Comparisons of Some Chi‐Squared Goodness‐of‐Fit Test Statistics in Sparse One‐Way Multinomials

The behavior of Pearson's X 2 test, the likelihood ratio test Y 2 and the two of its derivatives, G 2 and G k 2 , the Freeman‐Tukey test (FT) and the Cressie and Read test Statistic I (2/3) are examined in this study. Estimated attained α levels based on 1000 simulated samples when the approximating distribution is χ k ‐1 2 , are computed for these tests for the various values of k, n and seven null hypotheses. Results from estimated power computations indicate that none of the test statistics has a clear advantage over any others, and that the choice of which test to use must therefore rest mainly on the performances with regards to the attained α levels when the χ 2 approximation is invoked. In this respect, the log‐normal approximation proposed by Lawal and Upton (1980) is strongly recommended. This is closely followed by the I (2/3).