Comparison of tests of contingency tables.

We explore the use of bootstrap for testing independence of two categorical variables. We develop a theoretical justification for bootstrapping a contingency table and provide more accurate inference for small sample sizes. We also study the effect of equalized marginals on tests of independence. The small sample properties of the proposed and existing tests of independence are examined using Monte Carlo simulations. It is shown that the Fisher exact test and the Chi-squared test with continuity correction are very conservative and cannot be recommended to test independence with small sample sizes.