Psychological patterns in predicting disjunction and conjunction of clinical symptoms

An account of subjective probability judgment for joint events: Conjunctive and disjunctive

Probability judgment is a vital part of many aspects of everyday life. In the present paper, we present a new theory of the way in which individuals produce probability estimates for joint events: conjunctive and disjunctive. We propose that a majority of individuals produce conjunctive (disjunctive) estimates by making a quasi-random adjustment, positive or negative, from the less (more) likely component probability with the other component playing no obvious role. In two studies, we produce evidence supporting propositions that follow from our theory. First, the component probabilities do appear to play the distinct roles we propose in determining the joint event probabilities. Second, contrary to probability theory and other accounts of probability judgment, we show that the conjunctive-less likely probability difference is unrelated to the more likely disjunctive probability difference (in normative theory these quantities are identical). In conclusion, while violating the norms of probability judgment, we argue that estimates produced in the manner we propose will be close enough to the normative values especially given the changing nature of the external environment and the incomplete nature of available information.

Conditional Probabilities, Potential Surprise, and the Conjunction Fallacy

Tversky and Kahneman (1983) found that a relationship of positive conditional dependence between the components of a conjunction of two events increases the prevalence of the conjunction fallacy. Consistent with this finding, the results of two experiments reveal that dependence leads to higher estimates for the conjunctive probability and a higher incidence of the fallacy. However, contrary to the theoretical account proposed by Tversky and Kahneman, the actual magnitude of the conditional relationship does not directly affect the extent of the fallacy; all that is necessary is for a positive conditional relationship to exist. The pattern of results obtained can be accounted for in terms of Shackle's (1969) “potential surprise” theory of subjective probability. Surprise theory predicts that the impact of the conditional event will be at its maximum where the relationship is a negative one. Tversky and Kahneman's model, on the other hand, predicts the maximum effect when the relationship is positive. In all 12 scenarios tested, multiple regression analysis revealed that the standardized beta weight associated with the conditional event was greater when the relationship was a negative one. Thus the outcome was supportive of the surprise model rather than Tversky and Kahneman's account.

The Directionality of Verbal Probability Expressions: Effects on Decisions, Predictions, and Probabilistic Reasoning

Verbal phrases denoting uncertainty are of two kinds: positive, suggesting the occurrence of a target outcome, and negative, drawing attention to its nonoccurrence (Teigen & Brun, 1995). This directionality is correlated with, but not identical to, high and low p values. Choice of phrase will in turn influence predictions and decisions. A treatment described as having "some possibility" of success will be recommended, as opposed to when it is described as "quite uncertain," even if the probability of cure referred to by these two expressions is judged to be the same (Experiment 1). Individuals who formulate their chances of achieving a successful outcome in positive terms are supposed to make different decisions than individuals who use equivalent, but negatively formulated, phrases (Experiments 2 and 3). Finally, negative phrases lead to fewer conjunction errors in probabilistic reasoning than do positive phrases (Experiment 4). For instance, a combination of 2 "uncertain" outcomes is readily seen to be "very uncertain." But positive phrases lead to fewer disjunction errors than do negative phrases. Thus verbal probabilistic phrases differ from numerical probabilities not primarily by being more "vague," but by suggesting more clearly the kind of inferences that should be drawn. Copyright 1999 Academic Press.