In
survey methodology
Survey methodology is "the study of survey methods".
As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey da ...
, probability-proportional-to-size (pps) sampling is a
sampling process where each element of the
population
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 ...
(of size ''N'') has some (
independent
Independent or Independents may refer to:
Arts, entertainment, and media Artist groups
* Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s
* Independ ...
) chance
to be selected to the sample when performing one draw. This
is proportional to some known quantity
so that
.
One of the cases this occurs in, as developed by Hanson and Hurwitz in 1943,
[Hansen, Morris H., and William N. Hurwitz. "On the theory of sampling from finite populations." The Annals of Mathematical Statistics 14.4 (1943): 333-362.] is when we have several clusters of units, each with a different (known upfront) number of units, then each cluster can be selected with a probability that is proportional to the number of units inside it.
[Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Nashville, TN: John Wiley & Sons. ] So, for example, if we have 3 clusters with 10, 20 and 30 units each, then the chance of selecting the first cluster will be 1/6, the second would be 1/3, and the third cluster will be 1/2.
The pps sampling results in a fixed sample size ''n'' (as opposed to
Poisson sampling
In survey methodology, Poisson sampling (sometimes denoted as ''PO sampling'') is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sampl ...
which is similar but results in a random sample size with
expectancy Expectancy theory (or expectancy theory of motivation) proposes that an individual will behave or act in a certain way because they are motivated to select a specific behavior over others due to what they expect the result of that selected behavior ...
of ''n''). When selecting items with replacement the selection procedure is to just draw one item at a time (like getting ''n'' draws from a
multinomial distribution
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a ''k''-sided dice rolled ''n'' times. For ''n'' independent trials each of w ...
with ''N'' elements, each with their own
selection probability). If doing a without-replacement sampling, the schema can become more complex.
See also
*
Bernoulli sampling In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample. An essential p ...
*
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known co ...
*
Poisson process
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
*
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 ...
References
Sampling techniques
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