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Simpson's Paradox
“A trend can appear, disappear, or reverse when data are split into groups.”
01 / SUMMARY
In short
The paradox occurs when an aggregate association changes after stratifying by a third variable. Arithmetic alone cannot decide which comparison answers the causal or descriptive question.
03 / SCENE
In the wild
Treatment A wins within mild and severe cases, yet B looks better overall because it received a larger share of mild cases.
04 / LIMIT
The limit
Disaggregation is not always right either; a variable may be a confounder, mediator, or result of selection.
FINAL NOTE
What remains
Before choosing totals or subgroups, sketch how the data were generated.