Simpson’s Paradox

Simpson's paradox is a reversal or disappearance of an association when groups are combined, often because the compared alternatives have different mixtures of subgroups with different outcome rates. The arithmetic does not by itself determine which comparison answers the intended question.

Simpson's paradox occurs when an association within each of several groups reverses or disappears after aggregation. Different mixtures of groups can change the weighting of subgroup rates. The arithmetic is consistent: the overall rate is a weighted average, and the groups being compared may use different weights.

The correct analysis depends on the question and causal structure. Stratifying can help address a confounder, but conditioning on a mediator or collider can answer a different question or introduce bias. Do not automatically prefer detailed tables or aggregate totals. Explain which comparison is needed, why the grouping variable belongs in the analysis, and what causal claims the design supports.

When to use it

When aggregate and subgroup comparisons disagree, or when changing population composition may distort an apparent performance trend.

How it can help

Inspect subgroup counts and weights, define the question, and use causal reasoning to decide whether and how to adjust for the grouping variable.