# Sampling design

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In the theory of finite [population](/source/Population_(biology)) [sampling](/source/Sampling_(statistics)), a **sampling design** specifies for every possible [sample](/source/Sample_(statistics)) its [probability](/source/Probability) of being drawn.

## Mathematical formulation

[Mathematically](/source/Mathematics), a sampling design is denoted by the function P ( S ) {\displaystyle P(S)} which gives the probability of drawing a sample S . {\displaystyle S.}

## An example of a sampling design

During [Bernoulli sampling](/source/Bernoulli_sampling), P ( S ) {\displaystyle P(S)} is given by

- P ( S ) = q N sample ( S ) × ( 1 − q ) ( N pop − N sample ( S ) ) {\displaystyle P(S)=q^{N_{\text{sample}}(S)}\times (1-q)^{(N_{\text{pop}}-N_{\text{sample}}(S))}}

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

## Sample design for managerial research

In business research, companies must often generate samples of customers, clients, employees, and so forth to gather their opinions. Sample design is also a critical component of marketing research and employee research for many organizations. During sample design, firms must answer questions such as:

- What is the relevant population, sampling frame, and sampling unit?

- What is the appropriate margin of error that should be achieved?

- How should [sampling error](/source/Sampling_error) and non-sampling error be assessed and balanced?

These issues require very careful consideration, and good commentaries are provided in several sources.[1][2]

## See also

- [Bernoulli sampling](/source/Bernoulli_sampling)

- [Sampling probability](/source/Sampling_probability)

- [Sampling (statistics)](/source/Sampling_(statistics))

## References

1. **[^](#cite_ref-1)** Salant, Priscilla, I. Dillman, and A. Don. How to conduct your own survey. No. 300.723 S3.. 1994.

1. **[^](#cite_ref-2)** Hansen, Morris H., William N. Hurwitz, and William G. Madow. "Sample Survey Methods and Theory." (1953).

## Further reading

- Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, [ISBN](/source/ISBN_(identifier)) [0-387-40620-4](https://en.wikipedia.org/wiki/Special:BookSources/0-387-40620-4)

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