I'm sure Wayne is correct that there are proven typical differences in the brain function of left handers vs right handers. I can't refer to any actual studies, but I think there are stats out there that suggest left handers are over-represented at the top levels in racquet sports such as tennis. Another example, in baseball, I think lefties are known as hard throwing, if wild, pitchers.
In golf, though, we have to be careful who we label right handers and who we label left handers. In Canada, it is not uncommon for a player like me who plays golf right handed to find myself in a foursome with two and even three guys who play left handed. But in fact, I'm the only true left hander in the group. I think it has to do with Canadians playing hockey as youngsters. I'm left handed but when I started playing hockey as a kid I felt most comfortable with my right hand low, i.e., shooting from the right. My brother was just the opposite. One year my dad bought us clubs, a right handed set for my brother and a left handed set for me. We traded almost immediately.
Mike Weir is right handed. So is Mickelson, I think. Wasn't Hogan left handed?
I think it would be interesting to know the true handedness of golf course architects both classic and modern to see if there is any statistical over-representation one way or the other.