In 2021, the Delta variant of COVID was driving hospitalizations back up, despite the fact that the COVID vaccine had been available for some time. Of particular concern was that a majority of patients hospitalized with severe cases of COVID were vaccinated. People took this to be evidence that the vaccines were not effective against the new Delta variant. But, instead, this was a real-world example of how hidden variables can complicate statistical analysis. In particular, this is an example of Simpson’s paradox. In this video, we look at the data to reveal why the vaccine’s effectiveness didn’t lead to only or mostly unvaccinated people being hospitalized. This video is aligned with Chapter 11 of the book Recipes for Science: An Introduction to Scientific Methods and Reasoning, by Angela Potochnik, Matteo Colombo, and Cory Wright.