Simpson’s Paradox
A trend reverses when groups are combined.
Key idea
A trend reverses when groups are combined.
In depth
A trend present in several groups can reverse when groups are combined, because group sizes differ. It warns against ignoring lurking variables and shows why context matters.
Worked example
Treatment A has a higher success rate than B in both mild and severe cases, but a lower overall rate because A is given to more severe cases.
Real-world uses
- Explaining why a hospital may look worse overall but better in every department
Common mistake
Aggregating data without considering group structure.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Simpson’s Paradox?
A trend reverses when groups are combined. It is a topic at the expert level in Probability & Statistics.
Where is Simpson’s Paradox used in real life?
Real-world examples: Explaining why a hospital may look worse overall but better in every department.
What should I learn before Simpson’s Paradox?
Make sure you are comfortable with Correlation vs Causation, the previous topic in Probability & Statistics.
What is a common mistake with Simpson’s Paradox?
Aggregating data without considering group structure.
How can I practise Simpson’s Paradox?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Simpson’s Paradox?
Move on to Experiments of Chance next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.
- Linearity of Expectation – Expectation of sums is sum of expectations.