My previous post on fair dice focused on some intuitive ideas about die fairness, and the beginnings of a mathematical approach. Now I’d like to describe the tests my die roller does. These are what I’ve settled on so far as a way to get some numbers to describe and compare the fairness of different dice.
The chi-squared test
First off, there’s the chi-squared goodness-of-fit test. This is a test that looks at the deviations in the histogram to get a total number (the chi-squared statistic) that characterizes how far the histogram deviates from ideal. You can also compare the result statistic to a mathematically-determined threshold that will give you a confidence value for the test; a 95% confidence is often chosen.
So hey, that’s great! We can reduce the whole set of results and its histogram to a single number for a given die, and then find out whether that die is fair or not with 95% confidence! Super! Right? read more...