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Reasoning about conditional probabilities: the evidence for the frequentist hypothesis has relied on flawed comparisons

Gigerenzer and Hoffrage (1995) and Cosmides and Tooby (1996) proposed a frequentist hypothesis that claims that although people rarely make judgements about conditional probabilities that concord with the normative standards of Bayes's theorem, such judgements can be elicited when a problem is presented in terms of frequencies rather than probabilities. These two articles together reported 10 experiments with 89 problem versions in support of their prediction, with people consistently solving frequentist-formatted problems more frequently than probabilist-formatted problems. The results of two experiments reported here, however, show that their results can be explained as resulting from two experimental confounds that have to do with the presence vs. absence of a response format and with the use of whole numbers vs. decimal fractions. In Experiment 1 we found that the frequentist problems were solved only when presented with a response format that can encourage accurate guesses, and in Experiment 2 we found that frequentist- and probabilist- formatted problems were solved equally often when presented with the response format and with whole numbers rather than with decimal fractions. The results are discussed in terms of their negative implications for the frequentist hypothesis.

frequentist hypothesis; conditional probabilities; Bayes's theorem; frequentist- and probabilist- formatted problems


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