Quote:
Originally Posted by DonkoTheClown
That is a good point. If I am coming up way short of that 24%, should I be concerned? The question would also be how short would that number need to be for it to be outside of the statistical norm? Of course sample size is a big consideration here right? I think that I have 60,000+ hands from one site to sift through.
Using an assumption of a normal distribution (fine if the hand sample is large enough), when you test a sample against the population mean (expectation), if your sample is random then 68% of the time the sample mean will fall within 1 standard deviation of the population mean. 95% of the time, within 2 standard deviations, 99% of the time within 3 standard deviations, and 99.9% of the time within 4. To illustrate this, the standard deviation is the body of the bell curve, that is the area between two vertical lines drawn through both sides of the curve at the point where it changes from convex to concave. Half that width is 1 standard deviation (because it goes both ways). Multiple standard deviations fall in the tails.
You then need to figure the significance of your standard deviation using something like a T Test or a Z test (you can look up tables for this). This will relate your result to the sample size, which basically means the larger the sample the closer you should be to the expectation.
You can calculate the standard deviation from the sample size, the sample mean, and the population mean.
I wrote this off the top of my head while eating, so someone feel free to correct any error.
Edit: here's some java code to do the std dev and a T Test, and then you have to look it up in a table for the significance of the result.
Code:
public static double T_Test(double actual, double expected, double tieExp, int sampleSize) {
double obs = actual;
double p = expected; // this is already the sum of 1/2 tie plus win
double T = tieExp; // just the half for this player
double W = p - T;
double q = 1.0 - p;
double n = sampleSize;
double ttest=0;
ttest = ( (obs - p) / Math.sqrt( ((p*q)-(T/2.0)) / n ));
if (p==0) {
return 0;
} else {
return ttest;
}
}
This result tells you how many standard deviations your sample mean differs from the population mean.
Last edited by spadebidder; 08-26-2009 at 08:57 PM.