Code Quiz

Simpson's Paradox: Aggregating Stratified Rates

A causal-inference helper meant to compute overall recovery rates falls into an averaging trap tied to Simpson's paradox.

Codepython

import numpy as np

# Kidney-stone style data. Severity is a confounder of treatment vs recovery.
# Each entry: [recovered, total]
treatment_a = {'mild': [81, 87], 'severe': [192, 263]}
treatment_b = {'mild': [234, 270], 'severe': [55, 80]}

def overall_rate(data):
    # Aggregate the stratum-specific recovery rates into one overall rate
    rates = [rec / tot for rec, tot in data.values()]
    return np.mean(rates)

print('A:', overall_rate(treatment_a))
print('B:', overall_rate(treatment_b))

This code is supposed to report each treatment's true overall recovery rate, but it produces misleading numbers. What is the bug?

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