In statistics, sampling errors are incurred when the statistical characteristics of a population 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 estimators), such as means and quartiles, generally differ from the statistics of the entire population (known as parameters). The difference between the sample statistic and population parameter is considered the sampling error.[1] 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, or by specific methods incorporating some assumptions (or guesses) regarding the true population distribution and parameters thereof.
The sampling error is the error caused by observing a sample instead of the whole population.[1] 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.[2]
Effective Sampling
In statistics, a truly random sample means selecting individuals from a population with an equivalent probability; in other words, picking individuals from a group without bias. Failing to do this correctly will result in a sampling bias, which can dramatically increase the sample error in a systematic 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.[3]
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 determination are used to weigh the predicted accuracy of an estimator against the predicted cost of taking a larger sample.
As discussed, a sample statistic, such as an average or percentage, will generally be subject to sample-to-sample variation.[1] 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 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; for example in the bottleneck effect or 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, as certain alleles become more or less common), and has been referred to as "sampling error",[4] despite not being an "error" in the statistical sense.
Wikimedia Commons has media related to Sampling error.
^ abcSarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, ISBN0-387-40620-4
^Burns, N.; Grove, S. K. (2009). The Practice of Nursing Research: Appraisal, Synthesis, and Generation of Evidence (6th ed.). St. Louis, MO: Saunders Elsevier. ISBN978-1-4557-0736-2.
^Scheuren, Fritz (2005). "What is a Margin of Error?". (PDF). Washington, D.C.: American Statistical Association. Archived from the original (PDF) on 2013-03-12. Retrieved 2008-01-08.
^Campbell, Neil A.; Reece, Jane B. (2002). Biology. Benjamin Cummings. pp. 450–451. ISBN0-536-68045-0.
April 21, 2023
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In statistics sampling errors are incurred when the statistical characteristics of a population 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 estimators such as means and quartiles generally differ from the statistics of the entire population known as parameters The difference between the sample statistic and population parameter is considered the sampling error 1 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 or by specific methods incorporating some assumptions or guesses regarding the true population distribution and parameters thereof Contents 1 Description 1 1 Sampling Error 1 2 Effective Sampling 1 3 Sample Size Determination 1 4 Bootstrapping and Standard Error 2 In Genetics 3 See also 4 ReferencesDescription EditSampling Error Edit The sampling error is the error caused by observing a sample instead of the whole population 1 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 2 Effective Sampling Edit In statistics a truly random sample means selecting individuals from a population with an equivalent probability in other words picking individuals from a group without bias Failing to do this correctly will result in a sampling bias which can dramatically increase the sample error in a systematic 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 3 Sample Size Determination Edit 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 determination are used to weigh the predicted accuracy of an estimator against the predicted cost of taking a larger sample Bootstrapping and Standard Error Edit Main article Bootstrapping statistics As discussed a sample statistic such as an average or percentage will generally be subject to sample to sample variation 1 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 on the sample In Genetics EditThe term sampling error has also been used in a related but fundamentally different sense in the field of genetics for example in the bottleneck effect or 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 as certain alleles become more or less common and has been referred to as sampling error 4 despite not being an error in the statistical sense See also EditMargin of error Propagation of uncertainty Ratio estimator Sampling statistics References Edit Wikimedia Commons has media related to Sampling error a b c Sarndal Swenson and Wretman 1992 Model Assisted Survey Sampling Springer Verlag ISBN 0 387 40620 4 Burns N Grove S K 2009 The Practice of Nursing Research Appraisal Synthesis and Generation of Evidence 6th ed St Louis MO Saunders Elsevier ISBN 978 1 4557 0736 2 Scheuren Fritz 2005 What is a Margin of Error What is a Survey PDF Washington D C American Statistical Association Archived from the original PDF on 2013 03 12 Retrieved 2008 01 08 Campbell Neil A Reece Jane B 2002 Biology Benjamin Cummings pp 450 451 ISBN 0 536 68045 0 Retrieved from https en wikipedia org w index php title Sampling error amp oldid 1076115580, wikipedia, wiki, book, books, library,
