The Art of Statistics: Learning from Data

by David Spiegelhalter

This simple exercise reveals a major distinction between two types of uncertainty: what is known as aleatory uncertainty before I flip the coin – the ‘chance’ of an unpredictable event – and epistemic uncertainty after I flip the coin – an expression of our personal ignorance about an event that is fixed but unknown. The same difference exists between a lottery ticket (where the outcome depends on chance) and a scratch card (where the outcome is already decided, but you don’t know what it is). Statistics are used when we have epistemic uncertainty about some quantity of the world. For example, we conduct a survey when we don’t know the true proportion in a population that consider themselves religious, or we run a pharmaceutical trial when we don’t know the true average effect of a drug. As we have seen, these fixed but unknown quantities are called parameters and are often given a Greek letter.

Lottery vs scratch card