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In
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
, sampling errors are incurred when the statistical characteristics of a
population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. Governments typically quantify the size of the resident population within their jurisdiction by a process called a ...
are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics of the sample (often known as
estimatorsIn statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a ...

estimators
), such as means and quartiles, generally differ from the statistics of the entire population (known as
parameters A parameter (), generally, is any characteristic that can help in defining or classifying a particular system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified wh ...
). The difference between the sample statistic and population parameter is considered the sampling
error An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. In statistics Statistics is the discipline that concerns the collection, o ...
.Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. Since sampling is almost always done to estimate population parameters that are unknown, by definition exact measurement of the sampling errors will not be possible; however they can often be estimated, either by general methods such as
bootstrapping In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input. Etymology Tall boot A boot, plural boots, is a type of specific footwear Footwear refers to garments worn ...
, or by specific methods incorporating some assumptions (or guesses) regarding the true population distribution and parameters thereof.


Description


Sampling Error

The sampling error is the
error An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. In statistics Statistics is the discipline that concerns the collection, o ...
caused by observing a sample instead of the whole population. The sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter.


Effective Sampling

In
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
, a truly
random sample In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin w ...
means selecting individuals from a population with an equivalent
probability Probability is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained ...

probability
; in other words, picking individuals from a group without bias. Failing to do this correctly will result in a
sampling bias In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...
, which can dramatically increase the sample error in a
systematic Systematic may refer to: * Something related to systematics or Taxonomy (biology), taxonomy, a sub-discipline of biology * Short for systematic error * Systematic (band), an American hard rock band * Systematic Paris-Region, a French business clust ...
way. For example, attempting to measure the average height of the entire human population of the Earth, but measuring a sample only from one country, could result in a large over- or under-estimation. In reality, obtaining an unbiased sample can be difficult as many parameters (in this example, country, age, gender, and so on) may strongly bias the estimator and it must be ensured that none of these factors play a part in the selection process. Even in a perfectly non-biased sample, the sample error will still exist due to the remaining statistical component; consider that measuring only two or three individuals and taking the average would produce a wildly varying result each time. The likely size of the sampling error can generally be reduced by taking a larger sample.


Sample Size Determination

The cost of increasing a sample size may be prohibitive in reality. Since the sample error can often be estimated beforehand as a function of the sample size, various methods of
sample size determinationSample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population ...
are used to weigh the predicted accuracy of an estimator against the predicted cost of taking a larger sample.


Bootstrapping and Standard Error

As discussed, a sample statistic, such as an average or percentage, will generally be subject to sample-to-sample variation. By comparing many samples, or splitting a larger sample up into smaller ones (potentially with overlap), the spread of the resulting sample statistics can be used to estimate the
standard error The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpret ...
on the sample.


In Genetics

The term "sampling error" has also been used in a related but fundamentally different sense in the field of
genetics Genetics is a branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, ...

genetics
; for example in the or
founder effect In population genetics Population genetics is a subfield of genetics Genetics is a branch of biology concerned with the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) Though heredity had been observed ...

founder effect
, when natural disasters or migrations dramatically reduce the size of a population, resulting in a smaller population that may or may not fairly represent the original one. This is a source of
genetic drift Genetic drift (allelic drift or the Sewall Wright effect) is the change in the frequency of an existing gene In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical stru ...

genetic drift
, as certain
alleles An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is one of two, or more, forms of a given gene In biology, a gene (from ''genos'' "...Wilhelm Johannsen coined the word gene to describe the Mendelian_inheritance ...

alleles
become more or less common), and has been referred to as "sampling error", despite not being an "error" in the statistical sense.


See also

*
Margin of error The margin of error is a statistic expressing the amount of random sampling errorIn statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statis ...
*
Propagation of uncertainty In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...
* Ratio estimator *
Sampling (statistics) In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a ...


References

{{Reflist Sampling (statistics) Errors and residuals Auditing terms