Descriptive Statistics

Bivariate Analysis

Exercise 2. 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.

Analysis

First we clean the empty values in Status column then create a geom bar with general data of survivours and victims

dane2<-titanic
cleanStatus <- dane2[!dane2$Status == "", ]

ggplot(cleanStatus, aes(x = Status)) +
  geom_bar() +
  geom_text(stat = "count", aes(label = ..count..), position = position_dodge(width = 0.9), vjust = -0.5) +
  labs(title = "Survivors and Victims",
       x = "Status",
       y = "Count") +
  theme_minimal()

## Warning: The dot-dot notation (`..count..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(count)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Now lets look at gender in context of survival rates

ggplot(cleanStatus, aes(x = Status, fill = Gender)) +
  geom_bar(position = "dodge") +
  geom_text(stat = "count", aes(label = ..count..), position = position_dodge(width = 0.9), vjust = -0.5) +
  labs(title = "Survival Rate by Gender",
       x = "Status",
       y = "Count",
       fill = "Gender") +
  theme_minimal()

corelation estimation

cleanStatus$status_binary <- ifelse(cleanStatus$Status == "Survivor", 1, 0)
cleanStatus$gender_binary <- ifelse(cleanStatus$Gender == "Female", 1, 0)

status_gender <- table(cleanStatus$status_binary, cleanStatus$gender_binary)

phi_coefficient <- cor(cleanStatus$status_binary, cleanStatus$gender_binary)
print(phi_coefficient)

## [1] 0.4703662

0.47 result indicates a noticible relation between gender and survival rate. It is not an extremly strong relation but it’s not insignificant either. This suggests that females had a higher likelihood of surviving compared to males, but other factors also contribute to survival chances.

And now let’s move on to vizualising the survival rates in terms of being a crew member or a passenger

ggplot(cleanStatus, aes(x = Status, fill = Crew.or.Passenger.)) +
  geom_bar(position = "dodge") +
  geom_text(stat = "count", aes(label = ..count..), position = position_dodge(width = 0.9), vjust = -0.5) +
  labs(title = "Survival Rate by the Cause of the Excursion",
       x = "Status",
       y = "Crew Member or Passenger") +
  theme_minimal()

# corelation estimation

cleanStatus$Crew.or.Passenger_binary <- ifelse(cleanStatus$Crew.or.Passenger == "Passenger", 1, 0)

status_Crew.or.Passenger <- table(cleanStatus$status_binary, cleanStatus$gender_binary)

phi_coefficient <- cor(cleanStatus$status_binary, cleanStatus$Crew.or.Passenger_binary)

print(phi_coefficient)

## [1] 0.1496655

A correlation coefficient of 0.15 shows a weak positive relationship, meaning passengers were slightly more likely to survive than crew members on the Titanic.

Survival based on class

ggplot(cleanStatus, aes(x = Class...Department, fill = Status)) +
  geom_bar(position = "dodge") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  geom_text(stat = "count", aes(label = ..count..), position = position_dodge(width = 0.9), vjust = -0.5) +
  labs(title = "Survival Rate by class and department of passengers",
       x = "Status",
       y = "Count",
       fill = "Class Department") 

we single out only passengers of ship

onlyPassengers <- cleanStatus[!cleanStatus$Crew.or.Passenger. == "Crew", ]

ggplot(onlyPassengers, aes(x = Class...Department, fill = Status)) +
  geom_bar(position = "dodge") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  geom_text(stat = "count", aes(label = ..count..), position = position_dodge(width = 0.9), vjust = -0.5) +
  labs(title = "Survival Rate by class and department of passengers",
       x = "Status",
       y = "Count",
       fill = "Class Department")