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 ...
, 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 ...
(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
* Independe ...
) 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 which is similar but results in a random sample size with
expectancy 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 ...
*
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
References
Sampling techniques
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