title: Sampling design
text: # 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.
  
  