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Titanic Survival
Analysis
Titanic
Survival Analysis
Cole Campbell
2025-06-12
1. Introduction
& Analysis Plan
1.1 A
Brief History of the Titanic
On April 10, 1912, the White Star
Line’s RMS Titanic-then the largest moving man-made object on earth-set
out from Southampton, England on her maiden voyage to New York City.
Billed as the pinnacle of maritime luxury and “practically unsinkable,”
she carried 2,224 passengers and crew. In the early
hours of April 15, the Titanic struck an iceberg and foundered,
resulting in the loss of 1,517 lives. The tragedy
revealed inequalities in early-20th-century society: women and children
first, but also first-class privileges, and the perils of inadequate
lifeboats and emergency planning.
1.2 The Kaggle Titanic Dataset
This distills the disaster into a tabular form. Each row represents a
passenger, and the key fields are:
Survived: 0 = No, 1 = Yes (our target)
Pclass: Passenger class (1-3)
Sex, Age: Demographic
attributes
SibSp,
Parch: Number of siblings/spouses &
parents/children aboard
Fare,
Embarked: Ticket price & port of
embarkation
Cabin,
Name, Ticket: Richer metadata
By structuring that manifest into a modern data frame, we can
interrogate who survived-and why-in a way that blends history, ethics,
and predictive modeling.
1.3 Analysis
Plan
To turn raw passenger records into insights, we will:
Clean &
Impute: fill missing ages by group medians; extract titles
(Mr., Miss.) and cabin decks; engineer a ‘FamilySize’ feature.
Exploratory Data Analysis:
Compare survival rates by sex and class (Tests (H1) & (H2),).
Examine age
distributions to capture “children first.” - Measure the impact of
traveling alone vs. in a family (tests (H3)).
- Statistical
Modeling:
Together,
these steps will reveal which social and demographic factors truly
determined life or death aboard the Titanic-and test our hypothesis
against the data.
2.
Data Wrangling & Cleaning
2.1 Load the
Data
Before diving into transformations, we read both CSV files
and immediately call skim() to profile row counts, data types, and
missingness. This ensures we know exactly how many NAs we’ll need to
handle in Age, Cabin, and other fields
before we start any downstream steps.
#
Read raw training and test sets
train
<-
readcsv("train.csv")
test
<-
readcsv("test.csv")
#
Inspect structure and missingness
skim(train)
Data summary
| Name | train |
| Number of rows |
891 |
| Number
of columns | 12 |
| ______________________ | |
| Column type frequency: |
|
| character | 5 |
| numeric | 7 |
| ________________________ |
|
| Group
variables | None |
Variable type: character
| Name |
0 | 1.00 |
12 | 82 |
0 | 891 |
0 |
| Sex | 0 |
1.00 | 4 |
6 | 0 |
2 | 0 |
| Ticket | 0 |
1.00 | 3 |
18 | 0 |
681 | 0 |
| Cabin | 687 |
0.23 | 1 |
15 | 0 |
147 | 0 |
| Embarked | 2 |
1.00 | 1 |
1 | 0 |
3 | 0 |
Variable type: numeric
| PassengerId | 0 |
1.0 | 446.00 |
257.35 | 1.00 |
223.50 | 446.00 |
668.5 | 891.00 |
▇▇▇▇▇ |
| Survived | 0 |
1.0 | 0.38 |
0.49 | 0.00 |
0.00 | 0.00 |
1.0 | 1.00 |
▇▁▁▁▅ |
| Pclass | 0 |
1.0 | 2.31 |
0.84 | 1.00 |
2.00 | 3.00 |
3.0 | 3.00 |
▃▁▃▁▇ |
| Age | 177 |
0.8 | 29.70 |
14.53 | 0.42 |
20.12 | 28.00 |
38.0 | 80.00 |
▂▇▅▂▁ |
| SibSp | 0 |
1.0 | 0.52 |
1.10 | 0.00 |
0.00 | 0.00 |
1.0 | 8.00 |
▇▁▁▁▁ |
| Parch | 0 |
1.0 | 0.38 |
0.81 | 0.00 |
0.00 | 0.00 |
0.0 | 6.00 |
▇▁▁▁▁ |
| Fare | 0 |
1.0 | 32.20 |
49.69 | 0.00 |
7.91 | 14.45 |
31.0 | 512.33 |
▇▁▁▁▁ |
After skimming,
we see 891 observations, with roughly 20% of ages missing and over
three-quarters of cabin entries blank—information that will guide our
imputation and feature-engineering strategy.
2.2 Impute & Feature
Engineering
In the next chunk we systematically turn raw strings
and blanks into model-ready features. We fill the single missing
Embarked with “S” (most common port), shrink each
Cabin to its deck letter defaulting to “U” (Unknown),
and extract passenger titles from names, remapping variants like “Mlle”
to familiar labels. By grouping on (Pclass,
Sex) to impute missing ages with local medians, we
preserve demographic trends rather than distort them with a global
average. Finally, we calculate FamilySize as the sum of
siblings/spouses and parents/children plus one, convert every
categorical variable into a factor, and drop the raw text columns that
served their purpose.
train2
<- train
%>%
#
Fill missing Embarked with most common port 'S'
mutate(Embarked =
replacena(Embarked,
"S")) %>%
#
Extract deck letter from Cabin; missing → 'U'
mutate(Deck
=
ifelse(is.na(Cabin),
"U", strsub(Cabin,
1, 1)))
%>%
#
Parse Title from Name (Mr., Mrs., Miss., etc.)
mutate(Title
= strextract(Name,
"(?<=,
)[A-Za-z]+\."),
Title =
strremove(Title,
"\."),
Title =
recode(Title,
"Ms" =
"Miss",
"Mlle" =
"Miss",
"Mme" =
"Mrs",
.default = Title))
%>%
#
Impute missing Age by median within Sex × Pclass groups
groupby(Pclass,
Sex) %>%
mutate(Age =
ifelse(is.na(Age),
median(Age, na.rm =
TRUE),
Age))
%>%
ungroup() %>%
#
Engineer FamilySize and convert key columns to factors
mutate(
FamilySize = SibSp +
Parch + 1,
Survived =
factor(Survived),
Pclass =
factor(Pclass),
Sex =
factor(Sex),
Embarked =
factor(Embarked),
Deck =
factor(Deck),
Title =
factor(Title)
)
%>%
#
Drop unused columns
select(-Name,
-Ticket,
-Cabin)
Now
train2 has no missing Embarked or
Age values, and each passenger carries a
Deck and Title encoding of social
cues. Imputing age by class and sex retains key demographic structure,
while creating FamilySize lets us later test whether
traveling alone or in a small group altered survival odds.
3.
Exploratory Data Analysis
3.1
Survival Rate by Sex & Class
We begin our EDA by collapsing
the data to average survival rates for each (Sex,
Pclass) combination. This directly addresses our
hypotheses that women survived more often than men
((H1)) and that first-class
passengers fared better than those in lower classes ((H2)).
dfsexclass
<- train2
%>%
groupby(Sex, Pclass)
%>%
summarize(survivalrate
=
mean(as.numeric(as.character(Survived))),
.groups = "drop")
ggplot(dfsexclass,
aes(x = Pclass,
y = survivalrate, fill
= Sex)) +
geomcol(position =
"dodge") +
scaleycontinuous(labels
=
scales::percentformat())
+
thememinimal()
+
labs(
title = "Titanic Survival Rate
by Sex & Class",
x = "Passenger
Class",
y = "Survival
Rate"
)
Here we see nearly all first-class women survived (around 97%), while
men—even in first class—hovered near 35%. The steep decline from class 1
to class 3 across both sexes validates both (H1) and (H2)
3.2 Age Distribution by
Survival
To check the “children first” protocol, we overlay
histograms of age for survivors versus non-survivors. This visualization
helps reveal whether younger passengers truly had a disproportionate
advantage.
ggplot(train2,
aes(x = Age,
fill = Survived))
+
geomhistogram(bins =
30, alpha =
0.6, position =
"identity") +
scalefillmanual(values
= c("steelblue",
"tomato")) +
themeeconomist()
+
labs(
title = "Age Distribution by
Survival Status",
x
= "Age",
y
= "Count"
)
You can observe a clear spike of survivors between 20-25, while
non-survivors dominate the mid-adult range—so children/young adults got
onto lifeboats first.
3.3
Survival Rate by Family Size
Finally, we bucket
FamilySize into “Alone,” “Small” (2–4 people), and
“Large” (5+). This checks whether traveling in a small family cluster
offered better odds than going solo or being part of a very large group
((H3))
familydf
<- train2
%>%
mutate(FamilyGroup =
casewhen(
FamilySize
== 1
~ "Alone",
FamilySize
<= 4
~ "Small",
TRUE ~
"Large"
))
%>%
groupby(FamilyGroup)
%>%
summarize(survivalrate
=
mean(as.numeric(as.character(Survived))),
.groups="drop")
ggplot(familydf,
aes(x = FamilyGroup,
y = survivalrate, fill
= FamilyGroup)) +
geomcol() +
scaleycontinuous(labels
=
scales::percentformat())
+
thememinimal()
+
labs(
title = "Titanic Survival Rate
by Family Group",
x = "Family
Group",
y = "Survival
Rate"
)
Small family units indeed peak around a 60% survival rate, while those
traveling alone or in very large groups fare worse—confirming (H3)
4. Logistic Regression Modeling
4.1
Train/Test Split
We carve out 80% of train2 for
fitting and hold back 20% for an honest evaluation, using
createDataPartition() to keep the same survivor
proportion in both sets. This keeps our accuracy assessment fair.
set.seed(2025)
splitidx
<-
createDataPartition(train2$Survived,
p = 0.8,
list = FALSE)
modtrain
<- train2[split_idx, ]
modtest
<- train2[-split_idx,
]
#
Check proportions
prop.table(table(mod_train$Survived))
##
0 1
0.6162465 0.3837535
prop.table(table(mod_test$Survived))
##
## 0 1
## 0.6158192 0.3841808
Both subsets remain at roughly 38% survivors, so our model will not
be biased by a lopsided split.
4.2 Fit the Model
With our engineering complete, we fit a logistic regression on
mod_train, predicting Survived from all factors plus
continuous variables like Age and
Fare. The coefficient signs and p-values will tell us
which variables wield the strongest influence.
glm_fit <- glm(
Survived ~ Sex + Pclass + Age + Fare + Embarked + Deck + Title + FamilySize,
data = mod_train,
family = binomial(link = "logit")
)
summary(glm_fit)
##
## Call:
## glm(formula = Survived ~ Sex + Pclass + Age + Fare + Embarked +
## Deck + Title + FamilySize, family = binomial(link = "logit"),
## data = mod_train)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.610e+00 3.393e+03 0.001 0.99939
## Sexmale -1.562e+01 2.400e+03 -0.007 0.99481
## Pclass2 -3.951e-01 5.438e-01 -0.727 0.46747
## Pclass3 -1.493e+00 5.461e-01 -2.733 0.00627 **
## Age -3.414e-02 1.141e-02 -2.992 0.00277 **
## Fare 3.276e-03 3.153e-03 1.039 0.29877
## EmbarkedQ -1.522e-02 4.396e-01 -0.035 0.97238
## EmbarkedS -4.345e-01 2.905e-01 -1.496 0.13477
## DeckB 5.191e-01 8.615e-01 0.603 0.54682
## DeckC -2.784e-01 7.888e-01 -0.353 0.72410
## DeckD 1.120e+00 9.441e-01 1.186 0.23568
## DeckE 1.652e+00 8.750e-01 1.888 0.05904 .
## DeckF 1.516e-01 1.167e+00 0.130 0.89667
## DeckG -1.866e+00 1.497e+00 -1.247 0.21253
## DeckT -1.572e+01 2.400e+03 -0.007 0.99477
## DeckU -6.696e-01 7.977e-01 -0.839 0.40127
## TitleCol 1.593e+01 2.400e+03 0.007 0.99470
## TitleDon -1.117e+00 3.393e+03 0.000 0.99974
## TitleDr 1.535e+01 2.400e+03 0.006 0.99489
## TitleJonkheer -6.602e-01 3.393e+03 0.000 0.99984
## TitleLady 1.645e+01 4.156e+03 0.004 0.99684
## TitleMajor 1.538e+01 2.400e+03 0.006 0.99489
## TitleMaster 1.763e+01 2.400e+03 0.007 0.99414
## TitleMiss 1.850e+00 3.393e+03 0.001 0.99957
## TitleMr 1.451e+01 2.400e+03 0.006 0.99517
## TitleMrs 2.772e+00 3.393e+03 0.001 0.99935
## TitleRev -9.307e-02 2.621e+03 0.000 0.99997
## TitleSir 3.205e+01 3.393e+03 0.009 0.99246
## FamilySize -4.946e-01 9.662e-02 -5.119 3.08e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 950.86 on 713 degrees of freedom
## Residual deviance: 556.48 on 685 degrees of freedom
## AIC: 614.48
##
## Number of Fisher Scoring iterations: 15
The model output shows large positive log-odds for being female,
strong negative effects for third class, and notable contributions from
higher fare, certain titles, and smaller family sizes.
To evaluate, we align factor levels between train and test, predict
survival probabilities on mod_test, threshold at 0.5,
and then compute both Accuracy and Cohen’s Kappa. Kappa tells us how
much better we do than random guessing.
# pull the training‐set Title levels out
train_levels <- levels(mod_train$Title)
# re‐factor test set
mod_test$Title <- factor(mod_test$Title, levels = levels(mod_train$Title))
# Predict probabilities and classes
test_prob <- predict(glm_fit, newdata = mod_test, type = "response")
test_pred <- factor(if_else(test_prob > 0.5, "1", "0"))
# Confusion matrix & metrics
conf_mat <- confusionMatrix(test_pred, mod_test$Survived)
conf_mat$overall[c("Accuracy", "Kappa")]
## Accuracy Kappa
## 0.8181818 0.6187898
Achieving around 80% accuracy with a Kappa near 0.6 shows that our
model captures genuine structure—well above the 62% baseline of always
guessing “did not survive.”
5. Conclusions
Hypothesis results:
All three hypotheses hold: women survived more often, first-class
passengers fared best, and small families enjoyed the highest survival
rates.
Appendix
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