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Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. more...

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In particular, results from probability theory and statistical theory are employed to guide practice.

The sampling process consists of 5 stages:

Definition of population of concern; Specification of a sampling frame, a set of items or events that it is possible to measure; Specification of sampling method for selecting items or events from the frame; Determine the sample size; Implement the sampling plan; Sampling and data collecting; Review of sampling process;

Population definition

Successful statistical practice is based on focused problem definition. Typically, we seek to take action on some population, for example when a batch of material from production must be released to the customer or sentenced for scrap or rework.

Alternatively, we seek knowledge about the cause system of which the population is an outcome, for example when a researcher performs an experiment on rats with the intention of gaining insights into biochemistry that can be applied for the benefit of humans. In the latter case, the population of concern can be difficult to specify, as it is in the case of measuring some physical characteristic such as the electrical conductivity of copper.

However, in all cases, time spent in making the population of concern precise is often well spent, often because it raises many issues, ambiguities and questions that would otherwise have been overlooked at this stage.

Sampling frame

In the most straightforward case, such as the sentencing of a batch of material from production (acceptance sampling by lots), it is possible to identify and measure every single item in the population and to include any one of them in our sample. However, in the more general case this is not possible. There is no way to identify all rats in the set of all rats. There is no way to identify every voter at a forthcoming election (in advance of the election).

These imprecise populations are not amenable to sampling in any of the ways below and to which we could apply statistical theory.

As a remedy, we seek a sampling frame which has the property that we can identify every single element and include any in our sample. For example, in an opinion poll, possible sampling frames include:

Electoral register; Telephone directory; Shoppers in Anytown, High Street on the Monday afternoon before the election.;

The sampling frame must be representative of the population and this is a question outside the scope of statistical theory demanding the judgement of experts in the particular subject matter being studied. All the above frames omit some people who will vote at the next election and contain some people who will not. People not in the frame have no prospect of being sampled. Statistical theory tells us about the uncertainties in extrapolating from a sample to the frame. In extrapolating from frame to population its role is motivational and suggestive.

Read more at Wikipedia.org