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Sampling design

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated July 3, 2026

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

01Mathematical formulation

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

02An 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).

03Sample 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 and non-sampling error be assessed and balanced?

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

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Sources and credits

This article is adapted from the Wikipedia article “Sampling design”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Bernoulli sampling

In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample. An essential property of Bernoulli sampling is that all elements of the population have equal probability of being included in the sample.

Sampling probability

In statistics, in the theory relating to sampling from finite populations, the sampling probability of an element or member of the population, is its probability of becoming part of the sample during the drawing of a single sample. For example, in simple random sampling the probability of a particular unit i {\displaystyle i} to be selected into the sample is p i = ( N − 1 n − 1 ) ( N n ) = n N {\displaystyle p_{i}={\frac {\binom {N-1}{n-1}}{\binom {N}{n}}}={\frac {n}{N}}} where n {\displaystyle n} is the sample size and N {\displaystyle N} is the population size.

Sampling (statistics)

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. The subset, called a statistical sample, is meant to reflect the whole population, and statisticians attempt to collect samples that are representative of the population.