Sampling design

In the theory of finite population sampling, a sampling design specifies for every possible sample its probability of being drawn.

Mathematically, a sampling design is denoted by the function P(S) which gives the probability of drawing a sample S.

Examples of sampling designs

During Bernoulli sampling, P(S) is given by

$P(S)=q^{N}$

where for each element q is the probability of being included in the sample and N is the total number of elements in the population.

During Poisson sampling, P(S) is given by

$P(S)=\prod _{i=1}^{N}\pi _{i}$

where π_i represents the probability of including the i-th element of the population in the sample during the drawing of a single sample and N represents the total number of elements in the population.

Further reading

• SARNDAL, C.-E., SWENSSON, B., AND WRETMAN, J. 1992. Model Assisted Survey Sampling. Springer-Verlag, New York, NY.