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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Sampling error</span></span>

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<p>In <a href="Statistics" title="Statistics">statistics</a>, <b>sampling errors</b> are incurred when the statistical characteristics of a <a href="Statistical_population" title="Statistical population">population</a> are estimated from a subset, or <a href="Sample_(statistics)" class="mw-redirect" title="Sample (statistics)">sample</a>, of that population. Since the sample does not include all members of the population, statistics of the sample (often known as <a href="Estimator" title="Estimator">estimators</a>), such as means and quartiles, generally differ from the statistics of the entire population (known as <a href="Statistical_parameter" title="Statistical parameter">parameters</a>). The difference between the sample statistic and population parameter is considered the sampling <a href="Errors_and_residuals" title="Errors and residuals">error</a>.<sup id="cite_ref-Sarndal_1-0" class="reference"><a href="#cite_note-Sarndal-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> 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.

</p><p>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 <a href="Bootstrapping_(statistics)" title="Bootstrapping (statistics)">bootstrapping</a>, or by specific methods incorporating some assumptions (or guesses) regarding the true population distribution and parameters thereof.

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<div class="mw-heading mw-heading2"><h2 id="Description">Description</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Sampling_Error">Sampling Error</h3></div>

<p>The sampling error is the <a href="Errors_and_residuals_in_statistics" class="mw-redirect" title="Errors and residuals in statistics">error</a> caused by observing a sample instead of the whole population.<sup id="cite_ref-Sarndal_1-1" class="reference"><a href="#cite_note-Sarndal-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-Burns_&_Grove,_2009_2-0" class="reference"><a href="#cite_note-Burns_&_Grove,_2009-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Effective_Sampling">Effective Sampling</h3></div>

<p>In <a href="Statistics" title="Statistics">statistics</a>, a truly <a href="Random_sample" class="mw-redirect" title="Random sample">random sample</a> means selecting individuals from a population with an equivalent <a href="Probability" title="Probability">probability</a>; in other words, picking individuals from a group without bias. Failing to do this correctly will result in a <a href="Sampling_bias" title="Sampling bias">sampling bias</a>, which can dramatically increase the sample error in a <a href="Systematic_errors" class="mw-redirect" title="Systematic errors">systematic</a> 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.

</p><p>Even in a perfect 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.<sup id="cite_ref-Scheuren_3-0" class="reference"><a href="#cite_note-Scheuren-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Sample_Size_Determination">Sample Size Determination</h3></div>

<p>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 <a href="Sample_size_determination" title="Sample size determination">sample size determination</a> are used to weigh the predicted accuracy of an estimator against the predicted cost of taking a larger sample.

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<div class="mw-heading mw-heading3"><h3 id="Bootstrapping_and_Standard_Error">Bootstrapping and Standard Error</h3></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrapping (statistics)</a></div>

<p>As discussed, a sample statistic, such as an average or percentage, will generally be subject to sample-to-sample variation.<sup id="cite_ref-Sarndal_1-2" class="reference"><a href="#cite_note-Sarndal-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> 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 <a href="Standard_error" title="Standard error">standard error</a> on the sample.

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<div class="mw-heading mw-heading2"><h2 id="In_Genetics">In Genetics</h2></div>

<p>The term "sampling error" has also been used in a related but fundamentally different sense in the field of <a href="Genetics" title="Genetics">genetics</a>; for example in the <a href="Population_bottleneck" title="Population bottleneck">bottleneck effect</a> or <a href="Founder_effect" title="Founder effect">founder effect</a>, 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 <a href="Genetic_drift" title="Genetic drift">genetic drift</a>, as certain <a href="Alleles" class="mw-redirect" title="Alleles">alleles</a> become more or less common), and has been referred to as "sampling error",<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> despite not being an "error" in the statistical sense.

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<ul><li><a href="Margin_of_error" title="Margin of error">Margin of error</a></li>

<li><a href="Propagation_of_uncertainty" title="Propagation of uncertainty">Propagation of uncertainty</a></li>

<li><a href="Ratio_estimator" title="Ratio estimator">Ratio estimator</a></li>

<li><a href="Sampling_(statistics)" title="Sampling (statistics)">Sampling (statistics)</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Sampling_error" class="extiw external" title="commons:Category:Sampling error">Sampling error</a></span>.</div></div>

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<li id="cite_note-Sarndal-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Sarndal_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Sarndal_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Sarndal_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, <style data-mw-deduplicate="TemplateStyles:r1238218222">

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</style><a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-387-40620-4</bdi></span>

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<li id="cite_note-Burns_&_Grove,_2009-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Burns_&_Grove,_2009_2-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFBurnsGrove2009" class="citation book cs1">Burns, N.; Grove, S. K. (2009). <i>The Practice of Nursing Research: Appraisal, Synthesis, and Generation of Evidence</i> (6th ed.). St. Louis, MO: Saunders Elsevier. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4557-0736-2</bdi>.</cite></span>

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<li id="cite_note-Scheuren-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Scheuren_3-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFScheuren2005" class="citation book cs1">Scheuren, Fritz (2005). "What is a Margin of Error?". <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130312125540/http://www.amstat.org/sections/srms/pamphlet.pdf"><i>What is a Survey?</i></a> <span class="cs1-format">(PDF)</span>. Washington, D.C.: American Statistical Association. Archived from <a rel="nofollow" class="external text" href="http://www.amstat.org/sections/srms/pamphlet.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2013-03-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-01-08</span></span>.</cite></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFCampbellReece2002" class="citation book cs1">Campbell, Neil A.; Reece, Jane B. (2002). <i>Biology</i>. Benjamin Cummings. pp. <span class="nowrap">450–</span>451. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-536-68045-0</bdi>.</cite></span>

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