Examples
A well-known case of a spurious relationship can be found in the
time-series literature, where a spurious regression is a regression that provides misleading statistical evidence of a
linear relationship between independent
non-stationary variables. In fact, the non-stationarity may be due to the presence of a
unit root in both variables.^{
[3]}^{
[4]} In particular, any two
nominal economic variables are likely to be correlated with each other, even when neither has a causal effect on the other, because each equals a
real variable times the
price level, and the common presence of the price level in the two data series imparts correlation to them. (See also
Spurious correlation of ratios.)
An example of a spurious relationship can be seen by examining a city's
ice cream sales. These sales are 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.
Another commonly noted example is a series of Dutch statistics showing a positive correlation between the number of storks nesting in a series of springs and the number of human babies born at that time. Of course there was no causal connection; they were correlated with each other only because they were correlated with the weather nine months before the observations.^{
[5]} However Höfer et al. (2004) showed the correlation to be stronger than just weather variations as he could show in post reunification Germany that, while the number of clinical deliveries was not linked with the rise in stork population, out of hospital deliveries correlated with the stork population.^{
[6]}