EDA with Categorical Variables

Whether EDA (exploratory data analysis) is the main purpose of your project, or is mainly being used for feature selection/feature engineering in a machine learning context, it's important to be able to understand the relationship between your features and your target variable.

Many examples of EDA emphasize numeric features, but this notebook emphasizes categorical features.

import pandas as pd
import numpy as np

import matplotlib.pyplot as plt
from matplotlib.patches import Patch
from matplotlib.lines import Line2D
import seaborn as sns

The Dataset

This analysis uses the Titanic dataset in order to predict whether a given person survived or not

This dataset has the following columns:

Variable	Definition	Key
survival	Survival	0 = No, 1 = Yes
pclass	Ticket class	1 = 1st, 2 = 2nd, 3 = 3rd
sex	Sex
Age	Age in years
sibsp	# of siblings / spouses aboard the Titanic
parch	# of parents / children aboard the Titanic
ticket	Ticket number
fare	Passenger fare
cabin	Cabin number
embarked	Port of Embarkation	C = Cherbourg, Q = Queenstown, S = Southampton

To get started, we'll open up the CSV with Pandas.

(If you were using this for a machine learning project, you would additionally separate the dataframe into X and y, and then into train and test sets, but for the purposes of this example we'll assume that the entire titanic.csv contains training data.)

df = pd.read_csv("titanic.csv")

# PassengerId is a dataset artifact, not something useful for analysis
df.drop("PassengerId", axis=1, inplace=True)

# We want to use Age as one of the main examples, drop rows that are missing Age values
df.dropna(subset=["Age"], inplace=True)

df.head()

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	Survived	Pclass	Name	Sex	Age	SibSp	Parch	Ticket	Fare	Cabin	Embarked
0	0	3	Braund, Mr. Owen Harris	male	22.0	1	0	A/5 21171	7.2500	NaN	S
1	1	1	Cumings, Mrs. John Bradley (Florence Briggs Th...	female	38.0	1	0	PC 17599	71.2833	C85	C
2	1	3	Heikkinen, Miss. Laina	female	26.0	0	0	STON/O2. 3101282	7.9250	NaN	S
3	1	1	Futrelle, Mrs. Jacques Heath (Lily May Peel)	female	35.0	1	0	113803	53.1000	C123	S
4	0	3	Allen, Mr. William Henry	male	35.0	0	0	373450	8.0500	NaN	S

Numeric vs. Categorical EDA

Here we are trying to see the relationship between a given numeric feature and the target, which is categorical. Let's use the Age column as an example.

What Not to Do

One thought we might have would be just to use a scatter plot, since the categorical target has already been encoded as 0s and 1s:

fig, ax = plt.subplots(figsize=(10,5))

ax.scatter(df["Age"], df["Survived"], alpha=0.5)

ax.set_xlabel("Age")
ax.set_ylabel("Survived")

fig.suptitle("Age vs. Survival for Titanic Passengers");

Ok, we can see that age seems to matter some, but it's pretty hard to extract much useful information from this visualization. Let's try some other visualizations that tell us more

Multiple Histograms

Rather than using the y axis to represent the two categories, let's use two different colors. That means that we can use the y axis to represent counts rather than trying to discern this information from the density of dots.

fig, ax = plt.subplots()

ax.hist(df[df["Survived"]==1]["Age"], bins=15, alpha=0.5, color="blue", label="survived")
ax.hist(df[df["Survived"]==0]["Age"], bins=15, alpha=0.5, color="green", label="did not survive")

ax.set_xlabel("Age")
ax.set_ylabel("Count of passengers")

fig.suptitle("Age vs. Survival for Titanic Passengers")

ax.legend();

Multiple Density Estimate Plots

This is showing largely the same information as the histograms, except that it's a density estimate (estimate of the probability density function) rather than a count across bins. Seaborn has nice built-in functionality for this.

fig, ax = plt.subplots()

sns.kdeplot(df[df["Survived"]==1]["Age"], shade=True, color="blue", label="survived", ax=ax)
sns.kdeplot(df[df["Survived"]==0]["Age"], shade=True, color="green", label="did not survive", ax=ax)

ax.set_xlabel("Age")
ax.set_ylabel("Density")

fig.suptitle("Age vs. Survival for Titanic Passengers");

Multiple Box Plots

Here we lose some of the information about the distribution overall in order to focus in on particular summary statistics of the distribution

Matplotlib and Seaborn both have methods for this. The Seaborn one is built on top of the Matplotlib one.

fig, ax = plt.subplots()

sns.boxplot(x="Age", y="Survived", data=df, orient="h", palette={1:"blue", 0:"green"}, ax=ax)

ax.get_yaxis().set_visible(False)

fig.suptitle("Age vs. Survival for Titanic Passengers")

color_patches = [
    Patch(facecolor="blue", label="survived"),
    Patch(facecolor="green", label="did not survive")
]
ax.legend(handles=color_patches);

Categorical vs. Categorical EDA

Here we are trying to see the relationship between a given categorical variable and the target (which is also categorical). Let's use the Pclass (passenger class) feature as an example.

What Not to Do

Again, there is nothing preventing us from just making a scatter plot, since the passenger class is encoded as a number

fig, ax = plt.subplots()

ax.scatter(df["Pclass"], df["Survived"], alpha=0.5)

ax.set_xlabel("Passenger Class")
ax.set_ylabel("Survived")

fig.suptitle("Passenger Class vs. Survival for Titanic Passengers");

...but that plot is not really useful at all. It's really just telling us that at least 1 person falls into each category

Grouped Bar Charts

This shows the distribution across the categories, similar to the "multiple histograms" example for numeric vs. categorical

fig, ax = plt.subplots()

sns.catplot("Pclass", hue="Survived", data=df, kind="count", 
            palette={1:"blue", 0:"green"}, ax=ax)

plt.close(2) # catplot creates an extra figure we don't need

ax.set_xlabel("Passenger Class")

color_patches = [
    Patch(facecolor="blue", label="survived"),
    Patch(facecolor="green", label="did not survive")
]
ax.legend(handles=color_patches)

fig.suptitle("Passenger Class vs. Survival for Titanic Passengers");

fig, ax = plt.subplots()

sns.catplot("Survived", hue="Pclass", data=df, kind="count", 
            palette={1:"yellow", 2:"orange", 3:"red"}, ax=ax)

plt.close(2) # catplot creates an extra figure we don't need

ax.legend(title="Passenger Class")
ax.set_xticklabels(["did not survive", "survived"])
ax.set_xlabel("")

fig.suptitle("Passenger Class vs. Survival for Titanic Passengers");

Stacked Bar Charts

These can be used for counts (same as grouped bar charts) but if you use percentages rather than counts, they show proportions

# Create a dataframe with the counts by passenger class and survival
counts_df = df.groupby(["Pclass", "Survived"])["Name"].count().unstack()
counts_df

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Survived	0	1
Pclass
1	64	122
2	90	83
3	270	85

# Divide by the total number and transpose for plotting
pclass_percents_df = counts_df.div(counts_df.sum()).T
pclass_percents_df

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Pclass	1	2	3
Survived
0	0.150943	0.212264	0.636792
1	0.420690	0.286207	0.293103

fig, ax = plt.subplots()

pclass_percents_df.plot(kind="bar", stacked=True, color=["yellow", "orange", "red"], ax=ax)

ax.legend(title="Passenger Class")
ax.set_xticklabels(["did not survive", "survived"], rotation=0)
ax.set_xlabel("")
ax.set_ylabel("Proportion")

fig.suptitle("Passenger Class vs. Survival for Titanic Passengers");

# Use the same counts df, but now survived + did not survive add up to 1
survived_percents_df = counts_df.T.div(counts_df.T.sum()).T
survived_percents_df

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Survived	0	1
Pclass
1	0.344086	0.655914
2	0.520231	0.479769
3	0.760563	0.239437

fig, ax = plt.subplots()

survived_percents_df.plot(kind="bar", stacked=True, color=["green", "blue"], ax=ax)

ax.set_xlabel("Passenger Class")
ax.set_xticklabels([1, 2, 3], rotation=0)
ax.set_ylabel("Proportion")

color_patches = [
    Patch(facecolor="blue", label="survived"),
    Patch(facecolor="green", label="did not survive")
]
ax.legend(handles=color_patches)

fig.suptitle("Passenger Class vs. Survival for Titanic Passengers");

Numeric vs. Numeric vs. Categorical EDA

Sometimes it's interesting to see the relationship between two different numeric features and the target

What Not to Do

You could just make a scatter plot of the two numeric features

fig, ax = plt.subplots(figsize=(10, 5))

ax.scatter(df["Age"], df["Fare"], alpha=0.5)

ax.set_xlabel("Age")
ax.set_ylabel("Fare")

fig.suptitle("Age vs. Fare for Titanic Passengers");

That's fine if the relationship between Age and Fare is what interests you, but it doesn't give you any information about the relationship between these features and the target

Scatterplot with Color to Distinguish Categories

This kind of plot could help you understand how the two features relate to the target

fig, ax = plt.subplots(figsize=(10, 5))

ax.scatter(df[df["Survived"]==1]["Age"], df[df["Survived"]==1]["Fare"], c="blue", alpha=0.5)
ax.scatter(df[df["Survived"]==0]["Age"], df[df["Survived"]==0]["Fare"], c="green", alpha=0.5)

ax.set_xlabel("Age")
ax.set_ylabel("Fare")

color_patches = [
    Line2D([0], [0], marker='o', color='w', label='survived', markerfacecolor='b', markersize=10),
    Line2D([0], [0], marker='o', color='w', label='did not survive', markerfacecolor='g', markersize=10)
]
ax.legend(handles=color_patches)

fig.suptitle("Survival by Age and Fare for Titanic Passengers");

Summary

Most of the time if your target is a categorical variable, the best EDA visualization isn't going to be a basic scatter plot. Instead, consider:

Numeric vs. Categorical (e.g. Survived vs. Age)

• Multiple histograms
• Multiple density estimate plots
• Multiple box plots

Categorical vs. Categorical (e.g. Survived vs. Pclass)

• Grouped bar charts
• Stacked bar charts

Numeric vs. Numeric vs. Categorical (e.g. Age vs. Fare vs. Survived)

• Color-coded scatter plots