Definition

In a regression analysis, a lurking variable or factor is one that might significantly influence the output but is not explicitly included in the study. As a result, the change in the output variable might be incorrectly attributed to a different variable included in the study, leading to false or misleading conclusions. Also called confounding variable or confounder.

Simpson's Paradox, a phenomenon in which the direction of the association between two variables is reversed when data from several Samples are combined into a single sample, is an extreme case of the effect of a lurking variable.

Examples

Spurious correlation
The number of TV sets owned by each household in a population is highly positively correlated to the general health of the population. This may lead to the conclusion that having more TV sets improves health. But the truth is, there is a lurking variable: financial wealth, which influences both, the ability to buy more consumer goods and better health outcomes due to access to better nutrition, healthcare, etc. This variable was not considered in the equation, leading to the erroneous conclusion.

Simpson's Paradox
A popular example of the occurrence of this phenomenon is in the U.S. electoral process. If candidate A wins 35 of the states and candidate B wins 15, candidate would appear to have won the election. But if the states choosing candidate A are less populated than those electing candidate B, then candidate B could still be the winner with a larger share of the votes. The lurking variable here is the differing number of electoral votes each state carries.