The Art of Statistics: Learning from Data

by David Spiegelhalter

There are three types of populations from which a sample might be drawn, whether the data come from people, transactions, trees, or anything else. A literal population. This is an identifiable group, such as when we pick a person at random when polling. Or there may be a group of individuals who could be measured, and although we don’t actually pick one at random, we have data from volunteers. For example, we might consider the people who guessed at the number of jelly beans as a sample from the population of all maths nerds who watch YouTube videos. A virtual population. We frequently take measurements using a device, such as taking someone’s blood pressure or measuring air pollution. We know we could always take more measurements and get a slightly different answer, as you will know if you have ever taken repeat blood pressure measurements. The closeness of the multiple readings depends on the precision of the device and the stability of the circumstances – we might think of this as drawing observations from a virtual population of all the measurements that could be taken if we had enough time. A metaphorical population, when there is no larger population at all. This is an unusual concept. Here we act as if the data-point were drawn from some population at random, but it clearly is not – as with the children having heart surgery: we did not do any sampling, we have all the data, and there is no more we could collect. Think of the number of murders that occur each year, ...

Three types of population