The Statistical Anomaly

“There are lies, damned lies, and statistics.” How is that for starting off with a cliché one-liner!? However, it is true that statistics can be quite misleading or difficult to interpret at times. Enter Simpson's Paradox. I'm going to demonstrate two interesting real-world examples of this.

	Applicants	Admitted
Men	8442	44%
Women	4321	35%

The above numbers are grad school admissions at UC Berkeley from the fall of 1973. It sure seems that, compared to women, men were more likely to be admitted. Looking at these figures, would you accuse them of gender bias? Well, some people did, and sued the university!

So Berkeley decided to take a closer look at the numbers. Admissions are per department, so they wanted to find out which specific departments were guilty of a significant bias against women. Guess what... none of them were.