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> vars<-c("mpg","hp","wt")
> head(mtcars[vars])
mpg hp wt
Mazda RX4 21.0 110 2.620
Mazda RX4 Wag 21.0 110 2.875
Datsun 710 22.8 93 2.320
Hornet 4 Drive 21.4 110 3.215
Hornet Sportabout 18.7 175 3.440
Valiant 18.1 105 3.460
> summary(mtcars[vars])
mpg hp wt
Min. :10.40 Min. : 52.0 Min. :1.513
1st Qu.:15.43 1st Qu.: 96.5 1st Qu.:2.581
Median :19.20 Median :123.0 Median :3.325
Mean :20.09 Mean :146.7 Mean :3.217
3rd Qu.:22.80 3rd Qu.:180.0 3rd Qu.:3.610
Max. :33.90 Max. :335.0 Max. :5.424
</pre>
>**`summary()`** 函數提供最小值、最大值、四分位數和數值型變量的均值，以及因子向量和邏輯型向量的頻數統計> library(Hmisc) 載入需要的程輯包：grid 載入需要的程輯包：lattice 載入需要的程輯包：survival 載入需要的程輯包：Formula 載入需要的程輯包：ggplot2 載入程輯包：‘Hmisc’ The following objects are masked from ‘package:base’: format.pval, round.POSIXt, trunc.POSIXt, units > describe(mtcars[vars]) mtcars[vars] 3 Variables 32 Observations ------------------------------------------------------------------------------------------------ mpg n missing unique Info Mean .05 .10 .25 .50 .75 .90 .95 32 0 25 1 20.09 12.00 14.34 15.43 19.20 22.80 30.09 31.30 lowest : 10.4 13.3 14.3 14.7 15.0, highest: 26.0 27.3 30.4 32.4 33.9 ------------------------------------------------------------------------------------------------ hp n missing unique Info Mean .05 .10 .25 .50 .75 .90 .95 32 0 22 1 146.7 63.65 66.00 96.50 123.00 180.00 243.50 253.55 lowest : 52 62 65 66 91, highest: 215 230 245 264 335 ------------------------------------------------------------------------------------------------ wt n missing unique Info Mean .05 .10 .25 .50 .75 .90 .95 32 0 29 1 3.217 1.736 1.956 2.581 3.325 3.610 4.048 5.293 lowest : 1.513 1.615 1.835 1.935 2.140, highest: 3.845 4.070 5.250 5.345 5.424 ------------------------------------------------------------------------------------------------
> library(pastecs) 載入需要的程輯包：boot > stat.desc(mtcars[vars]) mpg hp wt nbr.val 32.0000000 32.0000000 32.0000000 nbr.null 0.0000000 0.0000000 0.0000000 nbr.na 0.0000000 0.0000000 0.0000000 min 10.4000000 52.0000000 1.5130000 max 33.9000000 335.0000000 5.4240000 range 23.5000000 283.0000000 3.9110000 sum 642.9000000 4694.0000000 102.9520000 median 19.2000000 123.0000000 3.3250000 mean 20.0906250 146.6875000 3.2172500 SE.mean 1.0654240 12.1203173 0.1729685 CI.mean.0.95 2.1729465 24.7195501 0.3527715 var 36.3241028 4700.8669355 0.9573790 std.dev 6.0269481 68.5628685 0.9784574 coef.var 0.2999881 0.4674077 0.3041285
> library(psych) 載入程輯包：‘psych’ The following object is masked from ‘package:boot’: logit > describe(mtcars[vars]) vars n mean sd median trimmed mad min max range skew kurtosis se mpg 1 32 20.09 6.03 19.20 19.70 5.41 10.40 33.90 23.50 0.61 -0.37 1.07 hp 2 32 146.69 68.56 123.00 141.19 77.10 52.00 335.00 283.00 0.73 -0.14 12.12 wt 3 32 3.22 0.98 3.33 3.15 0.77 1.51 5.42 3.91 0.42 -0.02 0.17
在比較多組個體或觀測時，關注的焦點經常是各組的描述性統計信息，而不是樣本整體的描述性統計信息。同樣地，在R中完成這個任務有若干種方法。我們將以獲取變速箱類型各水平的描述性統計量開始。
> aggregate(mtcars[vars], by=list(am=mtcars$am),mean) am mpg hp wt 1 0 17.1 160 3.77 2 1 24.4 127 2.41 > aggregate(mtcars[vars],by=list(am=mtcars$am),sd) am mpg hp wt 1 0 3.83 53.9 0.777 2 1 6.17 84.1 0.617 </pre> >由上面的分析結果可看出，am有兩個值，根據am的兩個值將`mtcars`數據集分為兩組，得出上面的`mpg`, `hp`, `wt` 的平均值以及標準差。<br> >其中， **`list(am=mtcars$am)`** 的使用，將 `am` 列標注為一個更有幫助的列標簽，而非 `Group.1`。<br> >遺憾的是，aggregate()僅允許在每次調用中使用平均數、標準差這樣的單返回值函數。它無法一次返回若干個統計量。要完成這項任務，可以使用 **`by()`** 函數。
> by(mtcars[vars],mtcars$am,summary) mtcars$am: 0 mpg hp wt Min. :10.4 Min. : 62 Min. :2.46 1st Qu.:14.9 1st Qu.:116 1st Qu.:3.44 Median :17.3 Median :175 Median :3.52 Mean :17.1 Mean :160 Mean :3.77 3rd Qu.:19.2 3rd Qu.:192 3rd Qu.:3.84 Max. :24.4 Max. :245 Max. :5.42 --------------------------------------------------------------------------------------------------- mtcars$am: 1 mpg hp wt Min. :15.0 Min. : 52 Min. :1.51 1st Qu.:21.0 1st Qu.: 66 1st Qu.:1.94 Median :22.8 Median :109 Median :2.32 Mean :24.4 Mean :127 Mean :2.41 3rd Qu.:30.4 3rd Qu.:113 3rd Qu.:2.78 Max. :33.9 Max. :335 Max. :3.57
格式：summaryBy(formula, dataframe, FUN=function)
> **`formula`** 支持格式：<br> > **var1 + var2 + var3 + …… +varN ~ groupvar1 + groupvar2 + …… +groupvarN**<br> > **`~`** 左邊的變量是需要分析的數值型變量，右側的變量是類別性的分組變量。<br> > **`function`** 可為任何內建或用戶自編的R函數。 <pre> > library(doBy) 載入需要的程輯包：survival 載入程輯包：‘survival’ The following object is masked from ‘package:boot’: aml > summaryBy(mpg+hp+wt~am,data=mtcars,FUN=mystats) am mpg.n mpg.mean mpg.stdev mpg.skew mpg.kurtosis hp.n hp.mean hp.stdev hp.skew hp.kurtosis wt.n wt.mean wt.stdev 1 0 19 17.14737 3.833966 0.01395038 -0.8031783 19 160.2632 53.90820 -0.01422519 -1.2096973 19 3.768895 0.7774001 2 1 13 24.39231 6.166504 0.05256118 -1.4553520 13 126.8462 84.06232 1.35988586 0.5634635 13 2.411000 0.6169816 wt.skew wt.kurtosis 1 0.9759294 0.1415676 2 0.2103128 -1.1737358
> library(reshape)
> dstats <- function(x) (c(n=length(x), mean=mean(x), sd=sd(x))
+ )
> dfm <- melt(mtcars, measure.vars=c("mpg","hp","wt"),id.vars=c("am","cyl"))
> cast(dfm,am+cyl+variable~.,dstats)
am cyl variable n mean sd
1 0 4 mpg 3 22.900000 1.4525839
2 0 4 hp 3 84.666667 19.6553640
3 0 4 wt 3 2.935000 0.4075230
4 0 6 mpg 4 19.125000 1.6317169
5 0 6 hp 4 115.250000 9.1787799
6 0 6 wt 4 3.388750 0.1162164
7 0 8 mpg 12 15.050000 2.7743959
8 0 8 hp 12 194.166667 33.3598379
9 0 8 wt 12 4.104083 0.7683069
10 1 4 mpg 8 28.075000 4.4838599
11 1 4 hp 8 81.875000 22.6554156
12 1 4 wt 8 2.042250 0.4093485
13 1 6 mpg 3 20.566667 0.7505553
14 1 6 hp 3 131.666667 37.5277675
15 1 6 wt 3 2.755000 0.1281601
16 1 8 mpg 2 15.400000 0.5656854
17 1 8 hp 2 299.500000 50.2045815
18 1 8 wt 2 3.370000 0.2828427分布特征的數值刻畫的確很重要，但是這并不能代替視覺呈現。對于定量變量，我們有直方 圖（6.3節）、密度圖（6.4節）、箱線圖（6.5節）和點圖（6.6節）。它們都可以讓我們洞悉那些依 賴于觀察一小部分描述性統計量時忽略的細節。
目前我們考慮的函數都是為定量變量提供概述的。下一節中的函數則允許考察類別型變量的 分布。
> 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
> attach(Arthritis)
> mytable1<-xtabs(~Treatment+Improved,data=Arthritis)
> mytable1
Improved
Treatment None Some Marked
Placebo 29 7 7
Treated 13 7 21
> margin.table(mytable1,1)
Treatment
Placebo Treated
43 41
> margin.table(mytable1,2)
Improved
None Some Marked
42 14 28
> prop.table(mytable,2)
Error in if (d2 == 0L) { : 需要TRUE/FALSE值的地方不可以用缺少值
> prop.table(mytable1,2)
Improved
Treatment None Some Marked
Placebo 0.6904762 0.5000000 0.2500000
Treated 0.3095238 0.5000000 0.7500000
> addmargins(mytable1)
Improved
Treatment None Some Marked Sum
Placebo 29 7 7 43
Treated 13 7 21 41
Sum 42 14 28 84
> addmargins(prop.table(mytable1))
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(prop.table(mytable1),2)
Improved
Treatment None Some Marked Sum
Placebo 0.34523810 0.08333333 0.08333333 0.51190476
Treated 0.15476190 0.08333333 0.25000000 0.48809524
table(A,B);
xtabs(~A+B,data=mydata):~符號右方出現的為要進行交叉分類的變量，以+作為分隔；
margin.table(table(A,B) or xtabs.table(~A+B),no.ofvariables): 生成邊際頻數和比例
prop.table(table(A,B),no.ofvariables): 生成比例
addmargins(table(A,B) or xtabs.table(~A+B) or prop.table(mytable1), no.ofvariables): 增加第幾個變量的合計，如果不加no.ofvariables則都加;
> mytable2<-xtabs(~Treatment+Sex+Improved,data=Arthritis) > mytable2 , , 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(mytable2) 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(mytable2,1) Treatment Placebo Treated 43 41 > margin.table(mytable2,2) Sex Female Male 59 25 > margin.table(mytable2,2) Sex Female Male 59 25 > margin.table(mytable2,3) Improved None Some Marked 42 14 28 > margin.table(mytable2,c(1,2,3)) , , 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 > margin.table(mytable2,c(1,3)) Improved Treatment None Some Marked Placebo 29 7 7 Treated 13 7 21 > ftable(prop.table(mytable2,c(2,3)) + ) Improved None Some Marked Treatment Sex Placebo Female 0.7600000 0.5833333 0.2727273 Male 0.5882353 0.0000000 0.1666667 Treated Female 0.2400000 0.4166667 0.7272727 Male 0.4117647 1.0000000 0.8333333 > ftable(addmargins(prop.table(mytable2,c(1,2)),3))*100 Improved None Some Marked Sum Treatment Sex Placebo Female 59.375000 21.875000 18.750000 100.000000 Male 90.909091 0.000000 9.090909 100.000000 Treated Female 22.222222 18.518519 59.259259 100.000000 Male 50.000000 14.285714 35.714286 100.000000
> mytable3<-xtabs(~Treatment+Improved,data=Arthritis);mytable3 Improved Treatment None Some Marked Placebo 29 7 7 Treated 13 7 21 > chisq.test(mytable3) Pearson's Chi-squared test data: mytable3 X-squared = 13.055, df = 2, p-value = 0.001463
> mytable4<-xtabs(~Treatment+Improved,data=Arthritis);mytable4 Improved Treatment None Some Marked Placebo 29 7 7 Treated 13 7 21 > fisher.test(mytable4) Fisher's Exact Test for Count Data data: mytable4 p-value = 0.001393 alternative hypothesis: two.sided
> mytable5<-xtabs(~Treatment+Improved+Sex, data=Arthritis) > mantelhaen.test(mytable5) Cochran-Mantel-Haenszel test data: mytable5 Cochran-Mantel-Haenszel M^2 = 14.632, df = 2, p-value = 0.0006647
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