On Feb 21, 2009, at 2:14 PM, LuKreme wrote: > Let's say I am trying to find out what the probability is of something > happening in a game, and let's say that the mechanics are hidden (so > no dice, but a computer calculation) > > Let's say I do something in the game 78 times, and 19 times I have a > 'positive' result. > > How sure am I that the 'positive result percentage' is 24.35897%?
You can't actually get a point estimate like that. Obviously if you try one more time you are going to get either 24.05063291% or 25.3164557%. What you can get is a range that is a function of both sample size and the risk that you are willing to take that the true value falls outside the range. In practice this means that you use the "plus four" method for computing a confidence interval. Let p* = (positive results + 2)/ (trials +4) and then your interval is p* + or - sqrt(p* (1-p*)/(trials + 4)) * Z. You get Z from a table in the back of a stat book or from a spreadsheet function. For example if I wanted to be 95% sure that my interval contained the true value I would type =NORMSINV(0.975) into Excel and get a value of 1.959963985. If I was willing to live with 90% confidence I'd use NORMSINV(0.95) and get 1.644853627. The variable is always (1 - half chance of the error I'm willing to accept) because I want a symmetric estimate with the chance of overestimating = the chance of underestimating. HTH. --- Neither a man nor a crowd nor a nation can be trusted to act humanely or to think sanely under the influence of a great fear. -Bertrand Russell, philosopher, mathematician, author, Nobel laureate (1872-1970) _______________________________________________ OSX-Nutters mailing list | [email protected] http://lists.tit-wank.com/mailman/listinfo/osx-nutters List hosted at http://cat5.org/
