In my opinion this question does not belong on this website.
Firstly, this is a site for experts. The intended users of this sites are using their stuff in the real world (yes, universities are also real world in this topic)
As we are all experts, this question has no purpose on this site. It only invites to summing up broad topics, or not being specific on the application anyway. A list of possible applications of statistical analyses is something you expect on a wikipedia-page (which is targeted on novices), not on an expert site.
Especially in the beginning of this site, I would suggest to not have this topics. If this is allowed now, every question of "Real world usages of method X" where X is an related method would possible qualify for the site.
IMHO this site should be a Q&A site, not a site for getting inspiration, hearing great stories, or bragging about your job.