Berkson Selection and Collider Bias

Berkson's Paradox (or Berkson's Bias) is a phenomenon where two independent variables become statistically associated when we condition on a shared effect (a collider). This often occurs through selection bias: when a dataset only includes records that satisfy a certain condition, independent traits can appear negatively correlated.

Interactive Experiment

Use the Berkson Selection interactive module to explore how selection rules affect the association between independent traits.

1. Set both Probability A and Probability B to 0.5.
2. Change the Selection rule to Either and observe the negative covariance in the selected population table.
3. Change the Selection rule to Exactly one. The negative correlation becomes even stronger (perfectly negative), as having one trait guarantees you don't have the other.
4. Change the Selection rule to None. Notice that the covariance remains 0, as no selection bias is introduced.
5. Try setting the probabilities to 0. Notice that if the selection rule makes it impossible to select anyone (e.g., probabilities are 0 but rule is "Either"), the conditional probabilities become unavailable.