Last semester, our apartment had a debate over whether video games cause violence. It came down to arguing logical mechanisms, but without any use of statistics by either side. The argument basically turned into my word vs your word, since there was no objective basis on which to judge anything.
If your answer were yes, you might propose the mechanism: “People who play violent video games are likely to imitate the characters they play, thus becoming more aggressive in real life.” This statement might be logically sound, but without any supporting evidence, it has little credence.
You could easily propose a counter-mechanism: “People who would otherwise commit violent crimes satisfy their urges in video games and not in real life, thus decreasing the crime rate.” Again, this seems plausible, but without any data, we simply don’t know whether this effect outweighs the other. We need real stats.
In any subject, one important concern is matching theories with empirical data. In the hard sciences, one tests the theory by experiment, and it is often possible to verify or deny claims with empirical data. But in the social sciences, experiments are sometimes impossible. To see what would happen if Germany had won World War II, we cannot simply recreate the circumstances of the war in a petri dish. So we must do the best we can with the limited data we have.
This lack of statistics affects many other issues, perhaps more important ones. For instance, in the public debate over gun control, there are clearly two competing mechanisms: “More guns = more shootings” and “More guns = more protection.” Each makes logical sense on its own, but the way to figure out the more accurate one is not by purely logical argumentation (which will lead nowhere), but by use of statistics, i.e. show the real effects of implementing or not implementing gun control laws. This would be much more fruitful than mindlessly yelling mechanisms across the void.