I'm planning on doing quantile regression for estimating pain relief after hip surgery. My aim is to construct for my patients information in this format:
4 out of 5 patients experience with your background experience at least a 50 % decrease in pain intensity one year after surgery
My problem is: Is 80 % perceived as very probable? Is 90 % much better?
What I'm looking for is some kind of reference article on how people perceive percentages to determine a good quantile. I've been looking on Google scholar for something useful but strangely I haven't found anything that I can use. There is plenty of articles on how to communicate risk, a good summary can be found here, but none of them discuss how percentages in this fashion.
I guess what I'm looking for is something like the p-value graph (originally posted in this question) but with "John Doe's" instead of "Scientist's".