In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, in the theory relating to
sampling from finite
populations
Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
, the sampling probability (also known as inclusion probability) of an
element or member of the population, is its
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
of becoming part of the sample during the drawing of a single sample. For example, in
simple random sampling
In statistics, a simple random sample (or SRS) is a subset of individuals (a sample (statistics), sample) chosen from a larger Set (mathematics), set (a statistical population, population) in which a subset of individuals are chosen randomization, ...
the probability of a particular unit
to be selected into the sample is
:
where
is the sample size and
is the population size.
Each element of the population may have a different probability of being included in the sample. The inclusion probability is also termed the "first-order inclusion probability" to distinguish it from the "second-order inclusion probability", i.e. the probability of including a pair of elements. Generally, the first-order inclusion probability of the ''i''th element of the population is denoted by the symbol π
''i'' and the second-order inclusion probability that a pair consisting of the ''i''th and ''j''th element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by π
''ij''.
See also
*
Sampling bias
In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human fa ...
*
Sampling design
Sampling may refer to:
*Sampling (signal processing), converting a continuous signal into a discrete signal
* Sampling (graphics), converting continuous colors into discrete color components
*Sampling (music), the reuse of a sound recording in ano ...
*
Sampling frame In statistics, a sampling frame is the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, and may include individuals, households or institutions.
Importance of the sampling fra ...
References
{{Reflist
Sampling (statistics)