Confounding
In statistics, a confounding variable (also confounding factor) is a variable in a quantitative research study that explains some or all of the correlation between the dependent variable and an independent variable. A confounder is a variable that is correlated (directly or inversely) to the independent variable and correlated to the dependent variable. A lurking variable is a covariate that is not taken in account for by the researchers of the quantitative study.
Confounding is a causal concept, and as such, cannot be described in terms of correlations nor associations (see causal definition).
The concept of confounding must be defined, and managed, in terms of the data generating model (as in the Figure above). Specifically, 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.
In the causal framework, denote as 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:
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