Confounding Variables Statistics Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumHospitals A and B both perform a surgery. Hospital A has a 90% survival rate, Hospital B has 95%. However, Hospital A takes more high-risk patients. When only high-risk patients are compared, Hospital A has a higher survival rate. Explain this paradox.
Solution
- 1 Step 1: This is Simpson's Paradox — the overall rates reverse when looking at subgroups because of a confounding variable (patient risk level).
- 2 Step 2: Hospital A takes more high-risk patients, which lowers its overall survival rate. But within each risk category, Hospital A actually performs better.
- 3 Step 3: The confounding variable (patient risk level) is unevenly distributed between hospitals, distorting the overall comparison.
Answer
This is Simpson's Paradox. Patient risk level is a confounding variable — Hospital A treats more high-risk patients, lowering its overall rate. Within each risk category, Hospital A actually performs better.
Simpson's Paradox occurs when a trend that appears in overall data reverses when the data is split into subgroups. It arises because a confounding variable is unequally distributed across groups. This paradox demonstrates why controlling for confounders is essential for valid comparisons.
About Confounding Variables
A confounding variable is a third variable that influences both the independent variable and the dependent variable simultaneously, creating a spurious association between them that can be mistaken for a direct causal relationship. Confounders are a major threat to the internal validity of observational studies.
Learn more about Confounding Variables →More Confounding Variables Examples
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