Population phi
0.000
Berkson's Paradox Simulator
Filter independent traits on a shared selection rule and see the selected-sample association emerge.
At a glance
- Computes
- Association between two independent traits inside a sample filtered on a shared rule.
- You supply
- Probability of each trait, population per run, and a random seed.
- Use when
- You need to show how selecting on an outcome manufactures a correlation.
- Not for
- Confounding, where a third cause creates the association before any selection. Simpson's Paradox Simulator
Selected phi
-0.500
- Selection rule
- selected if A or B
- Selection rate
- 75.0%
- Mean simulated selected phi
- Not run
| Cell | Population | Selected |
|---|
Value by category
Run the simulation to fill Monte Carlo metrics and convergence.
Mean selected phi against Trial; reference at Exact selected phi
| Trial | Mean selected phi |
|---|
phi = (both * neither - A-only * B-only) / sqrt(row and column margins)
How?
How this is calculated
The full population starts with independent binary traits. The selected sample keeps only cases where trait A or trait B is present, which removes the neither cell and can create a negative association.
Berkson's paradox is collider bias: use the causal DAG builder to trace how conditioning on a shared effect opens a non-causal path.
Formula: phi = (both * neither - A-only * B-only) / sqrt(row and column margins)
Sources
- Berkson's paradox overview. Wikipedia. Retrieved .
- Collider effect educational note. arXiv. Retrieved .
Method last reviewed