In the theory of finite population

Population

A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...

 sampling

Sampling (statistics)

In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....

, a sampling design specifies for every possible sample

Sample (statistics)

In statistics, a sample is a subset of a population. Typically, the population is very large, making a census or a complete enumeration of all the values in the population impractical or impossible. The sample represents a subset of manageable size...

 its probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 of being drawn.

Mathematically

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a sampling design is denoted by the function which gives the probability of drawing a sample

An example of a sampling design

During Bernoulli sampling

Bernoulli sampling

In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population that is sampled is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample during the drawing of a single sample...

, is given by


where for each element is the probability of being included in the sample and is the total number of elements in the sample and is the total number of elements in the population (before sampling commenced).

Further reading

• Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, ISBN 0-387-40620-4