Descriptive Statistics

Titanic Bivariate Analysis

Contingency 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.

Data Cleansing

##                          Status Disembarked.at Home.Country Age Year.of.Birth
## DE GRASSE, Mr J.           <NA>      Cherbourg               NA            NA
## EVANS, Miss                <NA>      Cherbourg               NA            NA
## MULLEN,                    <NA>      Cherbourg               NA            NA
## WOTTON, Mr Henry Swaffin   <NA>      Cherbourg               54          1858
## BRAND, Mr                  <NA>      Cherbourg               NA            NA
## FLETCHER, Miss N.          <NA>      Cherbourg               NA            NA
##                          Crew.or.Passenger. Gender Class...Department
## DE GRASSE, Mr J.                  Passenger   Male          2nd Class
## EVANS, Miss                       Passenger Female          2nd Class
## MULLEN,                           Passenger Female          2nd Class
## WOTTON, Mr Henry Swaffin          Passenger   Male          1st Class
## BRAND, Mr                         Passenger   Male          1st Class
## FLETCHER, Miss N.                 Passenger Female          1st Class
##                             Embarked     Job               Job.details
## DE GRASSE, Mr J.         Southampton                                  
## EVANS, Miss              Southampton                                  
## MULLEN,                  Southampton                                  
## WOTTON, Mr Henry Swaffin Southampton Butcher Butcher's Shop Proprietor
## BRAND, Mr                Southampton                                  
## FLETCHER, Miss N.        Southampton                                  
##                          Ticket.Number Fare.Price Fare_GBP Fare_today
## DE GRASSE, Mr J.                   761         P1      1.0     82.110
## EVANS, Miss                         88         P1      1.0     82.110
## MULLEN,                            404         P1      1.0     82.110
## WOTTON, Mr Henry Swaffin            86     P1 10s      1.5    123.165
## BRAND, Mr                            8     P1 10s      1.5    123.165
## FLETCHER, Miss N.                  405     P1 10s      1.5    123.165
##                                                                                        Profile.on.Encyclopedia.Titanica
## DE GRASSE, Mr J.                                http://www.encyclopedia-titanica.org/titanic-biography/j-de-grasse.html
## EVANS, Miss                                           http://www.encyclopedia-titanica.org/titanic-biography/evans.html
## MULLEN,                                              http://www.encyclopedia-titanica.org/titanic-biography/mullen.html
## WOTTON, Mr Henry Swaffin http://www.encyclopedia-titanica.org/titanic-cross-channel-passenger/henry-swaffin-wotton.html
## BRAND, Mr                                             http://www.encyclopedia-titanica.org/titanic-biography/brand.html
## FLETCHER, Miss N.                                http://www.encyclopedia-titanica.org/titanic-biography/n-fletcher.html

Survival by Passenger Class

We will create a contingency table to analyze the relationship between survival and passenger class.

##           
##            1st Class 2nd Class 3rd Class Deck Crew Engineering Crew
##   Victim         123       166       528        23              253
##   Survivor       201       119       180        43               71
##           
##            Restaurant Staff Victualling Crew
##   Victim                 66              337
##   Survivor                3               94

##           
##            Female Male
##   Victim      130 1366
##   Survivor    359  352

##           
##            Female Male
##   Victim      130 1366
##   Survivor    359  352

Statistics number

## [1] "Phi value"

## [1] 0.3387276

## [1] "Contingency Coeficient"

## [1] 0.3208222

## [1] "Cramer Value"

## [1] 0.3387276

## [1] "Tschuprow"

## [1] 0.2164277

Association between survival status and passenger class is moderate based on coefficients.

## [1] "Phi value"

## [1] 0.4703662

## [1] "Contingency Coeficient"

## [1] 0.4256325

## [1] "Cramer Value"

## [1] 0.4703662

## [1] "Tschuprow"

## [1] 0.4703662

Association between survival status and gender is significantly higher.

Chi-Square

## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 253.22, df = 6, p-value < 2.2e-16

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  contingency_table_gender
## X-squared = 485.87, df = 1, p-value < 2.2e-16

P values are small, so it also sugest significant correlation between survival status and passenger class or gender.

The results indicate that there is a statistically significant relationship between survival status and the passenger class or gender. Moreover we can conclude that gender correlation to survival status is slightly stronger that correlation between passenger class and survival status.

Plots