Lurking variable

A lurking variable (confounding factor or variable, or simply a confound or confounder) is a "hidden" variable in a statistical or research model that affects the variables in question but is not known or acknowledged, and thus (potentially) distorts the resulting data. This hidden third variable causes the two measured variables to falsely appear to be in a causal relation. Such a relation between two observed variables is termed a spurious relationship. An experiment that fails to take a confounding variable into account is said to have poor internal validity.

For example, ice cream consumption and murder rates are highly correlated. Now, does ice cream incite murder or does murder increase the demand for ice cream? Neither: they are joint effects of a common cause or lurking variable, namely, hot weather. Another look at the sample shows that it failed to account for the time of year, including the fact that both rates rise in the summertime.

In statistical experimental design, attempts are made to remove lurking variables such as the placebo effect from the experiment. Because we can never be certain that observational data are not hiding a lurking variable that influences both x and y, it is never safe to conclude that a linear model demonstrates a causal relationship with 100% certainty, no matter how strong the linear association.

This is maybe a little confusing. The placebo effect is a real effect of receiving treatment. If a doctor gives you a treatment, you are likely to do better than if you receive no treatment at all. As such it has nothing to do with confounding. The ice cream and murder example does. Both ice cream sales and murder rates are increased by a third factor - the confounding variable or confounder. Sometimes the confounding is pretty obvious, but often it is not.

There has been a lot of work on criteria for causality in science. There are a set of casual criteria, proposed by Austin Bradford Hill in a paper in the 1960's. Many working epidemiologists take these as a good place to start when considering confounding and causation.

Anecdotal evidence doesn't take account of confounders.