What is the opposite of anecdotes?

There doesn't seem to be an opposite to anecdotes. An anecdote is a "small" story that proves a point (i.e. anecdotal evidence). So the opposite is either a "large" story or evidence that is not anecdotal. Of course, an anecdotal story could be a rather long story and a "yarn" or a "tale" could be a rather short story. Certainly, a tale would be hard pressed to be a tale if it was a real short story. However, there are such things as long-winded anecdotes. Science seems to want to make the distinction clearer. Anecdotes are supposedly "non-scientific", which is rather odd to me. Does that mean that a tale, such as a non-fiction book, is not scientific. I mean it is possible to have a book that is nothing but anecdotes, but proves its point to a greater degree then using some scientific method, no? Not surprisingly, in the legal world "anecdotal" evidence can be very persuasive: more persuasive then scientific methods. Yes, I think when people are just chatting to prove some point and they use some anecdote do prove their point they might want to remind the person listening by saying "well, this is just anecdotal evidence". But usually the point has already been made.

That's my non-anecdotal and non-scientific take anyways.