getwd()
## [1] "/Users/nishitatamuly/Desktop/HU/ANLY 545 - R/R"
setwd("/Users/nishitatamuly/Desktop/HU/ANLY 545 - R/R")
getwd()
## [1] "/Users/nishitatamuly/Desktop/HU/ANLY 545 - R/R"
library(vcd)
## Loading required package: grid
library(vcdExtra)
## Loading required package: gnm
Q1
data <- UCBAdmissions
data
## , , Dept = A
##
## Gender
## Admit Male Female
## Admitted 512 89
## Rejected 313 19
##
## , , Dept = B
##
## Gender
## Admit Male Female
## Admitted 353 17
## Rejected 207 8
##
## , , Dept = C
##
## Gender
## Admit Male Female
## Admitted 120 202
## Rejected 205 391
##
## , , Dept = D
##
## Gender
## Admit Male Female
## Admitted 138 131
## Rejected 279 244
##
## , , Dept = E
##
## Gender
## Admit Male Female
## Admitted 53 94
## Rejected 138 299
##
## , , Dept = F
##
## Gender
## Admit Male Female
## Admitted 22 24
## Rejected 351 317
summary(UCBAdmissions) #total cases
## Number of cases in table: 4526
## Number of factors: 3
## Test for independence of all factors:
## Chisq = 2000.3, df = 16, p-value = 0
ftable(data) #number of applicants per dept
## Dept A B C D E F
## Admit Gender
## Admitted Male 512 353 120 138 53 22
## Female 89 17 202 131 94 24
## Rejected Male 313 207 205 279 138 351
## Female 19 8 391 244 299 317
colSums(data,dims = 2) #total applications per dept
## A B C D E F
## 933 585 918 792 584 714
prop.table(data) #admit proportion
## , , Dept = A
##
## Gender
## Admit Male Female
## Admitted 0.113124171 0.019664163
## Rejected 0.069155988 0.004197967
##
## , , Dept = B
##
## Gender
## Admit Male Female
## Admitted 0.077993814 0.003756076
## Rejected 0.045735749 0.001767565
##
## , , Dept = C
##
## Gender
## Admit Male Female
## Admitted 0.026513478 0.044631021
## Rejected 0.045293858 0.086389748
##
## , , Dept = D
##
## Gender
## Admit Male Female
## Admitted 0.030490499 0.028943880
## Rejected 0.061643836 0.053910738
##
## , , Dept = E
##
## Gender
## Admit Male Female
## Admitted 0.011710119 0.020768891
## Rejected 0.030490499 0.066062749
##
## , , Dept = F
##
## Gender
## Admit Male Female
## Admitted 0.004860804 0.005302696
## Rejected 0.077551922 0.070039770
aperm(data,c(3,2,1)) #proportion table by dept
## , , Admit = Admitted
##
## Gender
## Dept Male Female
## A 512 89
## B 353 17
## C 120 202
## D 138 131
## E 53 94
## F 22 24
##
## , , Admit = Rejected
##
## Gender
## Dept Male Female
## A 313 19
## B 207 8
## C 205 391
## D 279 244
## E 138 299
## F 351 317
ftable(prop.table(data,c(2,3)),row.vars="Dept",col.vars=c("Gender","Admit"))
## Gender Male Female
## Admit Admitted Rejected Admitted Rejected
## Dept
## A 0.62060606 0.37939394 0.82407407 0.17592593
## B 0.63035714 0.36964286 0.68000000 0.32000000
## C 0.36923077 0.63076923 0.34064081 0.65935919
## D 0.33093525 0.66906475 0.34933333 0.65066667
## E 0.27748691 0.72251309 0.23918575 0.76081425
## F 0.05898123 0.94101877 0.07038123 0.92961877
Q2
data("UKSoccer", package = "vcd")
ftable(UKSoccer)
## Away 0 1 2 3 4
## Home
## 0 27 29 10 8 2
## 1 59 53 14 12 4
## 2 28 32 14 12 4
## 3 19 14 7 4 1
## 4 7 8 10 2 0
summary(UKSoccer)
## Number of cases in table: 380
## Number of factors: 2
## Test for independence of all factors:
## Chisq = 18.699, df = 16, p-value = 0.2846
## Chi-squared approximation may be incorrect
sum(UKSoccer)
## [1] 380
UKSoccerNew<-addmargins(UKSoccer)
UKSoccerNew
## Away
## Home 0 1 2 3 4 Sum
## 0 27 29 10 8 2 76
## 1 59 53 14 12 4 142
## 2 28 32 14 12 4 90
## 3 19 14 7 4 1 45
## 4 7 8 10 2 0 27
## Sum 140 136 55 38 11 380
Homegoals <- 76*0+142*1+90*2+45*3+27*4
Awaygoals <- 140*0+136*1+55*2+38*3+11*4
totalgoals <- 565+404
#home marginalprop
round(565/(565+404),2)
## [1] 0.58
#away marginalprop
round(404/(565+404),2)
## [1] 0.42
#based on overal marginal proportions home teams scores more goals on average
prop.table(UKSoccer)
## Away
## Home 0 1 2 3 4
## 0 0.071052632 0.076315789 0.026315789 0.021052632 0.005263158
## 1 0.155263158 0.139473684 0.036842105 0.031578947 0.010526316
## 2 0.073684211 0.084210526 0.036842105 0.031578947 0.010526316
## 3 0.050000000 0.036842105 0.018421053 0.010526316 0.002631579
## 4 0.018421053 0.021052632 0.026315789 0.005263158 0.000000000