the "layered person-time data" rate ratio analysis and the SAS implementation. The specific contents included the following four aspects： ① the point estimation and the confidence interval estimation of the layer i rate ratio in the stratified person-time data； ② the homogeneity test of the rate ratios among the different layers； ③ the point estimation and the confidence interval estimation of the common rate ratio； ④ the linear trend test of the incidence density in the stratified person-time data. Through two examples， it showed the statistical calculation process based on the SAS software to realize the aforementioned four kinds of the analysis contents， including providing the SAS program code， the explanation of the SAS output results， and giving the statistical and professional conclusions.

The purpose of this article was to introduce the methods for the independence test of a special high-dimensional table （ie g×2×2 table） and its SAS implementation. There were three approaches， in the SAS software and the statistical textbooks， which could be used to perform the independence test for the data of a multiway table. The three kinds of methods were the generalized CMH χ2 test （for short， approach-1）， the weighted χ2 test with the weighted coefficients in its formula （for short， approach-2）， and the weighted χ2 test without the weighted coefficients in its formula （for short， approach-3）， respectively. This article revealed that the “approach-2” and “approach-3” were the same weighted χ2 test essentially， but with different manifestations. It also revealed that the weighted χ2 test statistic estimation was approximately equal to the CMH χ2 test statistic estimation in the “approach-1”. Based on an example and the SAS software， the article introduced the concrete approaches for the independence test of the g×2×2 table data， explained the output results， and made the statistical and professional conclusions.

The purpose of this paper was to introduce the independence test and the SAS implementation for the "unstratified person-time data" and the "stratified person-time data". In "person-time data"， the sample size in each level of the treatment factor was expressed as "person-years". Furthermore， it was necessary to use the "incidence density" to replace the "incidence rate" in the usual qualitative data analysis. The paper introduced the concrete approaches of comparing the "incidence density" of the "unstratified person-time data" and the "stratified person-time data" in detail， and demonstrated the whole process of using SAS software to realize the calculation through two examples， including the SAS program code， the SAS output results， the results explanation and the conclusion statement.

The purpose of the paper was to introduce the relative risk analysis method of g×2×2 table data and the calculation method based on SAS software. The contents included the following aspects： firstly， the homogeneity test of the data in the g×2×2 table was performed； secondly， when the data met the homogeneity requirements， the point estimation and confidence interval estimation of the common relative risk based on the correction method were implemented； thirdly， when the data did not meet the requirements of homogeneity， the common relative risk RRDL and its 95% confidence interval were estimated， based on the DerSimonian-Laird method （DL method for short）； fourthly， when the data met and did not meet the requirements of homogeneity， the hypothesis of "whether the common relative risk equals to 1" was tested. Combining two examples and based on SAS software， the paper completed the following three tasks： ① the homogeneity test for the relative risk； ② the point estimation of the common relative risk； ③the confidence interval estimation of the common relative risk. The last two tasks were performed under the conditions of the data met and did not meet the homogeneity requirements， respectively. The output results of SAS software were explained， and the statistical and professional conclusions were made.

The purpose of this article was to introduce the types of a multiway table data and their corresponding statistical analysis methods. Based on the data types of the result variables， common high-dimensional table data could be divided into the following three categories， namely， the high-dimensional table data with binary variables， multi-valued nominal variables and multi-valued ordinal variables as the result variables. There were two main categories of the statistical analysis methods for the multiway table data. The first category was the generalized difference analysis， in which the contents included "weighted χ2 test""CMH χ2 test" and "Meta analysis"， the second category was the regression analysis， in which the contents included "log linear regression model analysis""Logistic regression model analysis" "probit regression model analysis" and "discrete choice model analysis".

The purpose of the paper was to introduce the methods for the homogeneity test of odds ratio of a special multiway table （i.e g×2×2 table） and its SAS implementation. In the FREQ procedure of SAS/STAT， five approches for the homogeneity tests of odds ratio were introduced in detail. They were "Breslow-Day test""Breslow-Day-Tarone test""Q test""I2 measurement statistic and its uncertainty limit" and "Zelen΄s exact test". In addition， the approaches for "the homogeneity tests of the relative risk and the difference of the risk rate" were also introduced. Combining two examples， the article introduced the concrete content of the homogeneity test for the odds ratio based on SAS software， explained the output results， and concluded the statistical and professional conclusions.

The purpose of this article was to introduce the odds ratio analysis method of g×2×2 table data and the calculation method based on SAS software. The contents included the following aspects： firstly， the homogeneity test of the odds ratio of the data in the g×2×2 table was performed； secondly， when the data met the homogeneity requirements， point estimation and confidence interval estimation for the common odds ratio based on the correction method were implemented； thirdly， when the data did not meet the homogeneity requirements， based on the approach of "the conditional distribution of the frequency in the （1，1） grid in each layer 2×2 table" ， these things， such as the point estimation and confident interval estimation as well as hypothesis testing about the common odds ratio， were accurately estimated and performed. All calculations were realized based on the FREQ procedure in SAS/STAT by means of two real examples. Furthermore， the output results of SAS software were explained， and the statistical and professional conclusions were made.

The purpose of this article was to introduce the χ2 test and SAS and R software implementation of three kinds of two-way unordered two-dimensional contingency table data except the four-fold table data. The three kinds of the tables referred to the two-way unordered “R×2”“2×C” and “R×C” （both R and C were greater than 2） contingency tables. Generally speaking， the purpose of analyzing them was to test whether the two attribute variables in the contingency table were independent. When certain prerequisites were met， the simple statistical analysis method that could be used was the χ2 test， when the specific prerequisites were not met， the Fisher’s exact test， which required the large amount of calculation， should be selected.

The purpose of this paper was to introduce the linear trend χ2 tests for the data of the two kinds of one-way ordinal two-dimensional contingency tables and the implementation of SAS and R software. The two one-way ordered two-dimensional contingency tables referred to the “R×2 contingency table” with R values ordinal variable as the cause variable and the “2×C contingency table”with C values ordinal variable as the outcome variable. Their linear trend tests required the use of the Cochran-Armitage’s linear trend χ2 test and the Lee’s linear trend χ2 test， respectively.

The purpose of this paper was to introduce the CMH χ2 test and SAS software implementation of the three kinds of R×C contingency table data. The first type was called “two-way unordered R×C contingency table data”. The CMH χ2 test corresponding to this type of data was essentially the Pearson’s χ2 test. The second type was called “R×C contingency table data with an ordinal outcome variable”. The CMH χ2 test corresponding to this kind of data was essentially a rank sum test. The third type was called “R×C contingency table data which was of two ordinal variables with different attributes”. The CMH χ2 test corresponding to the data was essentially Pearson’s correlation analysis or Spearman’s rank correlation analysis. When there were 1 or 2 “ordinal variables” in the R×C contingency table data， it was necessary to “assign or score” the ordinal variables before performing statistical analysis. In the FREQ procedure of SAS/STAT， there were four scoring methods. With different scoring approach， both the expression form and the calculation results of CMH χ2 test statistics could change accordingly.

The purpose of this paper was to introduce the χ2 test for the data of four-fold tables collected from the case-control design， the hypothesis test and interval estimation of odds ratio， and the implementation of SAS and R software. In view of the characteristics of case-control design， the concept of odds ratio， hypothesis testing and interval estimation were emphasized. It was given that the interpretation of the results calculated by SAS and R software， as well as the statistical conclusion and professional.

The purpose of this article was to introduce the χ2 test for the data of four-fold tables collected from the cross-sectional design and the realization of SAS and R software. Specifically， three methods were introduced， namely " Pearson΄s χ2 test"， "corrected Pearson΄s χ2 test" and "likelihood ratio χ2 test". The contents involved the test hypotheses， calculation principles and formulas， prerequisites， implementation of SAS and R software， interpretation of results and statement of conclusions of the aforementioned three statistical analysis methods.

The purpose of this article was to introduce the χ2 distribution and related contents， including χ2 distribution and non-central χ2 distribution. It focused on showing the definition of two χ2 distributions， the graph and the main properties of the probability density function. Among them， the two most important properties were： first， the limiting distribution of the χ2 distribution was the normal distribution； second， n-1s2σ2followed the χ2 distribution with n-1 degrees of freedom.In addition， it also explained the relationship between the χ2 distribution and the normal distribution， the relationship between χ2 test statistic and Z test statistic. Finally， it illustrated the computational approaches of the χ2 distribution based on the two SAS functions in SAS software.

The purpose of this paper was to introduce the McNemar΄s χ2 test and SAS and R software implementation of four-fold table data collected from the matched pairs design. Firstly， it was proposed that there were three situations for the data of four-fold table of the paired design， namely ①the data of paired design four-fold table with the special "gold standard" was worthy of statistical analysis； ②the data of four-fold table of the paired design without the special "gold standard" was not worthy of statistical analysis； ③the data of four-fold table collected from the matched pairs design with implicit "gold standard" was worthy of statistical analysis. Secondly， taking the "problems and data" in the first case as the object of statistical analysis， SAS and R software were used to analyze the differences， the calculation results were given and explained， and the statistical and professional conclusions were also made.

The purpose of this paper was to introduce the χ2 test for the data of four-fold tables collected from the cohort design， the hypothesis test and interval estimation of relative risk， and the implementation of SAS and R software. In view of the characteristics of cohort design， the concept of relative risk， hypothesis testing and interval estimation were emphasized. It was given that the interpretation of the results calculated by SAS and R software， as well as the statistical and professional conclusions.