A Comparison of Some Continuity Corrections for the Chi-Squared Test on 2×2 Tables

This article considers the two-sided test of independence in a 2 × 2 contingency table. The chi-squared approximation to the exact significance of Pearson's X 2 test is compared with four approximation methods adjusting for continuity. Computations were carried out for nearly 150,000 fourfold tables. It was found that both the uncorrected chi-squared test and the Yates correction may give misleading outcomes even for moderate sample sizes and expected values, whereas the other three methods provide closer approximations. Although fixed marginal totals are assumed, these corrections may also be applied to tables with random marginal totals, provided one is interested in the exact conditional significance.