Sampling design

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

Mathematical formulation

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

An example of a sampling design

During Bernoulli sampling, $P(S)$ is given by

$P(S)=q^{N_{\text{sample}}(S)}\times (1-q)^{(N_{\text{pop}}-N_{\text{sample}}(S))}$

where for each element $q$ is the probability of being included in the sample and $N_{\text{sample}}(S)$ is the total number of elements in the sample $S$ and $N_{\text{pop}}$ is the total number of elements in the population (before sampling commenced).

See also

• Statistical sampling
• Bernoulli sampling

Further reading

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