I'm terribly sorry about this super noob math question, but I've been reading for a while now and don't seem to find a starting point.
This is my problem:
My samples have very variable sizes. I want to sort them by "best" mean, but having into account the size of the sample.
In other words, I'm comparing 2 movies A and B with equal mean. However, Movie A was scored 10 by 2 users, and movie B was scored 10 by 1000 users. Of course, the average score of movie B should be way "heavier", as the sample is larger. How can I calculate this "weight"?
Also, if you've seen this scenary before, is variance involved in any way? I'm not sure if there could be a case in which Movie B has lower mean than Movie A but Movie B is still "heavier".
If you could point me in the right direction to solve this, I would be greatful!
This is exactly what I was looking for:
http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
And in my particular case:
http://www.evanmiller.org/how-not-to-sort-by-average-rating.html