The Bias Equation

The one idea: The gap you see between a treated group and a control group is two things added together — the real effect of the treatment, plus how different the two groups already were before anyone was treated. The number alone never tells you the mix, so a genuinely helpful program can look harmful, and a useless one can look great.

⚠️ The trap: "The treated group ended up ahead, so the treatment must be working." That feels right and it's wrong. What a dashboard shows is the real effect plus how different the two groups already were before anyone was treated — so a genuinely helpful program can look harmful and a useless one can look great, and the gap alone never tells you the mix.

Last lesson established that you only observe one of each unit's two potential outcomes, and that naive comparisons can flip the sign of a true effect. This lesson gives you the single equation that explains exactly why — and exactly what must be true for a comparison to be trusted. Matheus Facure, in Causal Inference for the Brave and True, treats it as something close to scripture, and he's right to: every method in the rest of this track is a strategy for attacking one term in it.

Here it is in words first: what you see on a dashboard equals the true effect on the treated group, plus how different the two groups already were. Written as an equation:

You never compute this by hand — it names what a dashboard gap is made of, not a calculation you run. The sentence above is the whole point. …