Anomalies in the Judgment of Statistical Association: Fallacies Based on Unidirectional Independence, Shifting Dependence, and Conjunction

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An experiment was performed in which subjects, trained in basic probability, were asked to judge the likelihood of one trait (A), e.g., intelligence, given another (B), e.g., submissiveness, relative to p(A) or p(A|B) They also ranked p(A), p(B), and p(A∩B) for relative size. A substantial proportion of judgments violated the laws of probability by endorsing relationships that implied independence was a function of the direction of association, i.e., p(A|B) = p(A) [or p(A|B̄)], but p(B|A)≠p(B) [or p(B|A)]. Further, many subjects endorsed relationships that implied independence in one direction changed to dependence with change in statistical comparison, i.e., p(A|B) = p(A) [or p(A|B̄)], but p(A|B)≠p(A|B̄) [or p(A)]. These violations of the laws of probability were correlated with each other. A tendency to perceive a positive relationship between two traits correlated with a tendency to commit the fallacy of conjunction. It was concluded that individuals made probabilistic judgments which did not incorporate understanding of probabilistic relationships between events. Also the departures from correct probabilistic reasoning could not be accounted for very well by confusion of causal explanations with diagnosticity of the traits.