数据使用的是Kock&Edward(1988)，一项风湿性关节炎新疗法的双盲临床试验的结果。

其中Treatment为治疗情况，表示为两种：Treated（用药治疗）、Placebo（安慰剂治疗），improved为改善情况，包括了无改善、一定程度改善和显著改善。

相关函数包括
table()
xtabs()
prop.table()
margin.table()
addmargins()
ftable()

相关实验操作
频数表创建、频数转化比例、二维列联表创建、生成边际频数和比例、添加以及创建边际和、三位列联表创建以及数据的一些处理。

> #引入数据
> library(vcd)> head(Arthritis)ID Treatment  Sex Age Improved
1 57   Treated Male  27     Some
2 46   Treated Male  29     None
3 77   Treated Male  30     None
4 17   Treated Male  32   Marked
5 36   Treated Male  46   Marked
6 23   Treated Male  58   Marked> #一维列联表
> mytable <- with(Arthritis,table(Improved))> mytable
ImprovedNone   Some Marked 42     14     28 > #转化为比例值
> prop.table(mytable)
ImprovedNone      Some    Marked 
0.5000000 0.1666667 0.3333333 > #转为百分比
> 
> prop.table(mytable)*100
ImprovedNone     Some   Marked 
50.00000 16.66667 33.33333 > #二维列联表
> mytable1 <- xtabs(~ Treatment+Improved,data=Arthritis)> mytable1Improved
Treatment None Some MarkedPlacebo   29    7      7Treated   13    7     21> #行和与行比
> #安慰剂治疗和用药治疗边际频数
> margin.table(mytable1,1)
Treatment
Placebo Treated 43      41 > #安慰剂治疗和用药治疗比例
> prop.table(mytable1,1)Improved
Treatment      None      Some    MarkedPlacebo 0.6744186 0.1627907 0.1627907Treated 0.3170732 0.1707317 0.5121951> #列和与列比
> #安慰剂治疗和用药治疗边际频数
> margin.table(mytable1,2)
ImprovedNone   Some Marked 42     14     28 > #安慰剂治疗和用药治疗比例
> prop.table(mytable1,2)Improved
Treatment      None      Some    MarkedPlacebo 0.6904762 0.5000000 0.2500000Treated 0.3095238 0.5000000 0.7500000> #各单元格所占比例
> prop.table(mytable1)Improved
Treatment       None       Some     MarkedPlacebo 0.34523810 0.08333333 0.08333333Treated 0.15476190 0.08333333 0.25000000> #添加边际和
> 
> addmargins(mytable1)Improved
Treatment None Some Marked SumPlacebo   29    7      7  43Treated   13    7     21  41Sum       42   14     28  84> addmargins(prop.table(mytable1))Improved
Treatment       None       Some     Marked        SumPlacebo 0.34523810 0.08333333 0.08333333 0.51190476Treated 0.15476190 0.08333333 0.25000000 0.48809524Sum     0.50000000 0.16666667 0.33333333 1.00000000> #使用CrossTable生成二维列联表
> library(gmodels)> CrossTable(Arthritis$Treatment,Arthritis$Improved)Cell Contents
|-------------------------|
|                       N |
| Chi-square contribution |
|           N / Row Total |
|           N / Col Total |
|         N / Table Total |
|-------------------------|Total Observations in Table:  84 | Arthritis$Improved 
Arthritis$Treatment |      None |      Some |    Marked | Row Total | 
--------------------|-----------|-----------|-----------|-----------|Placebo |        29 |         7 |         7 |        43 | |     2.616 |     0.004 |     3.752 |           | |     0.674 |     0.163 |     0.163 |     0.512 | |     0.690 |     0.500 |     0.250 |           | |     0.345 |     0.083 |     0.083 |           | 
--------------------|-----------|-----------|-----------|-----------|Treated |        13 |         7 |        21 |        41 | |     2.744 |     0.004 |     3.935 |           | |     0.317 |     0.171 |     0.512 |     0.488 | |     0.310 |     0.500 |     0.750 |           | |     0.155 |     0.083 |     0.250 |           | 
--------------------|-----------|-----------|-----------|-----------|Column Total |        42 |        14 |        28 |        84 | |     0.500 |     0.167 |     0.333 |           | 
--------------------|-----------|-----------|-----------|-----------|> #三位列联表
> 
> mytable2 <- xtabs(~ Treatment+Sex+Improved,data = Arthritis)> mytable2
, , Improved = NoneSex
Treatment Female MalePlacebo     19   10Treated      6    7, , Improved = SomeSex
Treatment Female MalePlacebo      7    0Treated      5    2, , Improved = MarkedSex
Treatment Female MalePlacebo      6    1Treated     16    5> #三位列联表边际频数
> margin.table(mytable2,1)
Treatment
Placebo Treated 43      41 > margin.table(mytable2,2)
Sex
Female   Male 59     25 > margin.table(mytable2,3)
ImprovedNone   Some Marked 42     14     28 > #治疗情况和改善情况的边际频数
> margin.table(mytable2,c(1,3))Improved
Treatment None Some MarkedPlacebo   29    7      7Treated   13    7     21> #治疗情况和性别各类改善情况比例
> ftable(prop.table(mytable2,c(1,2)))Improved       None       Some     Marked
Treatment Sex                                             
Placebo   Female          0.59375000 0.21875000 0.18750000Male            0.90909091 0.00000000 0.09090909
Treated   Female          0.22222222 0.18518519 0.59259259Male            0.50000000 0.14285714 0.35714286> ftable(prop.table(mytable2,c(1,2)),3)Improved       None       Some     Marked
Treatment Sex                                             
Placebo   Female          0.59375000 0.21875000 0.18750000Male            0.90909091 0.00000000 0.09090909
Treated   Female          0.22222222 0.18518519 0.59259259Male            0.50000000 0.14285714 0.35714286