Evaluation of evidence for sufficiency, for necessity, and for necessity-and-sufficiency

We report two experiments with 120 undergraduate subjects. The tasks presented clearly articulated hypotheses concerning necessity, sufficiency, and necessity-and-sufficiency, together with possible combinations of treatment conditions, and required subjects to judge whether, according to the hypotheses, the relevant outcomes will occur, will not occur, or might occur. The patterns of responses reveal how subjects understand the extensions of the concepts, i.e. what each hypothesis permits, requires, and excludes. Only necessity-and-sufficiency hypotheses generally led to logically adequate responses, and the most typical error for both necessity hypotheses and sufficiency hypotheses was to treat them as extensionally equivalent to necessity-and-sufficiency. This error tendency was more evident for necessity than for sufficiency hypotheses. Further, although responses to both necessity hypotheses and sufficiency hypotheses were affected by the complexity of the hypothesized conditions, responses to necessity-and-sufficiency hypotheses were not. We argue that the results are not a function of a response bias but reflect differences in the way the hypotheses are understood. Implications for the causal attribution literature are discussed.