titanic

this is the titanic case study

titanic.df <- read.csv(paste("Titanic Data.csv", sep=""))

total passengers

length(titanic.df$Survived)

## [1] 889

No of passengers survived in ship

table(titanic.df$Survived)

## 
##   0   1 
## 549 340

the required proportions and percentages are shown

mytable <- with(titanic.df, table(Survived))
mytable  # frequencies

## Survived
##   0   1 
## 549 340

prop.table(mytable) # proportions

## Survived
##         0         1 
## 0.6175478 0.3824522

prop.table(mytable)*100 # percentages

## Survived
##        0        1 
## 61.75478 38.24522

now required for the first class passengers who survived along with percantage and proportions

mytable <- xtabs(~ Pclass+Survived, data=titanic.df)
mytable # frequencies

##       Survived
## Pclass   0   1
##      1  80 134
##      2  97  87
##      3 372 119

prop.table(mytable) # proportions

##       Survived
## Pclass          0          1
##      1 0.08998875 0.15073116
##      2 0.10911136 0.09786277
##      3 0.41844769 0.13385827

prop.table(mytable)*100 # percentages

##       Survived
## Pclass         0         1
##      1  8.998875 15.073116
##      2 10.911136  9.786277
##      3 41.844769 13.385827

now required for the first class female passengers who survived along with proportions and percentage

mytable <- xtabs(~ Pclass+Sex+Survived, data=titanic.df)
mytable # frequencies

## , , Survived = 0
## 
##       Sex
## Pclass female male
##      1      3   77
##      2      6   91
##      3     72  300
## 
## , , Survived = 1
## 
##       Sex
## Pclass female male
##      1     89   45
##      2     70   17
##      3     72   47

prop.table(mytable) # proportions

## , , Survived = 0
## 
##       Sex
## Pclass      female        male
##      1 0.003374578 0.086614173
##      2 0.006749156 0.102362205
##      3 0.080989876 0.337457818
## 
## , , Survived = 1
## 
##       Sex
## Pclass      female        male
##      1 0.100112486 0.050618673
##      2 0.078740157 0.019122610
##      3 0.080989876 0.052868391

prop.table(mytable)*100 # percentages

## , , Survived = 0
## 
##       Sex
## Pclass     female       male
##      1  0.3374578  8.6614173
##      2  0.6749156 10.2362205
##      3  8.0989876 33.7457818
## 
## , , Survived = 1
## 
##       Sex
## Pclass     female       male
##      1 10.0112486  5.0618673
##      2  7.8740157  1.9122610
##      3  8.0989876  5.2868391

now required for all female passengers who survived along with their proportions and percentage

mytable <- xtabs(~ Survived+Sex, data=titanic.df)
mytable

##         Sex
## Survived female male
##        0     81  468
##        1    231  109

prop.table(mytable, 1)*100 #the percentage of survivors who were female

##         Sex
## Survived   female     male
##        0 14.75410 85.24590
##        1 67.94118 32.05882

prop.table(mytable, 2)*100 # the percentage of females on board the Titanic who survived

##         Sex
## Survived   female     male
##        0 25.96154 81.10919
##        1 74.03846 18.89081

————chi-square test————–

Hypothesis: The proportion of females onboard who survived the sinking of the Titanic was higher than the proportion of males onboard who survived the sinking of the Titanic.

mytable <- xtabs(~Sex+Survived, data=titanic.df)
addmargins(mytable)

##         Survived
## Sex        0   1 Sum
##   female  81 231 312
##   male   468 109 577
##   Sum    549 340 889

chisq.test(mytable)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  mytable
## X-squared = 258.43, df = 1, p-value < 2.2e-16

since,the value of p is less than 0.05.Hence,we reject the hypothesis. But no of female passengers survived more than men passengers.

The Pearson’s chi-squared test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance.