When the number of games is high, the numbers should match.Hart wrote:How would this compare to using a z-test on a proportion? I always thought that is how it was calculated but when I compare my numbers to yours they look very different.
For instance, with n1 = 120, n0 = 110, you have
mu = 120/230
sigma² = mu*(1-mu)/229
(mu-0.5)/sigma = 0.658568
Look it up in that table:
-> something between 0.7422 and 0.7454
My program gives 0.7447, so that matches very well.
If you add a few draws, for instance 100
mu = 170/330
sigma² = (120*(1-mu)² + 100*(0.5-mu)² + 110*(0-mu)²)/(329*330)
(mu - 0.5)/sigma = 0.661198
It is almost identical.