A big interest of mine is psychology, which deals a lot with correlational studies, some of which "went mad."
A correlational study conducted by Albert Bandura supports the idea that individuals (in this case, children) learn through imitating others. This is true, and Bandura's Bobo Doll Experiment took this idea further and proved that children in elementary school who are exposed to violent TV, video games, and movies, expressed increased aggression. In case you don't know, a Bobo doll is an egg shaped ballon creature that has a weight in the bottom so that when you hit it, it pops back up. In his experiment he videotaped a women who hit the Bobo doll, sat on it, kicked it, and hit it with a hammer a few times, all while yelling aggressive phrases such as, "sockaroo." He then showed a group of kindergardeners this video, who naturally loved it. Then he set the children free to play in a room with several Bobo dolls and a couple small hammers. As you might imagine, the children went to work on that doll. Hitting it, yelling at it, and so on. He then did the same thing with a real live clown, and the results were very similar. The children that didn't participate in hitting the real live clown but did with the bobo doll, most likely saw the bobo doll as a game, and did not see it as such with a real person.
In this case, the children did show increased aggression, but I do not believe that violence on TV, in video games, etc. is the CAUSE of violence in our world. For one thing, Bandura refined his experiment by showing the same video but the woman was punished at the end for hurting the doll. In this case, the number of children who hit the bobo doll dropped by more than half. This is relevant in the real world because violence leads to punishment whether it be timeout or more seriously, the police, and children learn this via observation just as the would violence. Violent people who end up in jail might have watched violent movies, played violent video games, or even saw real live violence in their home, but know the consequence just as well as anyone else. Therefor, I feel in this experiment correlation was a factor but causation is not justified.