Each of some promising theories explains human performances on the indicative Wason selection task. For example, participants usually select the 5 case, in the selection task with the conditional “if an E, then a not-5”. This tendency of the selection was explained by the heuristic-analytic theory, which is one of the dual-processing theories, that people are likely to regard a matching case as relevant to the truth of the conditional in the heuristic process (Evans, 1998). However, because a positive concept constructs a smaller set than its negative one does (a rarity assumption), it is more effective to get information on the truth of the conditional in a positive set than in a negative set. Thus the optimal data selection theories can also explain the effect. Yama (2001) found that the so-called matching bias was an amalgam of two different cognitive components, namely, relevance judgment by matching and the optimal data selection process. It was examined if the dual-processing theories captured the optimal data selection process with some evidences and concluded that, although the heuristic-analytic theory should be revised, the implication of the evidences could be discussed within the framework of the dual-processing theories.