We would like to determine which of the shifts from pre- to post- are significant. (In other words, at which institutions is the post-test data significantly different from the pre-test data.) I had originally done this for each institution separately using a paired-samples t-test.

One of our reviewers pointed out that we might be increasing the risks of incurring a Type I error this way, and suggested that we should do our analysis using ANOVA. I can see how to use ANOVA to determine whether the pretest data or the post-test data from the different schools are different from one another, but I cannot see how to use ANOVA to determine whether the pretest and post-test scores at a single institution are different from one another (this seems like going back to a t-test).

I think there may be some way to do this with post-hoc tests, but am not sure how to interpret the outputs of these tests.

This is all complicated by the fact that we have very different numbers of students at the different schools, and so many repeated-measures ANOVA designs do not seem appropriate.