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.