Post Hoc Pair-Wise Comparisons for the Chi-Square Test of Homogeneity of Proportions

This article presents a model for multiple pair-wise comparisons of selected categories (cells) of a contingency table after the chi-square test has rejected the null hypothesis of equality of population proportions. The model will determine which, if any, pair-wise proportions among the multiple cross-classifications have led to the rejection. The model is developed by considering the relationship between the chi-square distribution and a particular standardized normal.