Contingency tables are commonly used in research, but traditional statistical tests like the chi-square test may not work well with small sample sizes. A different test called the power-divergence statistic is recommended for sparse conditions. This study compared three tests for contingency tables under small sample conditions: the Pearson chi-square test, the likelihood ratio chi-square test, and the power-divergence statistic with a specific parameter. The researchers looked at how well these tests performed in terms of power and error rates with different table sizes, sample sizes, and effect sizes.