The word “spurious” means “not being what it purports to be”. A spurious correlation is a statistical term that has significance in both mathematics and sociology that describes a situation in which two variables have no direct connection (correlation), but it is incorrectly assumed they are connected as a result of either coincidence or the presence of a third hidden factor (“lurking variable” or “confounding factor”). Spurious correlations can be proven wrong with the phrase “correlation does not imply causation”.

Spurious correlations can potentially be troublesome in that people may want to base decisions and assumptions on these erroneous relationships, only to have that assumption immediately break down when tested in any significant way. If a person makes a big decision like investing in the stock market or buying a house, thinking it will be profitable based on a spurious correlation, that big decision may hold up in the short run, but because of its flimsy reasoning, it will probably be proven wrong after a while.

Broken down with variables A and B, with C being the lurking variable, a spurious correlation looks like this:

A causes B,

B causes A,

or

C causes both A and B

## Examples

Here’s a very basic and popular demonstration of a spurious correlation to get started with that’s called the “skirt length theory”. There was once a popular belief that the trends of the stock market were related to the lengths of women’s skirts. When it was popular for women to wear their skirts shorter, the stock market seemed to perform well. Conversely, the longer the skirts, the worse the market performed. This idea may sound foolish at first, but because this correlation is true about 25% of the time, there are people that continue to invest in the stock market when skirts are on the rise, so to speak. Obviously this correlation is spurious, or dubious, because what do women’s skirt lengths have to do with investing? Nothing. What may be the third, or lurking variable, is coincidence or perhaps skirt lengths signify overall loosening morals, which in turn may make potential investors more likely to pull the financial trigger thus making the market perform well.

Another, simpler example: A college student notices that on the days she sleeps in and skips her early classes there are a larger amount of traffic accidents on and around campus. The spurious correlation in this example is that she thinks her sleeping in means that more accidents will occur. In fact, what is actually happening is the reason she is staying in those days is because of bad weather (lurking variable), and bad weather tends to cause traffic accidents.

## Significance in Sociology

In the field of sociology, the main idea illustrated by spurious correlations is the concept of correlation vs. causation. Correlation is how two variables change together, regardless of their actual connection, and can be positive/direct or negative/inverse. Causation is when one variable causes the other to change. In both sociology and statistics, correlation and causation are determined by performing experiments. If a researcher notices a relationship between two variables and wants to find out if the connection is spurious or not, he may conduct an experiment and control for other factors.

Here’s a real world sociological situation where spurious correlations play a big part. A big social issue that seems to pop up in discussions fairly regularly is the death penalty, specifically, does the death penalty curb violent crime. The idea that someone will not commit a crime out of fear of being convicted then sentenced to death has been considered a spurious correlation by those that rally against the death penalty. They sometimes claim that because the death penalty is enacted so seldom that whatever year-to-year changes in violent crimes committed cannot be linked to fear of the death penalty, hence it is does not do what it sets out to accomplish.

Analyzing, experimenting with and finally debunking or proving spurious relationships also exercises a person’s critical thinking skills. In both an academic environment and in an everyday situation, an assumption may present itself and must be reasoned with to a degree and make the person think hard about what they are dealing with. For instance, an employer at a restaurant may tell a worker that business is slow on the days that particular worker is there. This may cause that worker to feel sorry for themselves and not like to go into work. But if they thought about it a bit deeper and realized “Hey, I only work in the beginning of the week and at non-peak hours”, then they now realize its not their fault and that the boss is being quite unprofessional.

## Significance in Statistics

Spurious correlations in the statistics world are related to experimental research techniques and data dredging, which is the practice of examining large compilations of data in order to find relationships without any predefined hypothesis to be tested. Because in data dredging all you are doing is finding superficial relationships between variables and not testing causation and correlation, many spurious correlations tend to pop up: A tends to go up when B goes up, so they must be correlated, without taking into account C. This practice is statistical in nature, but can be applied to any number of fields, including economics, geography or any other math-based studies.

Spurious correlations are used in statistics to predict direct causal relationships by employing observational data. Because normal real world experiments cannot be performed in statistics, regression analysis is performed in order to estimate the relationship among variables, and each field has its own version of analysis (econometrics in economics). And just like in the real world experiments, those performing regression analysis must take into account all confounding factors and include them among the regressors.

Spurious correlations can be found everywhere, not just in an academic environment, and most people are guilty of making them, no matter how basic they may be. It is important to be aware of them and to think critically about what the actual relationship is between two seemingly related variables. While they may not be as blatantly incorrect as the connection between the stock market and women’s skirts, it is important to be aware of them and not to make any big decisions based on a spurious correlation.

Page Last Updated: February 2020

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