Spurious relationship
In statistics, a spurious relationship or spurious correlation[1][2] is a mathematical relationship in which two or more events or variables are associated but not causally related, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "common response variable", "confounding factor", or "lurking variable").
An example of a spurious relationship can be found in the time-series literature, where a spurious regression is one 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.
Another example of a spurious relationship can be seen by examining a city's ice cream sales.
To allege that ice cream sales cause drowning, or vice versa, would be to imply a spurious relationship between the two.
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.
During the Pagan era, which can be traced back at least to medieval times more than 600 years ago, it was common for couples to wed during the annual summer solstice, because summer was associated with fertility.
At the same time, storks would commence their annual migration, flying all the way from Europe to Africa.
[5] In rare cases, a spurious relationship can occur between two completely unrelated variables without any confounding variable, as was the case between the success of the Washington Commanders professional football team in a specific game before each presidential election and the success of the incumbent President's political party in said election.
The rule eventually failed shortly after Elias Sports Bureau discovered the correlation in 2000; in 2004, 2012 and 2016, the results of the Commanders' game and the election did not match.
[6][7][8] In a similar spurious relationship involving the National Football League, in the 1970s, Leonard Koppett noted a correlation between the direction of the stock market and the winning conference of that year's Super Bowl, the Super Bowl indicator; the relationship maintained itself for most of the 20th century before reverting to more random behavior in the 21st.
A non-causal correlation can be spuriously created by an antecedent which causes both (W → X and W → Y).
Mediating variables, (X → M → Y), if undetected, estimate a total effect rather than direct effect without adjustment for the mediating variable M. Because of this, experimentally identified correlations do not represent causal relationships unless spurious relationships can be ruled out.
On the other hand, if the control culture does not die, then the researcher cannot reject the hypothesis that the drug is efficacious.
The body of statistical techniques used in economics is called econometrics.
The main statistical method in econometrics is multivariable regression analysis.
Just as an experimenter must be careful to employ an experimental design that controls for every confounding factor, so also must the user of multiple regression be careful to control for all confounding factors by including them among the regressors.
If a confounding factor is omitted from the regression, its effect is captured in the error term by default, and if the resulting error term is correlated with one (or more) of the included regressors, then the estimated regression may be biased or inconsistent (see omitted variable bias).
In addition to regression analysis, the data can be examined to determine if Granger causality exists.
The presence of Granger causality indicates both that x precedes y, and that x contains unique information about y.
