Image ppi and file size

I'm trying to understand how PPI and image dimension work. Thanks to this and this, I think I now have a pretty good understanding of what PPI is and how it is not important until I want to print an image. While working on the web, PPI is not important.

What I don't understand though is why when I change the PPIs for an image, the file size changes. I mean, there the same amount of information on the file, should't it occupy the same space?

Thanks!