# Statistical test for a random die roll? [duplicate]

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.

• 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, $\,$ B, $\,$ C, $\,$ D, ... (ctd) Dec 26, 2013 at 5:41
• (ctd)... and some potentially relevant discussion in E. Yes, the multinomial test should work, but the chi-square should do just about as well. Dec 26, 2013 at 5:42
• 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. Dec 26, 2013 at 9:38
• Thanks to all who referred me to other questions, I wasn't finding them on my own. Dec 26, 2013 at 22:52