How long will there be English departments? Every professional needs to be able to communicate ideas in writing. One would assume that in time English would be absorbed into other departments that applied it.
It's a bit like trickle-down economics.
But yes, most biological research doesn't require much mathematics.
http://en.wikipedia.org/wiki/Meta-analysis
Invented to look at telepathy, and Rhine was definitely a psychologist (though one the field unfairly tries to forget). That being said, I thought Glass was a psychologist but he was actually a statistician, so I suppose the modern form of meta-analysis was, in fact, invented by a statistician. Do psychometricians count as statisticians? If not, then quite a few more things were invented outside of statistics.
Psychology: not just for innumerate touchy feely hippies (just mostly).
Has an interesting history on the subject
For however long there will be people willing to pay tuition to enroll in one. Really, that's the answer to all questions in that form. No matter how worthy of independence a study might be, it exists or fails to exist primarily on the existence of a body of students willing to pay money to sit in those seats.*
* speaking purely in terms of undergraduate programs here
Writing English stories is just aiming at a different compiler in someone else's head.