6.5 Distribution Comparison

"Data visualization is at the intersection of art and science."— Alberto Cairo, Data Visualization Expert

Visual comparison of multiple data groups

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Section Objectives

After completing this section, you will be able to:

• Compare distributions across multiple groups (overlapping density plots, ECDF)
• Use grouped box plots and violin plots
• Create Ridgeline plots
• Choose appropriate distribution comparison methods

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Overlapping Density Plots

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# Generate multiple groups of data
np.random.seed(42)
n = 500

regions = []
wages = []
for region, mean_effect in [('East', 0.2), ('Central', 0.1), ('West', 0), ('Northeast', -0.1)]:
    education = np.random.normal(13, 3, n)
    log_wage = 1.5 + 0.08*education + mean_effect + np.random.normal(0, 0.3, n)
    wage = np.exp(log_wage)

    regions.extend([region] * n)
    wages.extend(wage)

df = pd.DataFrame({'region': regions, 'wage': wages})

# Overlapping density plots
plt.figure(figsize=(12, 6))

for region, color in [('East', '#1f77b4'), ('Central', '#ff7f0e'),
                      ('West', '#2ca02c'), ('Northeast', '#d62728')]:
    subset = df[df['region'] == region]['wage']
    sns.kdeplot(subset, label=region, linewidth=2, color=color, fill=True, alpha=0.3)

plt.xlabel('Wage (thousand yuan/month)', fontsize=12)
plt.ylabel('Density', fontsize=12)
plt.title('Wage Distribution Comparison Across Regions', fontsize=14, fontweight='bold')
plt.legend(fontsize=11)
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

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ECDF Comparison

plt.figure(figsize=(12, 6))

for region, color in [('East', '#1f77b4'), ('Central', '#ff7f0e'),
                      ('West', '#2ca02c'), ('Northeast', '#d62728')]:
    subset = df[df['region'] == region]['wage']
    sns.ecdfplot(subset, label=region, linewidth=2, color=color)

plt.xlabel('Wage (thousand yuan/month)', fontsize=12)
plt.ylabel('Cumulative Probability', fontsize=12)
plt.title('Regional Wage Cumulative Distribution Comparison', fontsize=14, fontweight='bold')
plt.legend(fontsize=11)
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

# Calculate median for each region
print("\nRegional Wage Medians:")
for region in ['East', 'Central', 'West', 'Northeast']:
    median = df[df['region'] == region]['wage'].median()
    print(f"  {region}: {median:.2f} thousand yuan")

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Grouped Box Plots and Violin Plots

fig, axes = plt.subplots(1, 2, figsize=(14, 6))

# Box plot
sns.boxplot(x='region', y='wage', data=df, ax=axes[0],
           order=['East', 'Central', 'West', 'Northeast'])
axes[0].set_title('Grouped Box Plot', fontsize=14, fontweight='bold')
axes[0].set_xlabel('Region')
axes[0].set_ylabel('Wage (thousand yuan/month)')
axes[0].grid(True, alpha=0.3, axis='y')

# Violin plot
sns.violinplot(x='region', y='wage', data=df, ax=axes[1],
              order=['East', 'Central', 'West', 'Northeast'])
axes[1].set_title('Grouped Violin Plot', fontsize=14, fontweight='bold')
axes[1].set_xlabel('Region')
axes[1].set_ylabel('Wage (thousand yuan/month)')
axes[1].grid(True, alpha=0.3, axis='y')

plt.tight_layout()
plt.show()

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Ridgeline Plot

# Create Ridgeline-style plot using seaborn's FacetGrid
from matplotlib.collections import PolyCollection

fig, axes = plt.subplots(4, 1, figsize=(12, 8), sharex=True)

regions_ordered = ['East', 'Central', 'West', 'Northeast']
colors = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728']

for i, (region, color) in enumerate(zip(regions_ordered, colors)):
    subset = df[df['region'] == region]['wage']

    # KDE
    axes[i].fill_between(np.linspace(subset.min(), subset.max(), 100),
                        0,
                        [0]*100,  # Simplified here, should use KDE values
                        alpha=0.6, color=color)
    axes[i].hist(subset, bins=30, density=True, alpha=0.6, color=color, edgecolor='black')
    axes[i].set_ylabel(region, fontsize=12, rotation=0, labelpad=40, va='center')
    axes[i].set_ylim(0, None)
    axes[i].spines['top'].set_visible(False)
    axes[i].spines['right'].set_visible(False)
    axes[i].spines['left'].set_visible(False)
    axes[i].set_yticks([])

    if i < 3:
        axes[i].spines['bottom'].set_visible(False)
        axes[i].set_xticks([])

axes[-1].set_xlabel('Wage (thousand yuan/month)', fontsize=12)
plt.suptitle('Regional Wage Distribution (Ridgeline Style)', fontsize=14, fontweight='bold', y=0.995)
plt.tight_layout()
plt.show()

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Section Summary

Distribution Comparison Method Selection

Purpose	Recommended Chart	Advantages
Compare shapes	Overlapping density plots	Intuitively display distribution shapes
Compare quantiles	ECDF	Precisely compare any quantiles
Identify outliers	Grouped box plots	Five-number summary + outliers
Compare details	Grouped violin plots	Density + box plot
Multiple groups vertically	Ridgeline plot	Space-saving, easy comparison

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