March 14, 2015

Correlation and Causation, Explained

When my first job was going through a series of layoffs, I couldn’t help but notice most of the people being laid off where new in their careers, like me. During our usual one-on-one I asked my boss if I should be worried. He replied “correlation does not imply causation.”

“Correlation does not imply causation” is one of my statistical pet peeves because it’s so often misunderstood and misused. It’s a typical response when the speaker wants to dismiss an observation or study he or she doesn’t agree with, without addressing the merits of the observation or study itself. If my boss had said “the square of the hypothesis is equal to the sum of the square of the sides” he would have been just as accurate, and just as irrelevant.

What is Correlation and Causation?

Correlation means two events tend to occur together more frequently, or infrequently, than could be explained by random chance.

Causation means one event causes another event.

If two events have a causal relationship, by definition there is also a correlation between the two. Events that are correlated is a superset of events that are causal. There exists some events that are correlated and not causal.


Ice cream sales and crime rates (or sometimes shark attacks) tend to be a favorite example of a correlated relationship that’s not causal. All three increase in the summer when the temperature rises and people tend to be out more. Since the rate of each event rises in warm weather, and falls in cold whether, the events are correlated. If you know crime rates have increased recently, there’s a good chance it’s summer and ice cream sales have also increased. Criminals aren’t turning to a life of crime to support their ice cream habit, and ice cream isn’t altering a persons’ brain chemistry making them more susceptible to their impulses. The relationship is not causal.

What can be deduced if a relationship is Causal vs Correlated?

If the relationship between two events is causal, then altering the causal event will effect the other.

If the relationship between two events is correlated you cannot assume you can control one event by manipulating another, however it is perfectly reasonable to make predictions about one event by observing another.

If I witnessed an increase in ice cream sales, I might expect to see more reports of shark attacks in the news. I can’t grantee a band on ice cream sales to change the crime rate and vice versa. I can hypothesize that the band may effect the crime rate, but I cannot guarantee it. I would first need to conduct an experiment to see if manipulating one event causes the other to change, ie that the relationship was causal and not just correlated. The observation that two events are correlated is usually the precursor to such an experiment.

If I noticed the layoffs seem to disproportionately include younger employees like myself, it’s statistically valid to be concerned. This conversation happened right around the time I decided to go to grad school, so while it may have been a statistically valid concern, it wasn’t a very practical one.

This mathematical post brought to you by the number Pi. Happy Pi day!

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