19 September 2008
I got busy in the kitchen collecting data for my little experiment. I rolled them in batches of 16 (all of my new dice) and did ten sets, so my actual sample size was N=160. The result was 18 sixes, when I expected 160/6 = 26.67, so this is actually less than I should find on average. This brings up a detail glossed over yesterday; This is a two sided test with equal probability of detecting outcome greater OR lesser than the assumed fair value (0.1667). In my zeal to test if these dice are rolling higher than expected I ignored the other possibility that they might roll lower - a possibility that cannot be ruled out and should not be excluded. I did set up the test to allow this the possibility, but I didn't explain it as such.
It seems that I need to state the assumptions of my experiment more formally.
There is an assumption I didn't state last time; that all of these dice are identical in the probabilities of the result (identically distributed). It could be that some of my dice consistently roll high and other roll low, which tend to cancel each other out and confound my experiment.