ANLY 545 Homework #1 - Huaxin Kang

install.packages(“vcd”) library(“vcd”)

Part I

Original data format

UCBAdmissions

## , , 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

1. Find the total number of cases contained in this table.

sum(UCBAdmissions)

## [1] 4526

2. For each department, find the total number of applicants.

colSums(UCBAdmissions, dims = 2)

##   A   B   C   D   E   F 
## 933 585 918 792 584 714

3. For each department, find the overall proportion of applicants who were admitted.

round(prop.table(margin.table(UCBAdmissions,c(1,3)),2),4)

##           Dept
## Admit           A      B      C      D      E      F
##   Admitted 0.6442 0.6325 0.3508 0.3396 0.2517 0.0644
##   Rejected 0.3558 0.3675 0.6492 0.6604 0.7483 0.9356

4. Construct a tabular display of department (rows) and gender (columns), showing the proportion of applicants in each cell who were admitted relative to the total applicants in that cell.

ftable(round(prop.table(UCBAdmissions,c(2,3)),2),row.vars="Dept",col.vars=c("Gender","Admit"))

##      Gender     Male            Female         
##      Admit  Admitted Rejected Admitted Rejected
## Dept                                           
## A               0.62     0.38     0.82     0.18
## B               0.63     0.37     0.68     0.32
## C               0.37     0.63     0.34     0.66
## D               0.33     0.67     0.35     0.65
## E               0.28     0.72     0.24     0.76
## F               0.06     0.94     0.07     0.93

Part II

data(UKSoccer, package="vcd")

1. Verify that the total number of games represented in this table is 380.

sum(UKSoccer)

## [1] 380

2. Find the marginal total of the number of goals scored by each of the home and away teams.

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

Home Total Goals:

76*0+142*1+90*2+45*3+27*4

## [1] 565

Away Total Goals:

140*0+136*1+55*2+38*3+11*4

## [1] 404

3. Express each of the marginal totals as proportions.

Overall goals total:

565+404

## [1] 969

Home Marginal Total Proportion:

round(565/(565+404),2)

## [1] 0.58

Away Marginal Total Proportion:

round(404/(565+404),2)

## [1] 0.42