In
sampling theory
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians atte ...
, the sampling fraction is the ratio of
sample
Sample or samples may refer to:
Base meaning
* Sample (statistics), a subset of a population – complete data set
* Sample (signal), a digital discrete sample of a continuous analog signal
* Sample (material), a specimen or small quantity of ...
size to
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 usi ...
size or, in the context of
stratified sampling
In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations.
In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each ...
, the ratio of the sample size to the size of the stratum.
The formula for the sampling fraction is
:
where ''n'' is the sample size and ''N'' is the population size. A sampling fraction value close to 1 will occur if the sample size is relatively close to the population size. When sampling from a finite population
without replacement, this may cause
dependence between individual samples. To correct for this dependence when calculating the sample
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...
, a
finite population correction (or finite population multiplier) of (N-n)/(N-1) may be used. If the sampling fraction is small, less than 0.05, then the sample variance is not appreciably affected by dependence, and the finite population correction may be ignored.
References
Sampling (statistics)
Statistical ratios
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