Comparing Tests for Association in Two- by-Two Tables with Zero Cell Counts

Abstract

This study compared the tests for association in two by two tables with zero cell counts. Pearson’s uncorrected chi-squared test, Pearson’s chi-squared test with the continuity correction, Pearson’s uncorrected chi-squared Monte Carlo simulation test, Fisher’s exact test, the Conditional Binomial Exact Test (CBET), Barnard’s exact test, Liebermeister’s test, Lancaster’s mid P-test and logistic regression with penalized maximum likelihood were considered. Criteria used 72 two by two tables with smallest counts and average p-value for Fisher’s exact test and Pearson’s uncorrected chi-squared test close to 0.05. CBET, Lancaster’s test, and the penalized maximum likelihood test give similar p-values closest to 0.05, suggesting that these three methods can be recommended for testing association in two by two tables with zero cell counts.