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Just a note

X2   =  Σ  (fi - i)2
  • X2 is Pearson's chi squared statistic, which under the null hypothesis is a random quantile of the χ2 distribution with (k - 1 - number of parameters estimated) degrees of freedom,
  • fi is observed frequency in the ith category, there being k categories in all,
  • i is the expected frequency in the ith category.