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Ambiguity, the certainty illusion, and the natural frequency approach to reasoning with inverse probabilities


  • John Fountain
  • Philip Gunby


People have difficulty reasoning with diagnostic information in uncertain situations, especially when an understanding and calculation of inverse conditional probabilities (Bayes theorem) is required. While natural frequency representations of inference tasks improve matters, they suffer from three problems: (1) calculation errors persist with a majority of subjects; (2) the representation suffers from an illusion of certainty that ignores ambiguity; and (3) the costs of repeatedly applying the representation to deal with imprecision and ambiguity in inference are prohibitive. We describe a user friendly, interactive, graphical software tool for calculating, visualizing, and communicating accurate inferences about uncertain states when relevant diagnostic test information (sensitivity, specificity, and base rate) is both imperfect and ambiguous in its application to a specific patient. The software is free, open-source, and runs on all popular PC operating systems (Windows, Mac, Linux).

Suggested Citation

  • John Fountain & Philip Gunby, 2011. "Ambiguity, the certainty illusion, and the natural frequency approach to reasoning with inverse probabilities," New Zealand Economic Papers, Taylor & Francis Journals, vol. 45(1-2), pages 195-207.
  • Handle: RePEc:taf:nzecpp:v:45:y:2011:i:1-2:p:195-207 DOI: 10.1080/00779954.2011.556079

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    References listed on IDEAS

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