Sampling error

(statistics) That portion of the difference between the value of a statistic derived from observations and the value that it is supposed to estimate; attributed to the fact that samples represent only a portion of a population.

A statistical error to which an analyst exposes a model simply because he or she is working with sample data rather than population or census data. Using sample data presents the risk that results found in an analysis do not represent the results that would be obtained from using data involving the entire population from which the sample was derived.

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The use of a sample relative to an entire population is often necessary for practical and/or monetary reasons. Although there are likely to be some differences between sample analysis results and population analysis results, the degree to which these can differ is not expected to be substantial.

Methods of reducing sampling error include increasing the sample size and ensuring that the sample adequately represents the entire population.

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Difference between the value obtained by sampling and the value that would have been obtained if the entire population had been investigated. The auditor is concerned that sampling error is minimized.

Any mistake in drawing a sample that keeps it from being unrepresentative; selection procedures that are biased; error introduced when a group is described on the basis of an unrepresentative sample.

Differences that occur between the true value of a characteristic of a population and the value estimated from a sample. To reduce the error as far as possible, random sampling is used.

In statistics, sampling error or estimation error is the error caused by observing a sample instead of the whole population^[1].

An estimate of a quantity of interest, such as an average or percentage, will generally be subject to sample-to-sample variation.^[1] These variations in the possible sample values of a statistic can theoretically be expressed as sampling errors, although in practice the exact sampling error is typically unknown. Sampling error also refers more broadly to this phenomenon of random sampling variation.

The likely size of the sampling error can generally be controlled by taking a large enough random sample from the population,^[2] although the cost of doing this may be prohibitive; see sample size and statistical power for more detail. If the observations are collected from a random sample, statistical theory provides probabilistic estimates of the likely size of the sampling error for a particular statistic or estimator. These are often expressed in terms of its standard error.

Sampling error can be contrasted with non-sampling error. Non-sampling error is a catch-all term for the deviations from the true value that are not a function of the sample chosen, including various systematic errors and any random errors that are not due to sampling. Non-sampling errors are much harder to quantify than sampling error.^[2]

See also

• Margin of error
• Propagation of error
• Sampling (statistics)

References

1. ^ ^{a b} Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, ISBN 0-387-40620-4
2. ^ ^{a b} Fritz Scheuren (2005). "What is a Margin of Error?", Chapter 10, in "What is a Survey?", American Statistical Association, Washington, D.C. Accessed 2008-01-08.

External links

• NIST: Selecting Sample Sizes

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