Key points are not available for this paper at this time.
Noel Cressie, Timothy R. C. Read, Pearson's X2 and the Loglikelihood Ratio Statistic G2: A Comparative Review, International Statistical Review / Revue Internationale de Statistique, Vol. 57, No. 1 (Apr., 1989), pp. 19-43
Cressie et al. (Sat,) studied this question.