A trend that shows up in every subgroup of the data reverses, or disappears, when the groups are combined. It happens when a third variable is unevenly spread across the groups, so the right answer depends on the causal story, not the arithmetic.
Card 1 of 244. Answer: A trend that shows up in every subgroup of the data reverses, or disappears, when the groups are combined. It happens when a third variable is unevenly spread across the groups, so the right answer depends on the causal story, not the arithmetic.
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Simpson's paradox is a reversal between aggregated and stratified data. It arises when a lurking variable is related both to the grouping and to the outcome, so combining groups mixes very different populations in different proportions. Edward Simpson described it in 1951; Udny Yule had noted the effect in 1903.
Example: in 1973 the University of California, Berkeley admitted about 44% of 8,442 male graduate applicants and 35% of 4,321 female ones. Department by department, women were admitted at similar or higher rates. Women applied more often to competitive departments that admitted few applicants of either sex, which pulled their overall rate down (Bickel, Hammel and O'Connell, Science, 1975).
Which table to trust depends on the causal structure. If the third variable is a confounder, such as department choice here, compare within groups; if it lies on the causal path, a mediator, the aggregate answers the question. In product analytics it shows up as mix shift: average order value can fall overall while rising in every country, simply because traffic moved toward a lower-value country.
