Berkson's paradox is the appearance of a spurious association after conditioning on a selection rule. Here, two Gaussian variables can look negatively correlated after conditioning on a combined threshold such as aX + bY > T. It is also a case of the explaining away effect.
A seeded bivariate normal sample is filtered by the selected rule. The table compares sample correlations before and after selection; the red line is fitted to the selected cases.
Selection can induce or reverse an association without changing the source population. Finite samples vary, and conditioning on a selection rule is not evidence of a causal effect between X and Y. This continuous illustration is not a reconstruction of hospital data.
Joseph Berkson (1946), Limitations of the application of fourfold table analysis to hospital data. Implementation.