The Development of a Correction Method for Ensuring a Continuity Value of The Chi-square Test with a Small Expected Cell Frequency


Kajita Matchima Jumlong Vongprasert Nipaporn Chutiman


     Using the chi-square test with a small expected cell frequency is an important problem in generally survey and experimental research because it cannot control type-I error led to amiss conclude the result in our work. The purposes of this work were first to develop a correction method for ensuring a continuity value of the chi-square test and secondly to compare its efficiency with other methods, namely; Yate’s correction and William’s correction by using simulation data. The comparisons were made with the following condition; two significant levels of 0.01 and 0.05, six contingency table sizes (2x2, 2x3, 2x4, 3x3, 3x4 and 4x4), a small expected cell frequency up to 30% of the total cell and a sample size between 5 to 10 times that of the total cell.
     We found that type I error in chi-square test with developed correction and significant level is similar values (can control type I error). The similarity values are higher than chi-square test without correction, Yate’s correction and William’s correction. Larger sample sizes resulted is better control type I error at both levels of significance. For the contingency table size 2x2 to 4x4, chi-square test with developed correction can control type I error better than chi-square test without correction and William’s correction at both 0.01 and 0.05 significant levels. The correction method used to control the type-I error was obtained using a developed correction in every condition.


Freund, J. E. (2004). Modern Elementary Statistics. New Jersey: Pearson Education, Inc.

Mcdonald, J. H. (2014). Handbook of Biological Statistics. Maryland: Sparky House Publishing.

Yates, F. (1934). Contingency tables involving small numbers and the χ 2 test. Supplement to the Journal of the Royal Statistical Society, 1(2), 217-235.

Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2013). Introduction to Probability and Statistics. Australia: Boosk/Cole, Cengage Learning.

Gu, X., & Lee, J. J. (2010). A simulation study for comparing testing statistics in response-adaptive randomization. BMC medical research methodology,
10, 48.

Research Articles


How to Cite
MATCHIMA, Kajita; VONGPRASERT, Jumlong; CHUTIMAN, Nipaporn. The Development of a Correction Method for Ensuring a Continuity Value of The Chi-square Test with a Small Expected Cell Frequency. Naresuan University Journal: Science and Technology (NUJST), [S.l.], v. 26, n. 1, p. 98-105, mar. 2018. ISSN 2539-553X. Available at: <>. Date accessed: 26 feb. 2024.