0

Suppose I roll a six-sided die 1000 times and write down the number of times each face comes up. How do I test whether the die is fair? Can I use a chi-squared test where the expected number of each face is 1000/6=167?

There also appears to be a multinomial test, but that seems less likely to be baked into stats packages and software.

Related question.

Community
  • 1
dfrankow
  • 2,816
  • 6
  • 30
  • 39
  • 2
    You can certainly use a chi-square (but don't round off the expected value; leave it at 1000/6). Some directly relevant posts: [A](http://stats.stackexchange.com/questions/3194/how-can-i-test-the-fairness-of-a-d20), $\, $ [B](http://stats.stackexchange.com/questions/68270/how-do-i-find-data-to-show-whether-a-shaved-die-is-really-loaded), $\, $ [C](http://stats.stackexchange.com/questions/58438/chi-squared-distribution-for-dice-not-returning-expected-values), $\, $ [D](http://stats.stackexchange.com/questions/14301/designing-a-test-for-a-psychic-who-says-he-can-influence-dice-rolls), ... (ctd) – Glen_b Dec 26 '13 at 05:41
  • (ctd)... and some potentially relevant discussion in [E](http://stats.stackexchange.com/questions/49210/grouping-trials-decreases-standard-error). Yes, the multinomial test should work, but the chi-square should do just about as well. – Glen_b Dec 26 '13 at 05:42
  • 1
    A multinomial exact test could need to consider ${1005 \choose 5} = 8,\!459,\!043,\!543,\!951$ cases. Even allowing for symmetrical possibilities, that leaves $12,\!193,\!703,\!764$ distinct cases, which is still rather large. There are further efficiencies possible, but this is still probably not the way to go. – Henry Dec 26 '13 at 09:38
  • Thanks to all who referred me to other questions, I wasn't finding them on my own. – dfrankow Dec 26 '13 at 22:52

1 Answers1

0

Apply the chi-square test of goodness of fit with number of possible cases - 1 degrees of freedom and the null hypothesis being the discrete uniform distribution as you pointed out. This is a textbook example for that.

Germaniawerks
  • 1,027
  • 1
  • 10
  • 15