Recently, a friend was looking for crime statistics on concealed-carry. She was debating someone whose idea of a citation was "Hey, I read it years ago in an article of Scientific American. I trust those peer-reviewed articles more than anything you can show me."
The way to deal with these people is not to become frustrated; it's to realize that they aren't listening and aren't ready to listen. They are arguing with you in order to hear themselves talk, and reinforcing their own beliefs by "refuting" (ie, ignoring) your arguments.
There's no point in arguing directly with people who don't want to see the evidence. But you can point out for the audience, if any, that the person on the other side is ignoring the evidence, and to do that, it helps to have some evidence at hand.