Chapter 07-Basic statistics(Part2 Frequency and contingency tables)
这一部分使用在vcd包中的Arthritis数据集。
> library(vcd)
载入需要的程辑包：MASS
载入需要的程辑包：grid
载入需要的程辑包：colorspace
> 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
1. generating frequency tables
(1) ONE-WAY TABLE
例01：
> mytable<-with(Arthritis,table(Improved))
> mytable
Improved
None Some Marked
42 14 28
>
> prop.table(mytable)
Improved
None Some Marked
0.5000000 0.1666667 0.3333333
>
> prop.table(mytable)*100
Improved
None Some Marked
50.00000 16.66667 33.33333
table()函数：简单的频率(frequency)表示;
· table()函数会缺省自动的忽略missing values(NAs)，要包含NA值需要使用选项useNA="ifany"
prop.table()函数：比例(proportion)表示;
prop.table()*100函数：百分数(percentage)表示。
(2)TWO-WAY TABLES
例02：
> mytable<-xtabs(~Treatment+Improved,data=Arthritis)
> mytable
Improved
Treatment None Some Marked
Placebo 29 7 7
Treated 13 7 21
（1）mytable<-table(A,B)
·A是行变量，B是列变量。
（2）xtabs()函数：使用公式方式的输入(formula style input)来创建一个列联表(contingency table)。
mytable<-xtabs(~A+B,data=mydata)
例03：
> margin.table(mytable,1)
Treatment
Placebo Treated
43 41
> prop.table(mytable,1)
Improved
Treatment None Some Marked
Placebo 0.6744186 0.1627907 0.1627907
Treated 0.3170732 0.1707317 0.5121951
> margin.table(mytable,2)
Improved
None Some Marked
42 14 28
> prop.table(mytable,2)
Improved
Treatment None Some Marked
Placebo 0.6904762 0.5000000 0.2500000
Treated 0.3095238 0.5000000 0.7500000
> prop.table(mytable)
Improved
Treatment None Some Marked
Placebo 0.34523810 0.08333333 0.08333333
Treated 0.15476190 0.08333333 0.25000000
margin.table()：产生marginal frequencies；
prop.table()：产生proportions。
·index(1)：指在table()中的第一个变量；
·index(2)：指在table()中的第二个变量。
例04：
> addmargins(mytable)
Improved
Treatment None Some Marked Sum
Placebo 29 7 7 43
Treated 13 7 21 41
Sum 42 14 28 84
> addmargins(prop.table(mytable))
Improved
Treatment None Some Marked Sum
Placebo 0.34523810 0.08333333 0.08333333 0.51190476
Treated 0.15476190 0.08333333 0.25000000 0.48809524
Sum 0.50000000 0.16666667 0.33333333 1.00000000
addmargins()：add marginal sums to these tables;
·缺省时为所有变量创建sum margins;
例04（变1）：仅仅添加一个 sum column
> addmargins(prop.table(mytable,1),2)
Improved
Treatment None Some Marked Sum
Placebo 0.6744186 0.1627907 0.1627907 1.0000000
Treated 0.3170732 0.1707317 0.5121951 1.0000000
例04（变2）：仅仅添加一个sum row
> addmargins(prop.table(mytable,2),1)
Improved
Treatment None Some Marked
Placebo 0.6904762 0.5000000 0.2500000
Treated 0.3095238 0.5000000 0.7500000
Sum 1.0000000 1.0000000 1.0000000
(3)MULTIDIMENSIONAL TABLES
例05：
> install.packages("gmodels")
--- 在此連線階段时请选用CRAN的鏡子 --- also installing the dependencies ‘gtools’, ‘gdata’
试开URL
’http://ftp.ctex.org/mirrors/CRAN/bin/windows/contrib/3.0/gtools_3.0.0.zip'
Content type 'application/zip' length 112950 bytes (110 Kb)
打开了URL
downloaded 110 Kb
试开URL
’http://ftp.ctex.org/mirrors/CRAN/bin/windows/contrib/3.0/gdata_2.13.2.zip'
Content type 'application/zip' length 850387 bytes (830 Kb)
打开了URL
downloaded 830 Kb
试开URL
’http://ftp.ctex.org/mirrors/CRAN/bin/windows/contrib/3.0/gmodels_2.15.4.zip'
Content type 'application/zip' length 76708 bytes (74 Kb)
打开了URL
downloaded 74 Kb
程序包‘gtools’打开成功，MD5和检查也通过
程序包‘gdata’打开成功，MD5和检查也通过
程序包‘gmodels’打开成功，MD5和检查也通过
下载的二进制程序包在
C:\Users\seven-wang\AppData\Local\Temp\RtmpIlHLxM\downloaded_packages里
> library(vcd)
载入需要的程辑包：MASS
载入需要的程辑包：grid
载入需要的程辑包：colorspace
> 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 | |
-----------------------------------------------|-------------|------------|-----------|--------------|
gmodels包中的CrossTable()函数：创建two-way tables models after PROC FREO in SAS or CROSSTABS SPSS.
例06：
> mytable<-xtabs(~Treatment+Sex+Improved,data=Arthritis)
> mytable
, , Improved = None
Sex
Treatment Female Male
Placebo 19 10
Treated 6 7
, , Improved = Some
Sex
Treatment Female Male
Placebo 7 0
Treated 5 2
, , Improved = Marked
Sex
Treatment Female Male
Placebo 6 1
Treated 16 5
> ftable(mytable)
Improved None Some Marked
Treatment Sex
Placebo Female 19 7 6
Male 10 0 1
Treated Female 6 5 16
Male 7 2 5
> margin.table(mytable,1)
Treatment
Placebo Treated
43 41
> margin.table(mytable,2)
Sex
Female Male
59 25
> margin.table(mytable,3)
Improved None Some Marked
42 14 28
> margin.table(mytable,c(,31))
Improved Treatment None Some Marked
Placebo 29 7 7
Treated 13 7 21
> ftable(prop.table(mytable,c(1,2)))
Improved None Some Marked
Treatment Sex
Placebo Female 0.59375000 0.21875000 0.18750000
Male 0.90909091 0.00000000 0.09090909
Treated Female 0.22222222 0.18518519 0.59259259
Male 0.50000000 0.14285714 0.35714286
2. Test of independence
例07：CHI-AQUARE TEST OF INDEPENDENCE
> library(vcd)
> mytable<-xtabs(~Treatment+Improved,data=Arthritis)
> chisq.test(mytable) Pearson's Chi-squared test data: mytable
X-squared = 13.055, df = 2, p-value = 0.001463
> mytable<-xtabs(~Improved+Sex,data=Arthritis)
> chisq.test(mytable) Pearson's Chi-squared test data: mytable
X-squared = 4.8407, df = 2, p-value = 0.08889 Warning message:
In chisq.test(mytable) : Chi-squared近似算法有可能不准
chisq.test()函数: 产生一个chi-square of independence of the row and column variables.
例08：FISHER'S EXACT TEST
> mytable<-xtabs(~Treatment+Improved,data=Arthritis)
> fisher.test(mytable) Fisher's Exact Test for Count Data data: mytable
p-value = 0.001393
alternative hypothesis: two.sided
fisher.test()函数：产生一个Fisher 's exact test。
·Fisher's exact test ：evaluate the hypothesis of independence of rows and columns in a contingency table with fixed marginals.
例09：COCHRAN-MANTEL-HAENSZEL TEST
> mytable<-xtabs(~Treatment+Improved+Sex,data=Arthritis)
> mantelhaen.test(mytable) Cochran-Mantel-Haenszel test data: mytable
Cochran-Mantel-Haenszel M^2 = 14.6323, df = 2, p-value = 0.0006647
mantelhaen.test()函数：提供一个Cochran-Mantel-Haenszel chi-aquare test of null ·hypothesis that two nominal variables are conditionally independent in each straum of a third variable.
3. measures of association
例10：
> library(vcd)
> mytable<-xtabs(~Treatment+Improved,data=Arthritis)
> assocstats(mytable)
X^2 df P(> X^2)
Likelihood Ratio 13.530 2 0.0011536
Pearson 13.055 2 0.0014626 Phi-Coefficient : 0.394
Contingency Coeff.: 0.367
Cramer's V : 0.394
vcd包中associstats()函数：计算 phi coefficient,contingency coefficient,Cramer's V.
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