Simpson’s Paradox

Updated: Nov 29, 2018

A paradox is a self-contradictory statement. An example could be found in Shakespeare’s famous Hamlet. In the play, Hamlet says, “I must be cruel to be kind.” This statement might not make sense to you at first. How can mean actions represent kindness? However, this is about Hamlet’s mother. Hamlet does not want his mother to marry his uncle--his dad’s murderer. So, he thinks the death of his uncle will be best for his mother. This month, I want to elaborate on Simpson’s Paradox.

Not those Simpsons! I am just kidding!

Simpson’s Paradox is about statistical probability. According to Princeton University, Simpson's Paradox (or the Yule-Simpson effect) is an apparent paradox in which a correlation (trend) present in different groups is reversed when the groups are combined. This is most commonly seen in college admissions. Let me demonstrate an example.

Students are accusing college Y of gender bias since the college’s student body has a lot more men than women. The college is trying to explain to the students they do not have a preference of men over women. They showed the students this chart.

The chart shows admission data broken down by major and gender. Roughly equal percentages of men and women are admitted into each major. However, if you look at the number of applicants admitted based on gender, you will see a seemingly different story. 970 men and 520 women are admitted. This is why some students suspect the college of gender bias.

Data everywhere can be misleading. Some tricky people tend to demonstrate data in a certain manner for their own good. My suggestion is the following: when viewing data, look at the whole picture.

This blog post was written by Your Stat Class' intern, Wenyu Shi, a former AP Statistics student.

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