The power of chi-square type goodness-of-fit test statistics
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A Monte Carlo simulation study is used to assess and compare the powers of four goodness-of-fit test statistics which are asymptotically Chi-Squared distributed: Pearson’s Chi-Square (CS), Log-Likelihood Ratio (LLR), Freeman-Tukey (FT) and Power Divergence with (PD). A discrete uniform distribution with 10 cells and observations per cell of 1, 2, 3, 5, 10 and 20 is used throughout. Six alternative distributions are considered: decreasing, step, triangular, platykurtic, leptokurtic and bimodal. For sample sizes less than 5 per cell all tests showed low power (less than 80%) except for the leptokurtic alternative. Although power relativity varies for different alternatives, overall the CS and PD are preferred test statistics.
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