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Just a note

G    =   2 [a ln(a) + b ln(b) + c ln(c) + d ln(d)
   + N ln(N) − (a+b) ln(a+b) − (a+c) ln(a+c)
  − (b+d) ln(b+d) − (c+d) ln(c+d)]


  • G is the likelihood ratio statistic, approximating to χ2 for large samples,
  • a, b, c, & d are the observed frequencies for each cell,
  • N is the total number of observations.