Just a little praise I think OML needs

[GreatGonzales]

(09-26-2012 04:42 AM)vivafringe Wrote:  This isn't true! It's a common fallacy that you always need a huge sample size to prove things. It turns out our data is so incredible that there is a huge probability that P1 is advantaged even with our tiny sample size. The standard statistical test for this type of data is, as mentioned in the other thread, to look at the ties. In the other thread, there were 17 tied games where the players won as 1p, and 2 tied games where the players won as 2p. Let's say we want to test whether there is an advantage to playing first. A naive view would be that player 1 has a 50% winrate vs. player 2. Let p be the winrate of player 1. We'll do a 2-sided test, even though a 1-sided could be argued to be more appropriate.

Ho (the null hypothesis): p = .5
Ha (the alternative hypothesis): p does not equal 0.5

The number of tied games where p1 follows a binomial distribution with n = 19, p = 0.5. Our p-value is 0.000729. In other words, if the actual winrate was 0.5, we would only expect a result this unusual 1 out of 1372 times.

Hope OML sees this.