# Sampling Design

Sampling design is a mathematical function that gives us the probability of any given sample being drawn.

Since sampling is the inherent foundation of nearly every research project, the study of sampling design is a crucial part of statistics, and is often a one or two semester course. It involves not only learning how to derive the probability functions which describe a given sampling method but also understanding how to design a best-fit sampling method for a real life situation.

## Examples of Sampling Design

Sampling design can be very simple or very complex. In the simplest, one stage sample design where there is no explicit stratification and a member of the population is chosen at random, each unit has the probability

n/N

of being in the sample, where n is the total number of units to be sampled, and N is number of units in the total population.

• systematic sample: where all members of a population are listed in order and samples are chosen at defined intervals
• stratified sample: where the population is first divided into strata and then samples are randomly selected from the strata (for instance, divide a population between men and women, then randomly select a given number of men and a given number of women)
• cluster strata: where a population is divided into clusters and first clusters are randomly selected, then random members of the selected clusters are sampled. (for instance, first randomly select a number of classes, then, from the class lists of those classes, randomly sample a number of students)

Each of these have their own sampling design function. The sampling method chosen will depend on the situation and priorities of the researcher. Sometimes, non-probability based sampling methods will be chosen; for instance, convenience sampling, where the sample is simply those easily reached and observed. Unlike systematic, stratified, or cluster sampling, these types of sampling cannot be easily described by a sampling design function.

## References

Mohadjer, Krenzke, & Van de Kerckhove. Technical Report. Chapter 4: Sampling Design. Survey of Adult Skills (PIAAC), OECD.

Maastricht University. Sampling Design, Course Catalogue. Retrieved from https://www.maastrichtuniversity.nl/meta/325263/sampling-design on September 3, 2018.

Raymo, Jim. Sample Design. Sociology 357 Class Notes.

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