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📊StatisticsData Paradox20 sec read

Simpson's Paradox: A Trend Can Completely Reverse When Subgroups Are Combined

A treatment can outperform another inside every separate patient subgroup—yet look worse overall once all rows are pooled together.

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🔄 Data Paradox

Stanford Encyclopedia of Philosophy

Key Metric+20 XP

If Treatment A beats B in both mild cases AND severe cases, must A also win in the combined total?

Key Insight

Imbalanced subgroup sizes mixed with a lurking confounder can flip the aggregate percentage upside down.

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📊 Statistics

Data Paradox

⚡ 20s58 words

Why / How?

01

Scientific Mechanism

In the famous 1973 UC Berkeley admissions study, overall acceptance looked skewed toward men—but department-by-department data showed women were accepted at equal or higher rates. The hidden confounding factor was that women disproportionately applied to the most competitive departments with tiny acceptance rates.

02

Why It Matters

Imbalanced subgroup sizes mixed with a lurking confounder can flip the aggregate percentage upside down.

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Stanford Encyclopedia — Simpson's Paradox
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What usually triggers Simpson's Paradox when analysts pool separate subgroups into one total chart?

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Quick Q&A Knowledge Cards

Quick Guess

If Treatment A beats B in both mild cases AND severe cases, must A also win in the combined total?

No, uneven sample mix can flip the total

Fact Check

What usually triggers Simpson's Paradox when analysts pool separate subgroups into one total chart?

An unmeasured confounding variable combined with uneven group sizes

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