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

Abstract

     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.