Homework 1 Anly 545

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

Exercise 2.3 (a) Find the total number of cases contained in this table.

data= UCBAdmissions
summary(data)

## Number of cases in table: 4526 
## Number of factors: 3 
## Test for independence of all factors:
##  Chisq = 2000.3, df = 16, p-value = 0

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

ftable(UCBAdmissions, row.vars="Dept", col.vars = c( "Admit"))

##      Admit Admitted Rejected
## Dept                        
## A               601      332
## B               370      215
## C               322      596
## D               269      523
## E               147      437
## F                46      668

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

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

##           Dept
## Admit               A          B          C          D          E
##   Admitted 0.64415863 0.63247863 0.35076253 0.33964646 0.25171233
##   Rejected 0.35584137 0.36752137 0.64923747 0.66035354 0.74828767
##           Dept
## Admit               F
##   Admitted 0.06442577
##   Rejected 0.93557423

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.

propt=prop.table(UCBAdmissions, c(2,3))

ftable(round(propt, 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

Exercise 2.5 (a) Verify that the total number of games represented in this table is 380.

install.packages("vcd",repos = "http://cran.us.r-project.org")

## 
## The downloaded binary packages are in
##  /var/folders/xj/tl6pm98x5qb3b_94_pxtg29h0000gn/T//RtmpfmFCjV/downloaded_packages

library(vcd)

## Loading required package: grid

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

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

addmargins(UKSoccer)

##      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

3. Express each of the marginal totals as proportions.

prop.table(addmargins(UKSoccer))

##      Away
## Home             0            1            2            3            4
##   0   0.0177631579 0.0190789474 0.0065789474 0.0052631579 0.0013157895
##   1   0.0388157895 0.0348684211 0.0092105263 0.0078947368 0.0026315789
##   2   0.0184210526 0.0210526316 0.0092105263 0.0078947368 0.0026315789
##   3   0.0125000000 0.0092105263 0.0046052632 0.0026315789 0.0006578947
##   4   0.0046052632 0.0052631579 0.0065789474 0.0013157895 0.0000000000
##   Sum 0.0921052632 0.0894736842 0.0361842105 0.0250000000 0.0072368421
##      Away
## Home           Sum
##   0   0.0500000000
##   1   0.0934210526
##   2   0.0592105263
##   3   0.0296052632
##   4   0.0177631579
##   Sum 0.2500000000