Week 11 — Uncertainty & Error Visualization

Communicating uncertainty, variability, and confidence through effective visual representations.

📖 Background & Motivation

Data visualizations often emphasize what is known—but communicating what is uncertain is equally critical for honest and transparent storytelling. This week explores how to represent statistical uncertainty, variability, and measurement error using visual design. Students will learn how to use error bars, confidence bands, sampling distributions, and bootstrap visualizations to convey uncertainty clearly and responsibly.

🔎 Learning Objectives

  • Understand the sources of uncertainty in data and models.
  • Differentiate between standard deviation, standard error, and confidence interval.
  • Visualize uncertainty with error bars, ribbons, and confidence bands.
  • Communicate uncertainty effectively without misleading interpretation.
  • Apply resampling or bootstrapping methods for visual inference.

📚 Readings & Resources

Sample Data Sources:

  • Simulated sample means and bootstraps
  • Gapminder GDP data (yearly changes)
  • Experimental datasets (e.g., survey or sensor data)

🛠️ Setup Checklist

Ensure your environment includes:

pip install seaborn matplotlib numpy pandas scipy

Verify that Seaborn is configured to display confidence intervals and that Matplotlib renders error bars correctly.

🧭 Lecture Outline

Session 1 (Theory Focus)

  1. What is uncertainty? Sources in data collection and modeling
  2. Standard deviation, standard error, and confidence intervals
  3. Visual metaphors for uncertainty (error bars, ribbons, shaded regions)
  4. Common pitfalls: false precision, overlapping intervals, and transparency
  5. Case studies: how media and research visualize uncertainty

Session 2 (Hands-on Focus)

  1. Plotting error bars with Seaborn and Matplotlib
  2. Adding confidence bands around regression lines
  3. Simulating sampling distributions and bootstrap intervals
  4. Improve one of your previous plots by including uncertainty
  5. Download the hands-on Jupyter Notebook

💻 Starter Notebook Snippets

Adding error bars

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

# Simulated means and standard errors
groups = ['A','B','C','D']
means = [20, 23, 25, 22]
se = [1.5, 2.0, 1.2, 1.8]

plt.bar(groups, means, yerr=se, capsize=5, color='#4e79a7')
plt.title('Bar chart with error bars')
plt.ylabel('Mean value')
plt.show()

Confidence intervals with Seaborn

import seaborn as sns
penguins = sns.load_dataset('penguins').dropna()
sns.lmplot(data=penguins, x='flipper_length_mm', y='body_mass_g', ci=95)
plt.title('Regression with 95% confidence interval')
plt.show()

Bootstrap sampling visualization

np.random.seed(42)
data = np.random.normal(50, 10, 100)
bootstrap_means = [np.mean(np.random.choice(data, size=100, replace=True)) for _ in range(1000)]

sns.histplot(bootstrap_means, kde=True)
plt.axvline(np.mean(data), color='red', linestyle='--', label='Observed mean')
plt.title('Bootstrap sampling distribution of the mean')
plt.legend()
plt.show()

🧪 In-Class Activity

  • Compare bar charts with and without error bars — what changes in interpretation?
  • Explore how sample size affects confidence interval width.
  • Visualize a bootstrap sampling distribution and discuss its meaning.
  • Redesign a visualization from your earlier project to include uncertainty representation.

🏠 Homework (Due next Thursday, Nov 13)

  1. Select a dataset of your choice (or use one from a prior week).
  2. Produce:
  3. One bar or line chart with error bars or confidence bands.
  4. One bootstrap visualization or sampling distribution.
  5. A short (200–300 words) reflection on how uncertainty affects the interpretation of your results.
  6. Submit .ipynb and .html.

Rubric (10 pts)

  • Correct calculation and visualization of uncertainty (4)
  • Clarity and labeling of intervals/bands (2)
  • Quality of interpretation and reflection (3)
  • Reproducibility and documentation (1)

🧩 Optional Extensions

  • Compare 68%, 90%, and 95% confidence intervals visually.
  • Add uncertainty bands to model predictions from Statsmodels.
  • Visualize uncertainty in map-based data (e.g., population margins of error).

✅ Submission Checklist

Before submitting, make sure:

  • Your assignment has fulfilled all the basic requirements listed above.

  • Use Quarto to render the notebook into HTML and zip the files for submission.

  • Double-check the visualizations and your reflections in the HTML are properly organized and displayed.