COMPARISONS OF SOME CHI-SQUARED GOODNESS-OF-FIT TEST STATISTICS IN SPARSE ONE-WAY MULTINOMIALS

The behavior of Pearson's X2 test, the likelihood ratio test Y2 and the two of its derivatives, G2 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 alpha levels based on 1000 simulated samples when the approximating distribution is chi(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 alpha levels when the chi2 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).