It seems obvious that people who fear another person is armed will be less inclined to attack. The stats will prove nothing but the obvious. However, you surely want to move away from the Gun Law of the old frontiers, where the survivor was right and the dead man was in the wrong, don't you.
Only recently, I discovered that the UK is more violent than USA or South Africa. Yet there is no real demand here for the right to carry guns or other weapons in public, and if there were a referendum, I bet a pound to a penny that the vote would be against. In fact, it is against the law to carry any offensive weapon in public.
OK, we might get hit with a bat, or knifed, but we perceive the danger is far less here than American scaremongers such as the NRA whine about over there.