4.3

a

JobSat <- matrix(c(1,2,1,0,3,3,6,1,10,10,14,9,6,7,12,11),4,4)
dimnames(JobSat) = list(income=c("<15K","15-25K","25-40K",">40K"),satisfaction=c("VeryD","LittleD","ModerateS","VeryS"))
JobSat <- as.table(JobSat)
JobSat
##         satisfaction
## income   VeryD LittleD ModerateS VeryS
##   <15K       1       3        10     6
##   15-25K     2       3        10     7
##   25-40K     1       6        14    12
##   >40K       0       1         9    11

b

ChiSquare Test

chisq.test(JobSat)
## Warning in chisq.test(JobSat): Chi-squared approximation may be incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  JobSat
## X-squared = 5.9655, df = 9, p-value = 0.7434

MonteCarlo Test

chisq.test(JobSat, simulate = TRUE)
## 
##  Pearson's Chi-squared test with simulated p-value (based on 2000
##  replicates)
## 
## data:  JobSat
## X-squared = 5.9655, df = NA, p-value = 0.7751

P value is not low for chisquare test. This implies there is relation between income levels and satisfaction levels. Both Chisquare and Montecarlo test produce approximately same result and data may not be enough to change conclusion, so the conclusion drawn from chisquare doesnot change.

c

library(vcdExtra)
## Warning: package 'vcdExtra' was built under R version 3.5.1
## Loading required package: vcd
## Warning: package 'vcd' was built under R version 3.5.1
## Loading required package: grid
## Loading required package: gnm
## Warning: package 'gnm' was built under R version 3.5.1
## 
## Attaching package: 'vcdExtra'
## The following object is masked _by_ '.GlobalEnv':
## 
##     JobSat
CMHtest(JobSat)
## Cochran-Mantel-Haenszel Statistics for income by satisfaction 
## 
##                  AltHypothesis  Chisq Df     Prob
## cor        Nonzero correlation 2.9830  1 0.084144
## rmeans  Row mean scores differ 4.4774  3 0.214318
## cmeans  Col mean scores differ 3.1036  3 0.375931
## general    General association 5.9034  9 0.749549

4.6

data("Mammograms",package = "vcdExtra")
Kappa(Mammograms)
##             value     ASE      z  Pr(>|z|)
## Unweighted 0.3713 0.06033  6.154 7.560e-10
## Weighted   0.5964 0.04923 12.114 8.901e-34
agreementplot(Mammograms,main = "unweighted", weights = 1)

agreementplot(Mammograms, main="Weighted")

c

assocstats(Mammograms)
##                     X^2 df   P(> X^2)
## Likelihood Ratio 92.619  9 4.4409e-16
## Pearson          83.516  9 3.2307e-14
## 
## Phi-Coefficient   : NA 
## Contingency Coeff.: 0.657 
## Cramer's V        : 0.503

Chisquare Values shows there is medium to strong association between the variables at 0.005 significance level. This implies the larger the chisquare value the stronger a relationship between the results of two raters.