Is there a statistical test for one participant measured many times? Pretty much throughout my undergrad and postgrad, I have always learned statistical models predicated upon things like large subject size. I also know that a lot of repeated measures designs typically work at reducing the error variance of a predictor by removing the error in between time periods. I know that this can sometimes be used as a way to increase the power of a test where there are far less participants in the study.
So to ask what is probably a really stupid question, is there a valid statistical test in which you could use a single participant measured hundreds of times to measure an independent and a dependent variable? I would think that normally this would be an issue in terms of generalizability to the rest of the population, but I'm just curious if there is such a thing in statistics, because I couldn't find something like this when I looked online and I imagine there is good reason for it.

Single subject analyses are used in some fields, for instance in psychophysics, where it a single participant might make thousands of perceptual decisions (possibly after having an electrode implanted, if the participant happens to be a rodent or money).
The biggest non-technical issue with this approach is that there is no way of knowing whether results will generalise to other people/animals, which is why it's a good idea to use a sample of participants.
