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).

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