People Misinterpret Conditional Probabilities.

Abstract

Abstract : This final report summarizes the results of the project Use of Protocol Analysis and Process Tracing Techniques to Investigate Probabilistic Inference. In probabilistic inference, people use uncertain information to change uncertain beliefs. That is, they must integrate base rate information (about what usually happens) with uncertain information about what is happening in the present. The research shows that the most recently presented information is given undue attention. Further, although subjects recognize that the base rate information in probabilistic inference word problems is relevant, they do not give it enough impact in their considerations. This is not because of their tendency to use available numerical expressions of probability as their response, but because of their inability to interpret conditional probabilities appropriately. Specifically, the subjects think that the conditional probability p (evidence/hypothesis), which is given in the word problems and which should be taken as an input to Bayes' Theorem, is p (hypothesis/ evidence), which is the output of Bayes' Theorem and which is the answer that they are asked to produce. This mistake causes subjects to produce answers that are independent of base rate information.