On Feb 21, 2009, at 9:47 PM, LuKreme wrote: > so in this example case, say I wanted 95% certainty, I would then plug > the number into the formula you gave, like this: > > p* = (21/80) =.2625
Well, actually it should be 21/82 but you get the idea. > > > .2625 ± [ sqrt(.2625 * .7375 / 82) * 1.9599 ] > > .2625 ± 0.095229752 = 0.167270248 <-> 0.357729752 > > So, I am 95% certain that the true probability is in the range of > 16.72% to 35.77% or so. So, my 'sense' that 19/78 is pretty close to > 25% is pretty much shit. > > If we move up and order of magnitude we get > > .2625 ± [ sqrt(.2625 * .7325 / 792 ) * 1.9599 ] > > .2625 ± 0.030537944 > > Still a 3% range even after nearly 800 trials. > > OK, that at least tells me that my 'sense' is completely worthless in > this case. What I have to do is decide the confidence interval I > want, and then calculate the possible range of values, which is > exactly opposite of what I was thinking (calculate the value, and then > calculate a ± confidence on that value). You have grasped it. The sampling distribution of a proportion is a bell shaped curve but a wider and flatter one than maybe you would intuit. Also, to cut the confidence interval in half you must quadruple the sample size so you run into a sort of diminishing returns to getting more data. I probably should have mentioned that you need to have a big enough sample that you have at least 5 successes and 5 failures before you can conclude anything. --- 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/
