How do I fix my tub that is not draining?

I live on the third floor of a house, it's a converted attic apartment. The drain in the bathtub doesn't drain the water, and I'm sure it's not clogged because I (on separate occasions) poured drano down the drain, and liquid plumbing snake. I use a strainer to catch all the hair, and I clean it regularly. What could be the problem, and how do i remedy it?