Application of Pearson’s X^2 Test of Independence with Small Expected Cell Frequencies. Abacus

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Mathematical Association of Nigeria


Pearson’s X^2 is re-examined within the context of small expected cell frequency (e_ij< 5), for the Pearson’s X^2 statistic to satisfy the asymptotic approximation to Chi-square distribution. This paper proposes scalar multiplier theta > 0, such that theta(e_ij') ≥ 5, where e_ij' is the smallest expected cell count in the contingency table under consideration. The product of the sample size ‘n’ and ‘theta ’ results in each cell count becoming (theta)n_ij, which does not cause any change in the cell probabilities. Thus the assumption of independence is thereby satisfied. This approach guarantees the safe application of Pearson’s X^2 for test of independence under small expected cell counts with the degrees of freedom also multiplied by theta.



Goodness-of-fit, chi-square, scalar multiplier, small expected cell frequency, independence hypothesis


Sanni, O. O. M., Abidoye, A. O. and Ikoba, N. A. (2016). Application of Pearson’s X2 Test of Independence with Small Expected Cell Frequencies. Abacus, The Journal of Mathematical Association of Nigeria, 43 (2); 193-199,