Confounding variable

In statistics, a confounder (also confounding variable or confounding factor) is a variable that influences both the dependent variable and independent variable causing a spurious association. Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations.

Confounding is defined in terms of the data generating model (as in the Figure above). Let X be some independent variable, Y some dependent variable. To estimate the effect of X on Y, the statistician must suppress the effects of extraneous variables that influence both X and Y. We say that, X and Y are confounded by some other variable Z whenever Z is a cause of both X and Y.

Let ${\displaystyle P(y\mid {\text{do}}(x))}$ be the probability of event Y = y under the hypothetical intervention X = x. X and Y are not confounded if and only if the following holds:

${\displaystyle P(y\mid {\text{do}}(x))=P(y\mid x)}$

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