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

- Journal title : Korean Journal of Applied Statistics
- Volume 23, Issue 4, 2010, pp.777-781
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2010.23.4.777

Title & Authors

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

Kang, Seung-Ho; Kwon, Tae-Hyuk;

Kang, Seung-Ho; Kwon, Tae-Hyuk;

Abstract

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.

Keywords

Exact test;type I error;homogeneity;binomial distribution;

Language

English

References

1.

Conover, W. J. (1968). Uses and abuses of the continuity correction, Biometrics, 24, 1028.

2.

Conover, W. J. (1974). Some reasons for not using the Yates’ continuity correction on 2 ${\times}$ 2 contingency tables (With comments), Journal of the American Statistical Association, 69, 374–382.

3.

Fisher, R. A. (1925). Statistical Methods for Research Workers, Edinburgh, Oliver and Boyd.

4.

Grizzle, J. E. (1967). Continuity correction in the $X^2$ test for2 ${\times}$ 2 tables, American Statistician, 21, 28–32.

5.

Haviland, M. G. (1990). Yates’s correction for continuity and the analysis of 2${\times}$ 2 contingency tables,
Statistics in Medicine, 9, 363–367.

6.

Indrayan, A. (2008). Medical biostatistics, Chapman & Hall/CRC, Boca Raton.

7.

Kang, S. H. and Ahn, C. (2008). Tests for the homogeneity of two binomial proportions in extremely unbalanced 2${\times}$ 2 contingency tables, Statistics in Medicine, 27, 2524–2535.

8.

Kang, S. H., Lee, Y. and Park, E. S. (2006). The sizes of the three popular asymptotic tests for testing homogeneity of two binomial proportions, Computational Statistics and Data Analysis, 51, 710–722.

9.

Mantel, N. and Greenhouse, S. W. (1968). What is the continuity correction?, American Statistician, 22,
27–30.

10.

Martin Andres, A. and Silva Mato, A. (1994). Choosing the optimal unconditioned test for comparing two independent proportions, Computational Statistics and Data Analysis, 17, 555–574.

11.

Martin Andres, A., Sanchez Quevedo, M. J. and Silva Mato, A. (1998). Fisher’s mid-p-value arrangement in 2${\times}$ 2 comparative trials, Computational Statistics and Data Analysis, 29, 107–115.

12.

Rosner, B. (2000). Fundamentals of Biostatistics, third edition, PWS-Kent, New York.