Simpson's Paradox
Definition
In Simpson's paradox, a relationship can change direction after combining or splitting groups.
In Simpson's paradox, a statistical association reverses after data are aggregated or divided into groups.
Simply explained
A comparison can look different overall than in each individual group because the groups have different compositions.
Why it matters in practice
The term helps to select, develop, evaluate AI systems in a well-founded manner and realistically assess their technical risks.
Example from business
A conversion rate increases in every customer segment but decreases overall because the segment proportions have shifted.
Limits and pitfalls
- Aggregated metrics without relevant confounding variables can lead to wrong decisions; mere correlation does not explain causation.
Origin & history
Edward Simpson described the phenomenon in 1951; related observations can be found earlier with Yule.
Use in mid-sized companies
- Possible example: A conversion rate increases in every customer segment but decreases overall because the segment proportions have shifted.
Frequently asked questions
What does Simpson's paradox mean?
In Simpson's paradox, a statistical association reverses after data are aggregated or divided into groups. What should one watch out for? Aggregated metrics without relevant confounding variables can lead to wrong decisions; mere correlation does not explain causation.
Sources
- The Interpretation of Interaction in Contingency Tables · Simpson, The Interpretation of Interaction in Contingency Tables
Source checked on 10.10.2026. Editorial application examples are hypothetical; no evidence of real customer results.
Editorially reviewed on: