Conditionals and conditional probability

The authors report 3 experiments in which participants were invited to judge the probability of statements of the form if p then q given frequency information about the cases pq, p not q, not pq, and not p not q (where not = not). Three hypotheses were compared: (a) that people equate the probability with that of the material conditional, 1 - P(p not q); (b) that people assign the conditional probability, P(q/p); and (c) that people assign the conjunctive probability P(pq). The experimental evidence allowed rejection of the 1st hypothesis but provided some support for the 2nd and 3rd hypotheses. Individual difference analyses showed that half of the participants used conditional probability and that most of the remaining participants used conjunctive probability as the basis of their judgments.