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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 appropriatedoi:10.22237/jmasm/1209615180 fatcat:wl46dcmwrjddxpzpnok2irvkzm