Confounding factor

A confounding factor (or variable) is an unseen variable that is also correlated with two or more other variables. The confounding factor is one of the most important reasons correlation does not equal causation, as the causality could be the confounding factor, and may well be counter-intuitive. These have to be examined and controlled in experiments and statistical studies.

The fallacy is a false cause, imprecision fallacies, and an informal fallacy.

Alternate names

 * common cause
 * joint effect
 * lurking variable
 * single causation
 * spurious relationship
 * uncontrolled factors

Example
In epidemiology, a confounder (affluence of a country, in the example above):
 * 1) Is correlated with the predictor (e.g. abortion rates)
 * 2) Is correlated with the outcome (e.g. breast cancer)
 * 3) Is not part of the causal pathway between predictor and outcome (abortion does not cause breast cancer through the development level of a country)
 * 4) Substantially alters the estimated predictor/outcome relationship when included in the model, conventionally >10%

A variable in the causal pathway between predictor and outcome may, instead, be an effect modifier. In either case, failure to include the extra variable in the analysis results in a distorted estimate of the predictor/outcome relationship.

Abortion Breast Cancer (ABC) Link
Let us suppose for the sake of the argument that breast cancer rates in a country are correlated with abortion rates; that does not necessarily mean that there may be a causal link between the two. There is a confounding factor in that both of these are correlated with the affluence of the country. In affluent countries, people tend to live longer, and by living longer, they are more likely to develop breast cancer (sad but true), as it correlates with age far more than any other factor. Additionally, in a more developed country, the rate of abortion tends to be higher; so the higher the rates of abortion, the higher rates of breast cancer. Both correlate to the confounding factor, the affluence of the country, rather than each other.