When testing the null hypothesis of independence in a two-way contingency table, the likelihood ratio test statistic is approximately distributed as Chi-squared d for large sample sizes (N) but may not be for small samples. This paper presents expressions which match the mean of the statistic to Chi-squared d as far as N−1 and N−2, derives a method of estimating the expressions from observed data and evaluates them using Monte Carlo simulations. It is concluded that using appropriate dividing factors, rejection rates after matching are more accurate than for either the unadjusted likelihood ratio statistic or the Pearson approximation which is the main alternative statistic. Minimum cell frequencies necessary for high test accuracy are smaller than those commonly given in textbooks.