Fairly random, but Let me continue before you just say it's strictly writing, and then think about it, and ultimately decide. :P
I have always called myself left handed, but I do a lot of things normally done by right handed people. I keep my keys on the right side of my jeans, my pens in my right pocket, use most tools in my right hand (depending on the circumstances), etc. but I write with my left hand, and trying to write with my right hand is an illegible mess.
So in your opinion, is it defined only by which hand you write with, or is it defined in some other way?