This paper proposes a method of partitioning the total chi-square statistic obtained for matched dichotomous data when the test statistic shows the existence of significant differences between experimental conditions in the response rates by subjects to a specified experimental outcome. Expressions are obtained for the calculation of the total Chi-square values obtained as a result of partitioning and the difference between total and component chi-square values among others. The proposed method enables the determination of those groups or combination of groups of experimental conditions that may be responsible for the existence of significant differences between all the experimental conditions in the response rates by subjects to a specified experimental outcome. The proposed method is illustrated with data.