A spurious relationship, also known as a spurious correlation, is a mathematical relationship between two or more variables that are associated but not causally related. This can occur due to coincidence or the presence of a third, unseen factor, which is referred to as a "common response variable," "confounding factor," or "lurking variable". For example, a spurious relationship can be seen in the time-series literature, where a spurious regression provides misleading statistical evidence of a linear relationship between independent non-stationary variables. Another example of a spurious relationship can be seen by examining a citys ice cream sales. The sales might be highest when the rate of drownings in city swimming pools is highest. To allege that ice cream sales cause drowning, or vice versa, would be to imply a spurious relationship between the two. In reality, a heat wave may have caused both. The heat wave is an example of a hidden or unseen variable, also known as a confounding variable.

Spurious relationships can be identified by using common sense and by including all variables that might impact the findings in the statistical model to control their impact on the dependent variable. Spurious correlations can appear in the form of non-zero correlation coefficients and as patterns in a graph. Confounding variables can create a spurious correlation that produces a non-zero correlation coefficient and a graph that displays a relationship. An unidentified spurious relationship can undermine the internal validity of research.