• Source: Probability-proportional-to-size sampling

In survey methodology, probability-proportional-to-size (pps) sampling is a sampling process where each element of the population (of size N) has some (independent) chance




p

i




{\displaystyle p_{i}}

to be selected to the sample when performing one draw. This




p

i




{\displaystyle p_{i}}

is proportional to some known quantity




x

i




{\displaystyle x_{i}}

so that




p

i


=



x

i




∑

i
=
1


N



x

i







{\displaystyle p_{i}={\frac {x_{i}}{\sum _{i=1}^{N}x_{i}}}}

.: 97 
One of the cases this occurs in, as developed by Hanson and Hurwitz in 1943, 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.: 250  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 with N elements, each with their own




p

i




{\displaystyle p_{i}}

selection probability). If doing a without-replacement sampling, the schema can become more complex.: 93 




See also


Bernoulli sampling
Poisson distribution
Poisson process
Sampling design




References

Kata Kunci Pencarian:

• Variabel acak
• Statistika
• Statistika matematika
• Model generatif
• Efek pengacau
• Eksperimen semu
• Probability-proportional-to-size sampling
• Sampling (statistics)
• Sampling distribution
• Design effect
• Stratified sampling
• Sample size determination
• Effect size
• Probability distribution
• Metropolis–Hastings algorithm
• Reservoir sampling