[R] 4.基本统计分析

R in action整理

1.描述性统计

数据使用R自带的mtcars,mpg每加仑行驶英里数,hp马力,wt车重

1)连续型变量描述性统计

myvars<-c("mpg","hp","wt")

①summary():

>summary(mtcars[myvars])
      mpg           hp            wt     
 Min.   :10   Min.   : 52   Min.   :1.5  
 1st Qu.:15   1st Qu.: 96   1st Qu.:2.6  
 Median :19   Median :123   Median :3.3  
 Mean   :20   Mean   :147   Mean   :3.2  
 3rd Qu.:23   3rd Qu.:180   3rd Qu.:3.6  
 Max.   :34   Max.   :335   Max.   :5.4 

②misc包的describe():

>describe(mtcars[myvars])
    vars  n  mean    sd median trimmed   mad  min   max range skew kurtosis    se
mpg    1 32  20.1  6.03   19.2    19.7  5.41 10.4  33.9  23.5 0.61    -0.37  1.07
hp     2 32 146.7 68.56  123.0   141.2 77.10 52.0 335.0 283.0 0.73    -0.14 12.12
wt     3 32   3.2  0.98    3.3     3.1  0.77  1.5   5.4   3.9 0.42    -0.02  0.17

注:trimmed截尾默认0.1,skew偏度,kurtosis峰度

③pastecs包的stat.desc()

>stat.desc(mtcars[myvars])
               mpg      hp     wt
nbr.val       32.0   32.00  32.00
nbr.null       0.0    0.00   0.00
nbr.na         0.0    0.00   0.00
min           10.4   52.00   1.51
max           33.9  335.00   5.42
range         23.5  283.00   3.91
sum          642.9 4694.00 102.95
median        19.2  123.00   3.33
mean          20.1  146.69   3.22
SE.mean        1.1   12.12   0.17  #平均数的标准误
CI.mean.0.95   2.2   24.72   0.35  #平均数置信度为95%的置信区间
var           36.3 4700.87   0.96
std.dev        6.0   68.56   0.98  #标准差
coef.var       0.3    0.47   0.30  #变异系数

2)分组描述性统计

myvars<-c("mpg","hp","wt")

①aggregate():

>aggregate(mtcars[myvars],by=list(am=mtcars$am),mean)
am mpg  hp  wt
1  0  17 160 3.8
2  1  24 127 2.4

注:如果list(mtcars$am),则am列为Group.1而不是am

②psych包中的describeBy():

>describeBy(mtcars[myvars],list(am=mtcars$am))
 Descriptive statistics by group 
am: 0
    vars  n  mean    sd median trimmed   mad  min   max range  skew kurtosis    se
mpg    1 19  17.1  3.83   17.3    17.1  3.11 10.4  24.4    14  0.01    -0.80  0.88
hp     2 19 160.3 53.91  175.0   161.1 77.10 62.0 245.0   183 -0.01    -1.21 12.37
wt     3 19   3.8  0.78    3.5     3.8  0.45  2.5   5.4     3  0.98     0.14  0.18
----------------------------------------------------------------------------------
am: 1
    vars  n  mean    sd median trimmed   mad  min   max range skew kurtosis    se
mpg    1 13  24.4  6.17   22.8    24.4  6.67 15.0  33.9  18.9 0.05    -1.46  1.71
hp     2 13 126.8 84.06  109.0   114.7 63.75 52.0 335.0 283.0 1.36     0.56 23.31
wt     3 13   2.4  0.62    2.3     2.4  0.68  1.5   3.6   2.1 0.21    -1.17  0.17

2.频数表

数据使用vcd包的Arthritis

1)一维

>table(Arthritis$Improved)
  None   Some  Marked 
    42     14      28 

2)二维

①xtabs:

>mytable<-xtabs(~Treatment+Improved,data=Arthritis)  #~A+B,A为行变量,B为列变量
>mytable
         Improved
Treatment None Some Marked
  Placebo   29    7      7
  Treated   13    7     21

#可使用addmargins(mytale),addmargins(prop.table(mytable))来生成边际频数和比例

②gmodels包的CrossTable()

>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 |           | 
--------------------|-----------|-----------|-----------|-----------|

3)多维

mytable<-xtabs(~Treatment+Improved+Sex, data=Arthritis)  #~A+B+C,A列1,B列2,C行,分别对应1 2 3

①ftable():

>ftable(mytable)

                   Sex Female Male

Treatment Improved                

Placebo   None             19   10

          Some              7    0

          Marked            6    1

Treated   None              6    7

          Some              5    2

          Marked           16    5

同样可以使用margin.table(mytable,x)  #x也可以写成c(x,y)的形式,为数字,分别对应A B C下标的123

>margin.table(mytable,c(1,3))
         Sex
Treatment Female Male
  Placebo     32   11
  Treated     27   14

或者ftable(addmargins(prop.table(mytable,c(1,2)),3)),得到对应百分比

> ftable(addmargins(prop.table(mytable,c(1,2)),3))*100
                   Sex    Female      Male       Sum
Treatment Improved                                  
Placebo   None          65.51724  34.48276 100.00000
          Some         100.00000   0.00000 100.00000
          Marked        85.71429  14.28571 100.00000
Treated   None          46.15385  53.84615 100.00000
          Some          71.42857  28.57143 100.00000
          Marked        76.19048  23.80952 100.00000

4)独立性检验(变量是否相关或独立)

①卡方检验chisq.test()  #二维

先创建包含所需要的变量的表格,此处先检验治疗方式和改善情况的关系

mytable<-xtabs(~Treatment+Improved,data=Arthritis)  

chisq.test(mytable)对其进行检验

>chisq.test(mytable)

        Pearson's Chi-squared test

data:  mytable
X-squared = 13.055, df = 2, p-value = 0.001463  

#统计学中"="都放在原假设,H0:两者相互独立
p值反应原假设发生的概率 p<0.01说明原假设发生概率很小(即不相互独立)
在99%以上的可信度上认为两者有关

同样尝试找出治疗方式与性别的关系,先建立表格

mytable<-xtabs(~Treatment+Sex,data=Arthritis)

chisq.test(mytable)
 chisq.test(mytable)

        Pearson's Chi-squared test with Yates' continuity correction

data:  mytable
X-squared = 0.38378, df = 1, p-value = 0.5356

#根据上述原理,治疗方式与性别相互独立

②Fisher检验

先创建包含所需要的变量的表格,此处以治疗方式和改善情况的为例

mytable<-xtabs(~Treatment+Improved,data=Arthritis)  

fisher.test(mytable)

> fisher.test(mytable)

        Fisher's Exact Test for Count Data

data:  mytable
p-value = 0.001393
alternative hypothesis: two.sided

#同样的H0:两者独立,p值反应原假设发生的状况

②Corchran-Mantel-Haenszel检验

3.相关

数据为state.x77的1-6列

1)相关类型及计算

①cor(x,use= ,method= )  #x:矩阵或数据框,use:缺失数据的处理方法,method:相关类型

Pearson基差关系:默认,两个定量变量之间的线性相关程度

Spearman等级相关系数:定序变量之间的相关程度

Kendall’s Tay相关系数:非参数的等级相关度量

默认得到一个方阵(所有变量之间的两两关系),同样可以计算非方形的相关矩阵,设定x,y,然后cov(x,y)

②ggm包的pcor(u,s)  #排除其他若干变量的干扰,计算两变量之间的相关系数

2)相关性的显著性检验

cor.test(x,y,alternative= ,method= )  #默认为双侧检验,persons

H0:两者相关系数为0,用p值去衡量相关性的显著水平

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