Risk and Decision Making: The “Logic” of Probability
- Manfred Borovcnik
Risk-communication is a hot topic, whether it concerns the benefits and harms of screening or the chance of a catastrophic earthquake. It is challenging to explain both unpredictability and uncertain knowledge to the public, and yet these are also essential elements in education in probability and statistics. I shall argue that current approaches in communicating risk and uncertainty can contribute substantially to educational practice. In particular, Gigerenzer’s recommendation for ‘natural frequencies’ – whole-number outcomes starting from a defined population of cases can be adapted to teaching probability based on a natural sequence of stages: empirical multiple narratives from experimentation represented as 2-way tables and frequency trees, to expected outcomes in multiple future experiments, and finally to probability trees. Issues of relative and absolute risk continually arise in topical stories, and representations that make these transparent are as relevant in the classroom as in the news. Any predictions of expected outcomes will depend on assumptions, and in practice P-values are used (and often misused) to inform the public about evidence against hypotheses, say regarding the Higgs Boson or Paul the Psychic Octopus. This Fisherian idea neatly starts to integrate probability and observation, with likelihood ratios arising as the natural measure for deciding between competing hypotheses. Examples of public communication, and classroom materials, will be used to illustrate these ideas.