Lesson · 4 min Stretch

Two Groups, One Trend

In one line A trend in the combined data can flip when you split the data into groups.

Simpson’s paradox is what happens when a trend that appears in several groups reverses when the groups are combined. It is not a trick of arithmetic. It happens when the groups differ in size and in how hard their cases are.

Suppose Clinic A treats mostly mild cases and Clinic B mostly severe ones. B may do better than A for mild cases and better for severe cases, yet show a lower overall success rate, simply because so many of its patients were severe.

The lesson is to ask what is hidden in a combined number. Before comparing two totals, check whether the groups being compared are alike, and look at the rates inside each subgroup.

The two clinics

Two clinics report success rates: A at 82 percent and B at 76 percent. A manager moves funding to A.

Dana, a statistician, splits the data. For mild cases B has the higher rate, and for severe cases B also has the higher rate. B sees far more severe patients, which pulls its total down. The manager reverses the decision.

Try this today When a rate looks bad or good overall, ask how it looks inside each group.

Cite or share this lesson

A plain reference you can paste into notes or an essay:

Quest2Reason. “Two Groups, One Trend.” https://quest2reason.com/learn/lesson/two-groups-one-trend. Accessed 13 November 2026.

Sources

Stanford Encyclopedia of Philosophy, “Simpson’s Paradox” — The paradox, with the Berkeley admissions case.
Bickel, Hammel and O’Connell, “Sex Bias in Graduate Admissions: Data from Berkeley” (Science, 1975) — The admissions study behind the university example: women applied more to the departments that were harder to enter.
Wikipedia, “Simpson’s paradox” — A trend that reverses when groups are combined.