## Sunday, November 15, 2020

### [wdyofvtu] chi-squared test for uniformity

here is a Haskell program that calculates the chi-squared test statistic from a list of integers on standard input delimited by whitespace, testing the hypothesis that the input integers are number of occurrences of independent and identically distributed (IID) samples from a discrete uniform distribution.  the mathematical heavy lifting is done by the statistics Haskell package.

suppose we roll a d3 die 51 times and get 10, 11, and 30 as the number of occurrences of each face, "observations" in the language of chi-squared tests.  the "expected outcome" is 51/3 = (17, 17, 17).  the probability of a result as skewed as our observation or worse coming from a fair die is 0.00056959.  our die is probably not fair.

\$ echo '10 11 30' | ./chi-square-uniform
n 3
sum 51
chi^2 14.941176470588236
mkPValue 5.69593143522451e-4

instead, consider 33 rolls distributed (10, 11, 12):

\$ echo '10 11 12' | ./chi-square-uniform
n 3
sum 33
chi^2 0.18181818181818182
mkPValue 0.9131007162822623

the hypothesis of fair die is not rejected.