regression
The coefficient that flips sign
It is a moment that ambushes every careful modeler: a predictor shows a clear positive effect on the outcome, until you add one more variable to the regression and its coefficient flips negative — and both fits are arithmetically correct. Confront Simpson's paradox in regression: explain why controlling for a variable can reverse an association — when the added variable is a genuine confounder whose adjustment reveals the truth versus a mediator or collider whose adjustment manufactures a lie. Decide which covariates belong in the model. Get it wrong and you report a protective effect that is really harmful, or adjust away the very pathway you meant to measure — the arithmetic never warns you; only the causal structure tells you which regression to believe.
Who this problem belongs to
The two figures whose methods fit it best, out of 71 in contention.
Pearl's causal revolution, culminating in his do-calculus and structural causal models developed from the 1980s through the 2000s, gives the precise formal machinery this problem demands: a graphical criterion, the back-door criterion, for deciding exactly which variables must be controlled for versus which must be left alone. His causal-diagram framework distinguishes a confounder, whose adjustment reveals the truth, from a mediator or collider, whose adjustment manufactures a spurious association, which is the entire crux of Simpson's paradox in regression. His 2000 book Causality formalized what statisticians had puzzled over informally for a century. No one else on this roster owns the precise, general answer to 'which covariates belong in the model' as completely as Pearl does.
Rubin's potential-outcomes framework, formalized from 1974 onward, gives a rigorous language for exactly what a regression coefficient means causally and when adjusting for a covariate helps versus hurts, built on the ignorability condition that plays the same functional role as Pearl's back-door criterion in a different formal idiom. His decades of applied causal-inference work confronting confounding in observational studies, alongside his propensity-score methodology developed with Rosenbaum, directly operationalizes deciding which covariates belong in an adjustment set. He arrived at these tools somewhat later than Pearl's graphical formalism and from a different, potential-outcomes rather than graph-theoretic, tradition, but his framework answers this problem's causal question with comparable rigor and enormous applied influence.
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
71 figures are scored on this problem. Draw it in a battle to see where you land.