install.packages("https://cran.rstudio.com/bin/windows/contrib/4.1/faraway_1.0.7.zip", repos = NULL)
## 將程式套件安載入 'C:/Users/user/Documents/R/win-library/4.1'
## (因為 'lib' 沒有被指定)
## package 'faraway' successfully unpacked and MD5 sums checked
library(faraway)
## Warning: 套件 'faraway' 是用 R 版本 4.1.2 來建造的
library(e1071)
## Warning: 套件 'e1071' 是用 R 版本 4.1.2 來建造的
library(moments)
## Warning: 套件 'moments' 是用 R 版本 4.1.1 來建造的
##
## 載入套件：'moments'
## 下列物件被遮斷自 'package:e1071':
##
## kurtosis, moment, skewness
data("hsb")
str(hsb)
## 'data.frame': 200 obs. of 11 variables:
## $ id : int 70 121 86 141 172 113 50 11 84 48 ...
## $ gender : Factor w/ 2 levels "female","male": 2 1 2 2 2 2 2 2 2 2 ...
## $ race : Factor w/ 4 levels "african-amer",..: 4 4 4 4 4 4 1 3 4 1 ...
## $ ses : Factor w/ 3 levels "high","low","middle": 2 3 1 1 3 3 3 3 3 3 ...
## $ schtyp : Factor w/ 2 levels "private","public": 2 2 2 2 2 2 2 2 2 2 ...
## $ prog : Factor w/ 3 levels "academic","general",..: 2 3 2 3 1 1 2 1 2 1 ...
## $ read : int 57 68 44 63 47 44 50 34 63 57 ...
## $ write : int 52 59 33 44 52 52 59 46 57 55 ...
## $ math : int 41 53 54 47 57 51 42 45 54 52 ...
## $ science: int 47 63 58 53 53 63 53 39 58 50 ...
## $ socst : int 57 61 31 56 61 61 61 36 51 51 ...
head(hsb)
## id gender race ses schtyp prog read write math science socst
## 1 70 male white low public general 57 52 41 47 57
## 2 121 female white middle public vocation 68 59 53 63 61
## 3 86 male white high public general 44 33 54 58 31
## 4 141 male white high public vocation 63 44 47 53 56
## 5 172 male white middle public academic 47 52 57 53 61
## 6 113 male white middle public academic 44 52 51 63 61
summary(hsb)
## id gender race ses schtyp
## Min. : 1.00 female:109 african-amer: 20 high :58 private: 32
## 1st Qu.: 50.75 male : 91 asian : 11 low :47 public :168
## Median :100.50 hispanic : 24 middle:95
## Mean :100.50 white :145
## 3rd Qu.:150.25
## Max. :200.00
## prog read write math science
## academic:105 Min. :28.00 Min. :31.00 Min. :33.00 Min. :26.00
## general : 45 1st Qu.:44.00 1st Qu.:45.75 1st Qu.:45.00 1st Qu.:44.00
## vocation: 50 Median :50.00 Median :54.00 Median :52.00 Median :53.00
## Mean :52.23 Mean :52.77 Mean :52.65 Mean :51.85
## 3rd Qu.:60.00 3rd Qu.:60.00 3rd Qu.:59.00 3rd Qu.:58.00
## Max. :76.00 Max. :67.00 Max. :75.00 Max. :74.00
## socst
## Min. :26.00
## 1st Qu.:46.00
## Median :52.00
## Mean :52.41
## 3rd Qu.:61.00
## Max. :71.00
#平均數
aggregate(cbind(read, write, math, science, socst) ~ gender+race, data = hsb, mean)
## gender race read write math science socst
## 1 female african-amer 46.76923 48.84615 47.53846 40.69231 49.69231
## 2 male african-amer 46.85714 47.00000 45.28571 46.71429 49.00000
## 3 female asian 51.75000 58.87500 56.75000 50.87500 52.25000
## 4 male asian 52.33333 55.66667 58.66667 53.00000 47.66667
## 5 female hispanic 45.90909 48.90909 45.27273 45.18182 50.27273
## 6 male hispanic 47.30769 44.38462 49.23077 45.53846 45.69231
## 7 female white 53.40260 56.49351 53.77922 53.15584 53.90909
## 8 male white 54.51471 51.29412 54.19118 55.38235 53.42647
#標準差
aggregate(cbind(read, write, math, science, socst) ~ gender+race, data = hsb, sd)
## gender race read write math science socst
## 1 female african-amer 7.2933057 9.546781 7.378069 9.525270 11.535341
## 2 male african-amer 7.3581830 9.504385 4.535574 8.577379 10.311806
## 3 female asian 9.1456469 7.529703 11.106626 10.920982 10.606602
## 4 male asian 0.5773503 10.115994 8.736895 5.291503 7.637626
## 5 female hispanic 12.2429943 6.744695 6.842381 5.492143 9.100450
## 6 male hispanic 8.6639542 9.115358 6.833177 10.211231 9.195874
## 7 female white 9.7969648 7.261331 8.807329 7.691528 10.136154
## 8 male white 10.8373217 10.317438 10.056938 10.392347 11.603288
#偏態
aggregate(cbind(read, write, math, science, socst) ~ gender+race, data = hsb, skewness)
## gender race read write math science socst
## 1 female african-amer 1.0908453 0.2163986 1.48488184 0.73940428 -0.30003839
## 2 male african-amer -0.5014614 0.2805474 0.21617314 -0.98118254 -0.64522406
## 3 female asian -0.0720213 -0.8936840 -0.18751759 -0.15405549 0.13198759
## 4 male asian 0.7071068 -0.6993411 -0.45563859 -0.59517006 0.38180177
## 5 female hispanic 0.8336115 0.4399599 -0.07735766 0.56561271 0.43962390
## 6 male hispanic 0.3505098 0.6740362 0.38302113 0.10751219 0.01372901
## 7 female white 0.2652688 -0.8495136 0.05270082 0.01337789 -0.49165481
## 8 male white -0.1477733 -0.3818725 0.14096486 -0.50797997 -0.58469114
#峰度
aggregate(cbind(read, write, math, science, socst) ~ gender+race, data = hsb, kurtosis)
## gender race read write math science socst
## 1 female african-amer 5.293553 2.441087 4.698841 2.597492 2.554017
## 2 male african-amer 2.571704 1.213593 1.944268 2.552533 2.315460
## 3 female asian 1.788177 2.911449 1.718401 1.825103 2.708239
## 4 male asian 1.500000 1.500000 1.500000 1.500000 1.500000
## 5 female hispanic 3.454724 1.920618 2.362541 2.095000 1.880657
## 6 male hispanic 2.303890 3.191498 1.951063 2.659911 1.923078
## 7 female white 2.254607 3.211956 2.336165 2.573160 2.609000
## 8 male white 2.193766 2.045456 2.284359 2.425587 2.560890
my_summary <- function(x) {
require(moments)
funs <- c(mean, sd, skewness, kurtosis)
sapply(funs, function(f) f(x, na.rm = TRUE))
}
sapply(hsb[, c(7:11)], my_summary)
## read write math science socst
## [1,] 52.2300000 52.7750000 52.6450000 51.8500000 52.4050000
## [2,] 10.2529368 9.4785860 9.3684478 9.9008908 10.7357935
## [3,] 0.1948373 -0.4784158 0.2844115 -0.1872277 -0.3786624
## [4,] 2.3630520 2.2385271 2.3373193 2.4283076 2.4585395
#數字代表: 1=平均數；2=標準差；3=偏態；4=峰度
with(hsb, aggregate(hsb[, 7:11], by = list(gender, race), FUN = my_summary))
## Group.1 Group.2 read.1 read.2 read.3 read.4 write.1
## 1 female african-amer 46.7692308 7.2933057 1.0908453 5.2935531 48.8461538
## 2 male african-amer 46.8571429 7.3581830 -0.5014614 2.5717042 47.0000000
## 3 female asian 51.7500000 9.1456469 -0.0720213 1.7881765 58.8750000
## 4 male asian 52.3333333 0.5773503 0.7071068 1.5000000 55.6666667
## 5 female hispanic 45.9090909 12.2429943 0.8336115 3.4547239 48.9090909
## 6 male hispanic 47.3076923 8.6639542 0.3505098 2.3038901 44.3846154
## 7 female white 53.4025974 9.7969648 0.2652688 2.2546065 56.4935065
## 8 male white 54.5147059 10.8373217 -0.1477733 2.1937664 51.2941176
## write.2 write.3 write.4 math.1 math.2 math.3
## 1 9.5467809 0.2163986 2.4410868 47.53846154 7.37806868 1.48488184
## 2 9.5043850 0.2805474 1.2135932 45.28571429 4.53557368 0.21617314
## 3 7.5297031 -0.8936840 2.9114493 56.75000000 11.10662608 -0.18751759
## 4 10.1159939 -0.6993411 1.5000000 58.66666667 8.73689495 -0.45563859
## 5 6.7446949 0.4399599 1.9206184 45.27272727 6.84238130 -0.07735766
## 6 9.1153576 0.6740362 3.1914975 49.23076923 6.83317698 0.38302113
## 7 7.2613312 -0.8495136 3.2119560 53.77922078 8.80732855 0.05270082
## 8 10.3174375 -0.3818725 2.0454564 54.19117647 10.05693843 0.14096486
## math.4 science.1 science.2 science.3 science.4 socst.1
## 1 4.69884144 40.69230769 9.52527003 0.73940428 2.59749181 49.69230769
## 2 1.94426762 46.71428571 8.57737889 -0.98118254 2.55253276 49.00000000
## 3 1.71840106 50.87500000 10.92098243 -0.15405549 1.82510261 52.25000000
## 4 1.50000000 53.00000000 5.29150262 -0.59517006 1.50000000 47.66666667
## 5 2.36254116 45.18181818 5.49214315 0.56561271 2.09499993 50.27272727
## 6 1.95106288 45.53846154 10.21123062 0.10751219 2.65991060 45.69230769
## 7 2.33616461 53.15584416 7.69152804 0.01337789 2.57316021 53.90909091
## 8 2.28435866 55.38235294 10.39234709 -0.50797997 2.42558706 53.42647059
## socst.2 socst.3 socst.4
## 1 11.53534146 -0.30003839 2.55401720
## 2 10.31180553 -0.64522406 2.31545975
## 3 10.60660172 0.13198759 2.70823885
## 4 7.63762616 0.38180177 1.50000000
## 5 9.10044954 0.43962390 1.88065695
## 6 9.19587421 0.01372901 1.92307798
## 7 10.13615444 -0.49165481 2.60899977
## 8 11.60328849 -0.58469114 2.56089041