The power of Chi-Square type goodness-of-fit test statistics

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 λ = 23 (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.