Comparative performance of three statistical tests of homogeneity for sparse i x j contingency tables

The Type I error rates and statistical power of three tests of homogeneity of variance for sparse I × J contingency tables were investigated in a Monte Carlo study. The Pearson chi-square, likelihood ratio chi-square, and the Read and Cressie power-divergence statistic with λ = 2/3 were compared under a variety of table dimensions, sample sizes, marginal distributions, and effect sizes. The results suggested that, for small samples, the Pearson chi-square evidenced power advantages in large tables, while the power-divergence statistic was more powerful in small tables. The power estimates for these tests converged with large samples. The likelihood ratio chi-square showed excessively liberal Type I error rates and was not recommended for the analysis of sparse tables.