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In statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
, sampling error or estimation error is the error
Errors and residuals in statistics

In statistics and Optimization , statistical errors and residuals are two closely related and easily confused measures of "deviation of a sample from the mean": the error of a sample is the deviation of the sample from the population mean or actual function, while the residual of a sample is the difference between the sa...
 caused by observing a sample instead of the whole population.

An estimate of a quantity of interest, such as an average or percentage, will generally be subject to sample-to-sample variation. These variations in the possible sample values of a statistic
Statistic

A statistic is the result of applying a function to a Data set.More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution: the term is used both for the function and for the value of the function on a given sample....
 can theoretically be expressed as sampling errors, although in practice the exact sampling error is typically unknown.






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In statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
, sampling error or estimation error is the error
Errors and residuals in statistics

In statistics and Optimization , statistical errors and residuals are two closely related and easily confused measures of "deviation of a sample from the mean": the error of a sample is the deviation of the sample from the population mean or actual function, while the residual of a sample is the difference between the sa...
 caused by observing a sample instead of the whole population.

An estimate of a quantity of interest, such as an average or percentage, will generally be subject to sample-to-sample variation. These variations in the possible sample values of a statistic
Statistic

A statistic is the result of applying a function to a Data set.More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution: the term is used both for the function and for the value of the function on a given sample....
 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
Random sample

A sample is a subject chosen from a population for investigation. A random sample is one chosen by a method involving an unpredictable component....
 from the population, although the cost of doing this may be prohibitive; see sample size
Sample size

The sample size of a statistical sample is the number of observations that constitute it. It is typically denoted n, a positive integer ....
 and statistical power
Statistical power

The power of aStatistical hypothesis testing is the probability that the test will reject a false null hypothesis . As power increases, the chances of a Type II error decrease....
 for more detail. If the observation
Observation

Observation is either an activity of a living being , consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments....
s are collected from a random sample, statistical theory
Statistical theory

The theory of statistics includes a number of topics:Statistical models of the sources of data and typical problem formulation:#survey sampling from a finite population...
 provides probabilistic
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
 estimates of the likely size of the sampling error for a particular statistic
Statistic

A statistic is the result of applying a function to a Data set.More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution: the term is used both for the function and for the value of the function on a given sample....
 or estimator
Estimator

In statistics, an estimator is a function of the observable sample data that is used to estimate an unknown population parameter ; an estimate is the result from the actual application of the function to a particular Sampling_ of data....
. These are often expressed in terms of its standard error
Standard error (statistics)

The standard error of a method of measurement or estimation is the standard deviation of the sampling distribution associated with the estimation method....
.

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 error
Systematic error

Systematic errors are biases in measurement which lead the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute....
s and any random errors that are not due to sampling. Non-sampling errors are much harder to quantify than sampling error.

See also

  • Margin of error
    Margin of error

    The margin of error is a statistic expressing the amount of random sampling error in a statistical survey's results. The larger the margin of error, the less faith one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole Statistical population....
  • Propagation of error
  • Sampling (statistics)
    Sampling (statistics)

    Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference....


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