Abstract: 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.
Keywords and phrases: goodness-of-fit, power, chi-square tests, discrete.
