Homework #1–Exercises 2.3 and 2.5

library(vcd)

## Warning: package 'vcd' was built under R version 3.3.3

## Loading required package: grid

library(vcdExtra)

## Warning: package 'vcdExtra' was built under R version 3.3.3

## Loading required package: gnm

## Warning: package 'gnm' was built under R version 3.3.3

str(UCBAdmissions)  #A Three-Way table of frequencies

##  table [1:2, 1:2, 1:6] 512 313 89 19 353 207 17 8 120 205 ...
##  - attr(*, "dimnames")=List of 3
##   ..$ Admit : chr [1:2] "Admitted" "Rejected"
##   ..$ Gender: chr [1:2] "Male" "Female"
##   ..$ Dept  : chr [1:6] "A" "B" "C" "D" ...

plot(UCBAdmissions)

dim(UCBAdmissions)

## [1] 2 2 6

dimnames(UCBAdmissions)

## $Admit
## [1] "Admitted" "Rejected"
## 
## $Gender
## [1] "Male"   "Female"
## 
## $Dept
## [1] "A" "B" "C" "D" "E" "F"

sum(UCBAdmissions)

## [1] 4526

Tables are often created from raw data, in case form or frequency form, using the functions, table() and xtabs(). For smallish frequency tables that are already in tabular form, you can enter the frequencies in a matrix, and then assign dimnames and other attributes.

```

Let’s generate a frequency table from discrete factor variables in a data frame using the table() function, set.seed(), etc.:

set.seed(123456)    #Reproducibility
n<-100
Admit<-factor(sample(c("Admitted", "Rejected"), n, replace=TRUE))
Gender<-factor(sample(c("Male", "Female"), n, replace = TRUE))
Dept<-factor(sample(c("A", "B", "C", "D", "E", "F"), n, replace=TRUE))
DFdata<-data.frame(Admit, Gender, Dept)

head(DFdata, 6)

##      Admit Gender Dept
## 1 Rejected   Male    B
## 2 Rejected Female    A
## 3 Admitted   Male    F
## 4 Admitted   Male    B
## 5 Admitted Female    A
## 6 Admitted Female    C

str(DFdata)

## 'data.frame':    100 obs. of  3 variables:
##  $ Admit : Factor w/ 2 levels "Admitted","Rejected": 2 2 1 1 1 1 2 1 2 1 ...
##  $ Gender: Factor w/ 2 levels "Female","Male": 2 1 2 2 1 1 1 2 1 1 ...
##  $ Dept  : Factor w/ 6 levels "A","B","C","D",..: 2 1 6 2 1 3 5 1 5 2 ...

plot(DFdata)

Rows, columns, and individual values in a data frame can be manipulated in the same way as a matrix, using subscripting ([,]).

DFdata[2,3]

## [1] A
## Levels: A B C D E F

Also, variables can be extracted using the $ operator: use Dept

DFdata$Dept

##   [1] B A F B A C E A E B F B A F C D B B F D B F D C C F B D C A C D B E F
##  [36] B C C C D F B A C A C A D B F E F C B D B A F D D D E A E E F E D A A
##  [71] E C C D F F D C B E F F D B C B F A F F B D E E A D C C D B
## Levels: A B C D E F

For Exercise 2.3 (a), (b), and (c), we have the following:

(a) From above (sum(UCBAdmissions)) the total number of cases contained in this table is 4526

(b) The total number of applicants for each department is the following:

table(DFdata$Dept)

## 
##  A  B  C  D  E  F 
## 14 19 18 18 12 19

(c) The overall proportion of applicants who are admitted

for each department is the following:

DFtab<-table(DFdata$Dept)

prop.table(DFtab)

## 
##    A    B    C    D    E    F 
## 0.14 0.19 0.18 0.18 0.12 0.19

(d) Below, we construct a tabular display of department (rows) and gender (columns). Then we create a tabular display showing the proportion of applicants in each cell who are admitted relative to the total applicants in that cell.

table(DFdata$Dept, DFdata$Gender)

##    
##     Female Male
##   A      5    9
##   B      6   13
##   C     10    8
##   D     13    5
##   E      9    3
##   F      9   10

Protab<-table(DFdata$Dept, DFdata$Gender)

prop.table(Protab)

##    
##     Female Male
##   A   0.05 0.09
##   B   0.06 0.13
##   C   0.10 0.08
##   D   0.13 0.05
##   E   0.09 0.03
##   F   0.09 0.10

For Exercises 2.5 (a), (b), (c), and (d), we have the following:

data("UKSoccer", Package = "vcd")

## Warning in data("UKSoccer", Package = "vcd"): data set 'vcd' not found

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

plot(UKSoccer)

(a) Find the total number of games represented in the table above:

sum(UKSoccer)

## [1] 380

Two-way frequency table: We will look at the table’s structure to

get a feel for its row-column format:

str(UKSoccer)

##  table [1:5, 1:5] 27 59 28 19 7 29 53 32 14 8 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ Home: chr [1:5] "0" "1" "2" "3" ...
##   ..$ Away: chr [1:5] "0" "1" "2" "3" ...

mytab<-ftable(UKSoccer [ ,1:5])

We can also find the total number of games represented in the table above using the following:

margin.table(mytab)

## [1] 380

(b) We show all marginal totals (below) of the number of goals scored by each of the home and away teams:

addmargins(mytab)

##                      Sum
##      27  29 10  8  2  76
##      59  53 14 12  4 142
##      28  32 14 12  4  90
##      19  14  7  4  1  45
##       7   8 10  2  0  27
## Sum 140 136 55 38 11 380

(c) We express each of the marginal totals as proportions below:

prop.table(mytab)

##      Away           0           1           2           3           4
## Home                                                                 
## 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