Population vs. Selected Sample
Scenarios
You only date people who are at least this attractive OR nice
How Selection Creates Spurious Correlations
You only date people who are at least this attractive OR nice
Berkson's Paradox (1946) reveals how selection based on a "collider" creates spurious correlations that don't exist in the full population. When you only observe a subset selected by a criterion involving two variables, those variables appear negatively correlated—even if they're completely independent or positively correlated in reality!
In the dating pool: If you only date people who are at least attractive OR nice (a minimum standard), then among your dates, these traits will appear negatively correlated. Why? The nice-but-plain people in your pool "made the cut" via niceness, while the pretty-but-rude ones made it via looks. The corner with low-both gets excluded!
Hospital studies: Patients are selected by illness. A spurious
negative correlation between two diseases appears because people with neither
aren't in the hospital.
COVID-19 research: Studies of hospitalized patients showed
misleading correlations because severe illness was the selection criterion.
Try it: Move the threshold slider and watch the correlation in the selected sample become increasingly negative as you raise standards—even though the true population correlation stays at zero (or even positive)!