描述性统计
在描述性统计量的计算方面， R有很多方法，这里仅展示基础包的函数
## mpg cyl disp
## Min. :10.40 Min. :4.000 Min. : 71.1
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8
## Median :19.20 Median :6.000 Median :196.3
## Mean :20.09 Mean :6.188 Mean :230.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0
## Max. :33.90 Max. :8.000 Max. :472.0
\(~\) #分组计算描述性统计量
\(~\) 使用aggregate()分组获取描述性统计量
> aggregate(mtcars[,1:3], by=list(am=mtcars$am), mean)
## am mpg cyl disp
## 1 0 17.14737 6.947368 290.3789
## 2 1 24.39231 5.076923 143.5308
\(~\) aggregate()仅允许在每次调用中使用平均数、标准差这样的单返回值函数。它无法一次返回若干个统计量。
by(data, INDICES, FUN, …, simplify =TRUE)函数用于将data中的数据，按照INDICES里面的内容拆分成若干个小的data frame，并且在每一小块data frame上应用FUN函数。
\(~\)
> by(mtcars, mtcars$am,summary)
## mtcars$am: 0
## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. :120.1 Min. : 62.0
## 1st Qu.:14.95 1st Qu.:6.000 1st Qu.:196.3 1st Qu.:116.5
## Median :17.30 Median :8.000 Median :275.8 Median :175.0
## Mean :17.15 Mean :6.947 Mean :290.4 Mean :160.3
## 3rd Qu.:19.20 3rd Qu.:8.000 3rd Qu.:360.0 3rd Qu.:192.5
## Max. :24.40 Max. :8.000 Max. :472.0 Max. :245.0
## drat wt qsec vs am
## Min. :2.760 Min. :2.465 Min. :15.41 Min. :0.0000 Min. :0
## 1st Qu.:3.070 1st Qu.:3.438 1st Qu.:17.18 1st Qu.:0.0000 1st Qu.:0
## Median :3.150 Median :3.520 Median :17.82 Median :0.0000 Median :0
## Mean :3.286 Mean :3.769 Mean :18.18 Mean :0.3684 Mean :0
## 3rd Qu.:3.695 3rd Qu.:3.842 3rd Qu.:19.17 3rd Qu.:1.0000 3rd Qu.:0
## Max. :3.920 Max. :5.424 Max. :22.90 Max. :1.0000 Max. :0
## gear carb
## Min. :3.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.000
## Median :3.000 Median :3.000
## Mean :3.211 Mean :2.737
## 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :4.000 Max. :4.000
## ------------------------------------------------------------
## mtcars$am: 1
## mpg cyl disp hp drat
## Min. :15.00 Min. :4.000 Min. : 71.1 Min. : 52.0 Min. :3.54
## 1st Qu.:21.00 1st Qu.:4.000 1st Qu.: 79.0 1st Qu.: 66.0 1st Qu.:3.85
## Median :22.80 Median :4.000 Median :120.3 Median :109.0 Median :4.08
## Mean :24.39 Mean :5.077 Mean :143.5 Mean :126.8 Mean :4.05
## 3rd Qu.:30.40 3rd Qu.:6.000 3rd Qu.:160.0 3rd Qu.:113.0 3rd Qu.:4.22
## Max. :33.90 Max. :8.000 Max. :351.0 Max. :335.0 Max. :4.93
## wt qsec vs am gear
## Min. :1.513 Min. :14.50 Min. :0.0000 Min. :1 Min. :4.000
## 1st Qu.:1.935 1st Qu.:16.46 1st Qu.:0.0000 1st Qu.:1 1st Qu.:4.000
## Median :2.320 Median :17.02 Median :1.0000 Median :1 Median :4.000
## Mean :2.411 Mean :17.36 Mean :0.5385 Mean :1 Mean :4.385
## 3rd Qu.:2.780 3rd Qu.:18.61 3rd Qu.:1.0000 3rd Qu.:1 3rd Qu.:5.000
## Max. :3.570 Max. :19.90 Max. :1.0000 Max. :1 Max. :5.000
## carb
## Min. :1.000
## 1st Qu.:1.000
## Median :2.000
## Mean :2.923
## 3rd Qu.:4.000
## Max. :8.000
\(~\)
使用psych包中的describeBy()分组计算概述统计量
> library(psych)
> describeBy(mtcars[,1:3], list(am=mtcars$am))
##
## Descriptive statistics by group
## am: 0
## vars n mean sd median trimmed mad min max range skew
## mpg 1 19 17.15 3.83 17.3 17.12 3.11 10.4 24.4 14.0 0.01
## cyl 2 19 6.95 1.54 8.0 7.06 0.00 4.0 8.0 4.0 -0.95
## disp 3 19 290.38 110.17 275.8 289.71 124.83 120.1 472.0 351.9 0.05
## kurtosis se
## mpg -0.80 0.88
## cyl -0.74 0.35
## disp -1.26 25.28
## ------------------------------------------------------------
## am: 1
## vars n mean sd median trimmed mad min max range skew kurtosis
## mpg 1 13 24.39 6.17 22.8 24.38 6.67 15.0 33.9 18.9 0.05 -1.46
## cyl 2 13 5.08 1.55 4.0 4.91 0.00 4.0 8.0 4.0 0.87 -0.90
## disp 3 13 143.53 87.20 120.3 131.25 58.86 71.1 351.0 279.9 1.33 0.40
## se
## mpg 1.71
## cyl 0.43
## disp 24.19
频数表和列联表
\(~\)
## am
## 0 1
## 19 13
> xtabs(~vs+am,data=mtcars)
## am
## vs 0 1
## 0 12 6
## 1 7 7
\(~\) –独立性检验 chisq.test()
\(~\) – Fisher精确检验 fisher.test()
\(~\)
相关
\(~\)
R可以计算多种相关系数，包括Pearson相关系数、Spearman相关系数、 Kendall相关系数、偏 相关系数
\(~\)
> x <- rnorm(10)
> y <- rnorm(10)
> cor(x,y)
## [1] -0.4982695
> cor(mtcars$mpg,mtcars$disp)
## [1] -0.8475514
\(~\)
t检验
\(~\)
在研究中最常见的行为就是对两个组进行比较。t检验就是对两组数据进行的检验
\(~\)
> x <- rnorm(10)
> y <- rnorm(10)
> t.test(x,y,var.equal=T)#指方差齐性，你能得到和我一样的结果么？为什么
##
## Two Sample t-test
##
## data: x and y
## t = 2.4758, df = 18, p-value = 0.02346
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.1194265 1.4579712
## sample estimates:
## mean of x mean of y
## 0.6183135 -0.1703853
> t.statistic <- replicate(1000,t.test(rnorm(10),rnorm(10),var.equal=T)$statistic)#replicate是重复执行某一命令的函数，1000 代表执行次数
> opar <- par(no.readonly=TRUE)
> par(fig=c(0, 0.8, 0, 1))#画图区域，前两个参数制定横向范围，后面两个参数制定纵向分布范围
> plot(t.statistic)#每次执行上述命令后t值的散点图
> par(fig=c(0.65, 1, 0, 1), new=TRUE)##在上幅图的右侧画分布图
> plot(density(t.statistic)$y,density(t.statistic)$x,axes=F,frame.plot=F, xlab="", ylab="",main="",type = "l")
