To propose a selection criteria for association rules with the same confidence. We concentrate on the association rule P [vector] Q, where P and Q are sets of distinct single item. A new criteria value is called the contrapositive proposition confidence by computing the confidence of its contrapositive rule. In our experiments, we simulated data from our synthetic data generation program. Experiments with simulated data show that in the case of distinct supports of the contrapositive rules, the increasing support of the contrapositive rule causes both contrapositive proposition confidence and confidence value increase. Finally, we analyzed the cause for the equivalent confidence rules to identify the trend of contrapositive proposition confidence for all cases.