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Yates' continuity correction of the chi-squared test for testing the homogeneity of two binomial proportions in contingency tables is developed to lower the value of the test statistic slightly. The effect of continuity correction is expected to decrease as the sample size increases. However, in extremely unbalanced contingency tables, we find some cases where the effect of continuity correction is eccentric and is larger than expected. In such cases, we conclude that the chi-squared test with continuity correction should not be employed as a test statistic in both asymptotic tests and exact tests.

The Eccentric Properties of the Chi-Squared Test with Yates' Continuity Correction in Extremely Unbalanced 2×2 Contingency Table