Most data sets contain one or more measurements from each of a collection of individuals (or other units). The measurements of interest usually vary in ways that cannot be explained in terms of other measurements from the individuals.

This unexplained variability can be modelled by considering the data to be a random sample from some underlying population.

Modelling unexplained variability in this way allows us to better assess features in the data. In particular, we can use it to assess the stability (and hence accuracy) of summary statistics, such as a sample mean or sample proportion.