Intended for healthcare professionals

Education And Debate

Simple tools for understanding risks: from innumeracy to insight

BMJ 2003; 327 doi: (Published 25 September 2003) Cite this as: BMJ 2003;327:741
  1. Gerd Gigerenzer, director (,
  2. Adrian Edwards, reader2
  1. 1Centre for Adaptive Behaviour and Cognition, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany
  2. 2Primary Care Group, Swansea Clinical School, University of Wales Swansea, Swansea SA2 8PP
  1. Correspondence to: G Gigerenzer

    Bad presentation of medical statistics such as the risks associated with a particular intervention can lead to patients making poor decisions on treatment. Particularly confusing are single event probabilities, conditional probabilities (such as sensitivity and specificity), and relative risks. How can doctors improve the presentation of statistical information so that patients can make well informed decisions?

    The science fiction writer H G Wells predicted that in modern technological societies statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. How far have we got, a hundred or so years later? A glance at the literature shows a shocking lack of statistical understanding of the outcomes of modern technologies, from standard screening tests for HIV infection to DNA evidence. For instance, doctors with an average of 14 years of professional experience were asked to imagine using the Haemoccult test to screen for colorectal cancer.1 2 The prevalence of cancer was 0.3%, the sensitivity of the test was 50%, and the false positive rate was 3%. The doctors were asked: what is the probability that someone who tests positive actually has colorectal cancer? The correct answer is about 5%. However, the doctors' answers ranged from 1% to 99%, with about half of them estimating the probability as 50% (the sensitivity) or 47% (sensitivity minus false positive rate). If patients knew about this degree of variability and statistical innumeracy they would be justly alarmed.

    Statistical innumeracy is often attributed to problems inside our minds. We disagree: the problem is not simply internal but lies in the external representation of information, and hence a solution exists. Every piece of statistical information needs a representation–that is, a form. Some forms tend to cloud minds, while others foster insight. We know of no medical institution that teaches …

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