# 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 ${\displaystyle P(S)}$ which gives the probability of drawing a sample ${\displaystyle S.}$

## An example of a sampling design

During Bernoulli sampling, ${\displaystyle P(S)}$ is given by

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

where for each element ${\displaystyle q}$ is the probability of being included in the sample and ${\displaystyle N_{\text{sample}}(S)}$ is the total number of elements in the sample ${\displaystyle S}$ and ${\displaystyle N_{\text{pop}}}$ 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 and non-sampling error be assessed and balanced?

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