数据仍然使用了上一节的数据，对数据进行了独立性检验测试，包括了卡方独立性检验、FisherJ精确检验和Cochran-Mantel-Haenszel检验，并计算了phi系数、列联系数和Cramer’s V系数。
> #卡方独立性检验
> library(vcd)
> mytable <- xtabs(~Treatment+Improved,data = Arthritis)
> #治疗情况和改善情况不独立
> chisq.test(mytable)
Pearson's Chi-squared test
data: mytable
X-squared = 13.055, df = 2, p-value = 0.001463
> mytable1 <- xtabs(~Improved+Sex,data = Arthritis)
> #性别和改善情况独立
> chisq.test(mytable1)
Pearson's Chi-squared test
data: mytable1
X-squared = 4.8407, df = 2, p-value = 0.08889
> #Fisher精确检验
>
> mytable2 <- xtabs(~Treatment+Improved,data = Arthritis)
> #原假设是：边界固定的列联表中行和列是相互独立的
> fisher.test(mytable2)
Fisher's Exact Test for Count Data
data: mytable2
p-value = 0.001393
alternative hypothesis: two.sided
> #Cochran-Mantel-Haenszel检验
>
> mytable3 <- xtabs(~Treatment+Improved+Sex,data = Arthritis)
> #患者的治疗与得到的改善在性别的每一水平下不独立
> mantelhaen.test(mytable3)
Cochran-Mantel-Haenszel test
data: mytable3
Cochran-Mantel-Haenszel M^2 = 14.632, df = 2, p-value = 0.0006647
> #相关性度量
> mytable4 <- xtabs(~Treatment+Improved,data = Arthritis)
> assocstats(mytable4)
X^2 df P(> X^2)
Likelihood Ratio 13.530 2 0.0011536
Pearson 13.055 2 0.0014626
Phi-Coefficient : NA
Contingency Coeff.: 0.367
Cramer's V : 0.394
Warning message:
In chisq.test(mytable1) : Chi-squared approximation may be incorrect
