<Dl> <Dd> χ 2 = ∑ i (O i − E i) 2 E i . (\ displaystyle \ chi ^ (2) = \ sum _ (i) (\ frac (\ left (O_ (i) - E_ (i) \ right) ^ (2)) (E_ (i))).) </Dd> </Dl> <Dd> χ 2 = ∑ i (O i − E i) 2 E i . (\ displaystyle \ chi ^ (2) = \ sum _ (i) (\ frac (\ left (O_ (i) - E_ (i) \ right) ^ (2)) (E_ (i))).) </Dd> <P> The approximation of G by chi squared is obtained by a second order Taylor expansion of the natural logarithm around 1 . This approximation was developed by Karl Pearson because at the time it was unduly laborious to calculate log - likelihood ratios . With the advent of electronic calculators and personal computers, this is no longer a problem . A derivation of how the chi - squared test is related to the G - test and likelihood ratios, including to a full Bayesian solution is provided in Hoey (2012). </P> <P> For samples of a reasonable size, the G - test and the chi - squared test will lead to the same conclusions . However, the approximation to the theoretical chi - squared distribution for the G - test is better than for the Pearson's chi - squared test . In cases where O i> 2 ⋅ E i (\ displaystyle O_ (i)> 2 \ cdot E_ (i)) for some cell case the G - test is always better than the chi - squared test . </P>

What is the ratio of g/g