How selecting on success creates fake correlations

Question

Among the quants your firm hired, math ability and coding ability appear negatively correlated, the strong mathematicians code worse and vice versa, even though in the broad applicant pool the two skills are unrelated.

Explain how conditioning on being hired can manufacture this negative correlation.

Accepted Answer

A collider is a common effect. Getting hired depends on both skills, the firm takes candidates who are strong enough at math or coding (or some weighted combination) to clear the bar. So "hired" is a common effect of the two abilities: two arrows point into it, math → hired ← coding. Such a variable is called a collider. Conditioning on a collider induces dependence. In the full applicant pool the two skills are independent. But once you restrict attention to the hired subset, that is, you condition on the collider, you create an artificial relationship. Intuitively: among the people who made…

How selecting on success creates fake correlations

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