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