- #1

- 713

- 5

it is well-known that the Chi-square test between an observed distribution

*O*and an expected distribution

*E*can be interpreted as a test based on (twice) the second order Taylor approximation of the Kullback-Leibler divergence, i.e.: [tex]2\,\mathcal{D}_{KL}(O \| E) \approx \sum_i \frac{(O_i-E_i)^2}{E_i} = \chi^2[/tex]

where

*i*is the bin of the histogram (or contigency table). A proof is given here (page 5).

The question is: how do we know that each of the error terms [itex]\frac{(O_i-E_i)^2}{E_i}[/itex] on the right side of the above equation follows a normal distribution

*N(0,1)*? There is probably some some assumption to be made...?