Contingency Analysis
Group 2.2
21 04 2021
Contingency tables - qualitative data
Introductory exercise
Do you believe in the Afterlife? https://nationalpost.com/news/canada/millennials-do-you-believe-in-life-after-life A survey was conducted and a random sample of 1091 questionnaires is given in the form of the following contingency table:
## Believe
## Gender Yes No
## Female 435 375
## Male 147 134
Our task is to check if there is a significant relationship between the belief in the afterlife and gender. We can perform this procedure with the simple chi-square statistics and chosen qualitative correlation coefficient (two-way 2x2 table).
## Believe
## Gender Yes No
## Female 0.3987168 0.3437214
## Male 0.1347388 0.1228231As you can see we can calculate our chi-square statistic really quickly for two-way tables or larger. Now we can standardize this contingency measure to see if the relationship is significant.
## [1] 0.01218871
Laboratory - 21/04/2021. Bivariate analysis for the ‘Titanic’ data.
Let’s consider the titanic dataset which contains a complete list of passengers and crew members on the RMS Titanic. It includes a variable indicating whether a person did survive the sinking of the RMS Titanic on April 15, 1912. A data frame contains 2456 observations on 14 variables.
The website http://www.encyclopedia-titanica.org/ offers detailed information about passengers and crew members on the RMS Titanic. According to the website 1317 passengers and 890 crew member were aboard.
8 musicians and 9 employees of the shipyard company are listed as passengers, but travelled with a free ticket, which is why they have NA values in fare. In addition to that, fare is truely missing for a few regular passengers.
In the following chunk, please find few significant correlations between nominal variables, present their distribution on the plot and in the form of a contingency table.
How to visualize cross-tabulations? Please find some hints here and here.
#Deleting rows with info about ppl other than victims or survivors
ship<-filter(titanic,Status!="")
head(ship)## Status Disembarked.at Home.Country Age
## COLERIDGE, Mr Reginald Charles Victim Not Disembarked England 29
## STOKES, Mr Philip Joseph Victim Not Disembarked England 25
## REEVES, Mr David Victim Not Disembarked England 36
## PARKER, Mr Clifford Richard Victim Not Disembarked Channel Islands 28
## MITCHELL, Mr Henry Michael Victim Not Disembarked Channel Islands 71
## PAIN, Dr Alfred Victim Not Disembarked Canada 23
## Year.of.Birth Crew.or.Passenger. Gender
## COLERIDGE, Mr Reginald Charles 1883 Passenger Male
## STOKES, Mr Philip Joseph 1887 Passenger Male
## REEVES, Mr David 1876 Passenger Male
## PARKER, Mr Clifford Richard 1884 Passenger Male
## MITCHELL, Mr Henry Michael 1841 Passenger Male
## PAIN, Dr Alfred 1888 Passenger Male
## Class...Department Embarked
## COLERIDGE, Mr Reginald Charles 2nd Class Southampton
## STOKES, Mr Philip Joseph 2nd Class Southampton
## REEVES, Mr David 2nd Class Southampton
## PARKER, Mr Clifford Richard 2nd Class Southampton
## MITCHELL, Mr Henry Michael 2nd Class Southampton
## PAIN, Dr Alfred 2nd Class Southampton
## Job Job.details
## COLERIDGE, Mr Reginald Charles Advertising Consultant Advertising Consultant
## STOKES, Mr Philip Joseph Bricklayer Bricklayer
## REEVES, Mr David Carpenter, Joiner Carpenter / Joiner
## PARKER, Mr Clifford Richard Clerk Clerk
## MITCHELL, Mr Henry Michael Coach Painter Coach Painter
## PAIN, Dr Alfred Doctor Doctor
## Ticket.Number Fare.Price Fare_GBP Fare_today
## COLERIDGE, Mr Reginald Charles 14263 P10 10s 10.5 862.155
## STOKES, Mr Philip Joseph 13540 P10 10s 10.5 862.155
## REEVES, Mr David 17248 P10 10s 10.5 862.155
## PARKER, Mr Clifford Richard 14888 P10 10s 10.5 862.155
## MITCHELL, Mr Henry Michael 24580 P10 10s 10.5 862.155
## PAIN, Dr Alfred 244278 P10 10s 10.5 862.155
## Profile.on.Encyclopedia.Titanica
## COLERIDGE, Mr Reginald Charles http://www.encyclopedia-titanica.org/titanic-victim/reginald-charles-coleridge.html
## STOKES, Mr Philip Joseph http://www.encyclopedia-titanica.org/titanic-victim/philip-joseph-stokes.html
## REEVES, Mr David http://www.encyclopedia-titanica.org/titanic-victim/david-reeves.html
## PARKER, Mr Clifford Richard http://www.encyclopedia-titanica.org/titanic-victim/clifford-richard-parker.html
## MITCHELL, Mr Henry Michael http://www.encyclopedia-titanica.org/titanic-victim/henry-michael-mitchell.html
## PAIN, Dr Alfred http://www.encyclopedia-titanica.org/titanic-victim/alfred-pain.htmltest<-group_by(ship,Status)
test<-summarise(test,n())
test## # A tibble: 2 x 2
## Status `n()`
## * <chr> <int>
## 1 Survivor 711
## 2 Victim 1496#Creating new dataset that contains only info about passengers
d <- ship %>% group_by(Class...Department) %>% summarise(Dead=sum(Status=="Victim"),Alive=sum(Status=="Survivor"))
deaths<-as.data.frame(d)
row.names(deaths)<-c('1st','2nd','3rd','Deck','Engineer','Restaurant','Victualling')
deaths<-deaths[,-1]
print(deaths)## Dead Alive
## 1st 123 201
## 2nd 166 119
## 3rd 528 180
## Deck 23 43
## Engineer 253 71
## Restaurant 66 3
## Victualling 337 94prop.table(deaths)## Dead Alive
## 1st 0.05573176 0.091073856
## 2nd 0.07521522 0.053919348
## 3rd 0.23923879 0.081558677
## Deck 0.01042139 0.019483462
## Engineer 0.11463525 0.032170367
## Restaurant 0.02990485 0.001359311
## Victualling 0.15269597 0.042591754Phi(deaths)## [1] 0.3387276ContCoef(deaths)## [1] 0.3208222CramerV(deaths)## [1] 0.3387276TschuprowT(deaths)## [1] 0.2164277mosaicplot(deaths)
Here, please interpret your findings.
Almost whole Restaurant Crew died. The higher passenger’s Class, the higher chances of surviving.