There are situations where you will be asked to compare the performance of your institution with another institution. This is commonly done with projects that I’m on where data collection occurs at a single site, and stakeholders want to compare the single site’s findings with a reference site. More commonly, stakeholders want to compare their performance to a published paper’s findings. In other words, we want to compare an observed finding to a theoretical one.
In the case of proportions, we can compare the proportion of individuals who experienced an event in single site to the proportion from a published study. To do that, we can use the one-sample z-test of proportions.
I wrote a guide on how to perform one-sample z-test of proportions to determine if the proportion of events observed is significantly different from an expected proportion, which is available on my RPubs site (link).