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Correlation Does Not Mean Causation

The most important lesson of the school year

If I could gift my students with only one single concept that they could take from my class and bring into the real world, it is this one: correlation does not mean causation.

Why does this matter?

So often, the attention-seeking media will infer a causal relationship to make better story. An informed population must be able to recognize this gross negligence.

  • “Wearing clothing that promotes alcohol use increases a young person’s chance of binge drinking”

  • “Margarine consumption linked to divorce, recent study reveals”

Image from Spurious Correlations by Tyler Vigen

I use a few ridiculous claims to introduce the concept to students:

Ice cream sales and shark attacks

There was a study that was done that found a strong correlation between the ice cream sales and number of shark attacks for a number of beaches that were sampled.

Conclusion: Increasing ice cream sales causes more shark attacks (sharks like to eat people that are full of ice cream).

Better Explanation: The confounding variable is temperature. Warmer temperatures cause ice cream sales to go up. Warmer temperatures also bring more people to the beaches, increasing the chances of shark attacks. This is known as common response, where two variables (ice cream sales and shark attacks) are both responding to changes in some third variable (temperature).

Number of movies that Nicholas Cage has starred in and deaths by getting tangled in the bedsheets 

An interesting correlation shows that years in which Nicholas Cage starred in more movies are correlated with years of higher number of deaths by getting tangled in the bedsheets.

Conclusion: Nicholas Cage causes people to get caught in their bedsheets.

Better Explanation: There may be no explanation here. These two variables might just show a correlation purely by chance.

Examples to use throughout the year

During the first minute or two of class, I will often share a quick thought or story. I am always intentional with these thoughts or stories and I often use them to revisit this concept.

1. On school spirit day, students wear red and black to show pride in our school. I start class with a thought:

“The administration is interested in getting more kids to sign up for AP classes. During first hour today, I stopped in Mr. Butterfield’s Geometry class and noticed 12/30 students wearing school colors. In our AP Statistics class we have 28/30. So I am going to recommend to the administration that we can increase AP participation by giving sophomore Geometry students free East Kentwood High School t-shirts”.

2. “We just did an analysis for every student that took the SAT and there is a very clear pattern. Students with higher GPAs tended to score higher on the SAT. In order to increase our overall SAT scores at EKHS, the administration has decided to give all students with less than a 2.0 GPA a gift: bumping their GPA up by 0.3”

3. “Last night when I was grading your tests, I decided to give each of you a handwriting grade (1-10 with 10 being best). After grading all the tests I made a scatterplot to see if there is a relationship between quality of handwriting and test scores. There is a strong, positive, linear relationship. Therefore, we will be spending 20 minutes now every Friday practicing our handwriting”.

And now that you have read this blog post, you are more knowledgeable about correlation and causation.

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