# How to compare two reviews, when one has more participants than the other

Hi I only did some basic stats at school but now I need to rank some data for a project, and I've run into this kind of scenario

Game A: 1000 Reviews, 900 Positive and 100 Negative, so 90% positive.

Game B: 20 Reviews, 20 Positive and 0 Negative, so 100% positive.

It clearly isn't fair to say Game B is better than Game A just because it have a higher percentage of positive reviews, but I still need a way to conclude their positive percentage. How should I do so?

EDIT: In my case, it's more than just two data, it's about hundred or thousands of data, some value are just extremely large and some are small.

• For each game , let $p$ be the probability of positive review (one different $p$ for each different game). Tou could present confidence intervals for each $p$. If you have many games and want a ranking, there are statistical methods for that too, but maybe complicated with only "basic stats". Then you would need to formulate more precisely your goal. Can you post a link to your data? – kjetil b halvorsen Aug 26 '15 at 17:15
• One approach that has been used is to calculate a "lower bound" on the positive proportion based on a binomial proportion confidence interval. Evan Miller discussed the Wilson interval, but any of the others could be used. This sort of approach has been widely used for comparing various kinds of ratings (e.g. I gather it's used by reddit in ranking comments). ... ctd – Glen_b Aug 26 '15 at 22:54
• ctd... This is the subject of a number of posts on our site, but you should probably start with this one since the discussion there (at least briefly) mentions problems and alternatives. [Edit -- It looks like reddit's use of it had - at the time this was written - some implementation issues.] – Glen_b Aug 26 '15 at 23:12