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.

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People who experience delusions have been found to request less information prior to making a decision than control participants on tasks that are unrelated to the theme of the delusion (Huq, Garety & Hemsley, 1988). Two studies investigated whether people with delusions have an absolute deficit in reasoning or a more specific data-gathering bias. In Expt 1, 12 people with delusions, 12 people with depression and 12 normal controls were shown the results of spinning a supposedly biased coin. The evidence provided varied in the number of heads to tails. In normal controls a high ratio of head to tails produces a high estimate that the coin is biased. In this experiment, where the evidence gathered was predetermined by the experimenter, all groups of participants were shown to reason in a similar way. Experiment 2 tested whether a difference would exist between the groups in conditions where participants were free to determine the amount of evidence seen, in contrast to when all of them viewed the same evidence. Two jars of beads in opposite but equal ratios (e.g. 85:15, 15:85) were shown to 15 people with delusions, 15 with depression and 15 normal controls. On the basis of beads being drawn one at a time, it was the participants' task to determine which jar they came from. When free to decide when they wished, people with delusions decided on the basis of less evidence than the other groups. However, as in Expt 1, the group with delusions did not differ when made to view the same amount of beads as other participants. Therefore, people with delusions have a data-gathering bias rather than a difficulty in employing the data in reasoning. This "jump to conclusions' bias generalized to a less discriminable ratio of beads (60:40), and was not a consequence of impulsiveness or memory deficit.

We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne (1989). These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects are given a third statement that qualifies the likelihood of the additional premise, then the uncertainty of the conclusions they choose is systematically related to the suggested uncertainty. Experiment 2 confirms these observations in problems that omit the additional premise and qualify the first premise directly. Experiment 3 shows that the qualifying statement also affects the perceived probability of the consequent given the antecedent of the conditional. Experiment 4 investigates the effect of suggested uncertainty on the fallacies and shows that increases in uncertainty reduce the number of certain conclusions that are chosen while affirming the consequent but have no effect on denying the antecedent. We discuss our results in terms of rule theories and mental models and conclude that the latter give the most natural account of our results.

Three experiments examined people's ability to incorporate base rate information when judging posterior probabilities. Speci®cally, we tested the (Cosmides, L., & Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgement under uncertainty. Cognition, 58, 1±73) conclusion that people's reasoning appears to follow Bayesian principles when they are presented with information in a frequency format, but not when information is presented as one case probabilities. First, we found that frequency formats were not generally associated with better performance than probability formats unless they were presented in a manner which facilitated construction of a set inclusion mental model. Second, we demonstrated that the use of frequency information may promote biases in the weighting of information. When participants are asked to express their judgements in frequency rather than probability format, they were more likely to produce the base rate as their answer, ignoring diagnostic evidence. q