No. 05

Simpson's Paradox

When the parts and the whole disagree

📊

The setup

1Two departments are admitting students; we compare acceptance rates by gender.
2In each department individually, women are accepted at a higher rate than men.
3Yet when you combine the departments, men come out ahead overall.

🤔 Intuition says: If women win in every department, they must win overall. Right?

🎚️ Find the tipping point

Women are admitted at a higher rate in both departments. But where people apply decides the overall result. Drag the sliders and watch the “Overall” bars flip.

% of men applying to the easy dept80

% of women applying to the easy dept20

🤯 Paradox ON: women lead in both departments (70.0% vs 45.0% overall for men) — yet men win overall, because they cluster in the easy department.

🏛️ The real case: UC Berkeley, 1973

The classic dataset that made this famous, served from the API.

Why it's a paradox

Men applied mostly to the easy-to-enter department; women applied mostly to the selective one.

The overall rate is a weighted average, and the weights differ wildly between groups.

This mirrors the real 1973 UC Berkeley admissions case, where the confounding variable was department choice.

💡 Key insight: Always check for a confounding variable before trusting an aggregated statistic.