So I’ve been following and intro stats class for a project of mine, and came across this curious definition:
- A statistic is number that describes a sample
- A parameter is number that describes a population
I got to wondering what a population really is, and couldn’t find the dividing line between the sample and the population. If you polled everyone in a state, would that data represent population data or sample data? It becomes clear that the population is a theoretical concept only, made-up to make a sampling distribution make sense.
More and more I find the Bayesian perspective demonstrably clearer. Sure, a statistic is a property of a sample of data. A parameter is always, however, a property of the model. There is never a dividing line here, and the limits of inference come down to the limits of the model, and the limits of the data in constraining the parameters of the model. There is no population.