Parameters

Data are usually collected to provide information about an underlying population distribution. Estimating the full shape of this underlying distribution would be ideal but there is limited information in the sample data so we usually need to restrict attention to a few specific numerical characteristics of the population distribution — parameters.

We usually focus on one or two parameters of the underlying population.

Estimating parameters

After identifying the population parameters that are of most interest — for example the mean of the population distribution, µ, or the proportion of values in a category of a categorical population, π, — we can usually estimate these values using the corresponding summary statistics from the sample. This is called inference about the parameter.

The rest of this chapter deals with estimation of a population parameter from a sample.

Examples

In the following examples, the population mean and standard deviation summarise important aspects of the population distribution. The sample mean and standard deviation provide estimates of these values.