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In statistics, a spurious correlation refers to a connection between two variables that appears to be casual but is not. With spurious correlation, any observed dependencies between variables are merely due to chance or are both related to some unseen confounder. Spurious correlation can be caused by small sample sizes or arbitrary endpoints.

Spurious relationships will initially appear to show that one variable directly affects another, but that is not the case. This misleading correlation is often caused by a third factor that is not apparent at the time of examination, sometimes called a confounding factor. "When two random variables track each other closely on a graph it is easy to suspect correlation where a change in one variable causes a change in the other variable. Setting aside causation, which is another topic, this observation can lead the reader of the chart to believe that the movement of variable A is linked to the movement of variable B or vice versa" (Kenton, 2021).

A funny example I found of spurious correlation would be per capita cheese consumption correlating with the number of people who died by becoming tangled in their bedsheets. These two factors seem to have absolutely nothing to do with each other, but let's take a deeper look at the statistics. The graph included below clearly shows that the increase in cheese consumption is closely followed by the increase in the number of people who died in the previously described way. "It is clear that there cannot be any causal link between the variables, ie, the change of one variable does not cause the change of the other" (Hrabac & Trkulja, 2020). However, it is also indisputable that there is a correlation between the two variables and that such correlation can be expressed numerically, regardless of whether it makes sense or not. This type of correlation is called linear, bivariate, or Pearson correlation, after one of the founders of modern statistical science, Karl Pearson.

References:

Hraba, P., & Trkulja, V. (2020). Of cheese and bedsheets - some notes on correlation.Croatian Medical Journal,61(3), 293-295. https://doi.org/10.3325/cmj.2020.61.293

Kenton, W. (2021, November 17).Spurious Correlation Definition. Investopedia. https://www.investopedia.com/terms/s/spurious_correlation.asp#:~:text=Spurious%20correlation%2C%20or%20spuriousness%2C%20occurs