In statistics, a confounding variable (also confounding factor, a confound, or confounder) is an extraneous variable in a statistical model that correlates (directly or inversely) with both the dependent variable and the independent variable. A perceived relationship between an independent variable and a dependent variable that has been misestimated due to the failure to account for a confounding factor is termed a spurious relationship, and the presence of misestimation for this reason is termed omitted-variable bias.
While specific definitions may vary, in essence a confounding variable fits the following four criteria, here given in a hypothetical situation with variable of interest ‘V’, confounding variable ‘C’ and outcome of interest ‘O’:
1. C is associated (inversely or directly) with O
2. C is associated with O, independent of V
3. C is associated (inversely or directly) with V
4. C is not in the causal pathway of V to O (C is not a direct consequence of V, not a way by which V produces O)
The above correlation-based definition, however, is metaphorical at best – a growing number of analysts agree that confounding is a causal concept, and as such, cannot be described in terms of correlations nor associations. … Confounding Variable