Back-Door Adjustment

Choose an adjustment set by clicking; the exact regression coefficient shows which sets remove confounding.

Day 52: The Back-Door Criterion

Adjustment set {Z3}: fails the back-door criterion.

coefficient on X

0.377

true causal effect

0.500

X → W → Y

X ← Z1 → Z3 ← Z2 → Y — open

X ← Z1 → Z3 → Y — blocked at Z3

X ← Z3 ← Z2 → Y — blocked at Z3

X ← Z3 → Y — blocked at Z3

Strength of Z1 and Z2 paths1.00Effect of W on Y (sets the true effect)0.50

A linear model with unit-variance disturbances. Click nodes to choose the adjustment set; the regression coefficient on X is computed exactly from the implied covariance matrix (no sampling noise). Z3 is both a confounder and a collider; W is a mediator. Open back-door paths are drawn in orange.

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