Editing Statistical population (section)

{{Short description|Complete set of items that share at least one property in common}}
{{For|the number of people|Population}}
In [[statistics]], a '''population''' is a [[Set (mathematics)|set]] of similar items or [[Event (probability theory)|events]] which is of interest for some question or [[Experiment (probability theory)|experiment]].<ref>{{Cite journal |last=Haberman |first=Shelby J. |date=1996 |title=Advanced Statistics |url=https://link.springer.com/book/10.1007/978-1-4757-4417-0 |journal=Springer Series in Statistics |language=en |doi=10.1007/978-1-4757-4417-0 |isbn=978-1-4419-2850-4 |issn=0172-7397|url-access=subscription }}</ref><ref>{{Cite web|title=Glossary of statistical terms: Population|website=[[Statistics.com]]|url=http://www.statistics.com/glossary&term_id=812|access-date=22 February 2016}}</ref>  A statistical population can be a group of existing objects (e.g. the set of all stars within the [[Milky Way galaxy]]) or a [[Hypothesis|hypothetical]] and potentially [[Infinite set|infinite]] group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker).<ref>{{MathWorld|Population}}</ref> 
A population with finitely many values <math>N</math> in the [[Support (mathematics)|support]]<ref>Drew, J. H., Evans, D. L., Glen, A. G., Leemis, L. M. (n.d.). Computational Probability: Algorithms and Applications in the Mathematical Sciences. Deutschland: Springer International Publishing. Page 141 https://www.google.de/books/edition/Computational_Probability/YFG7DQAAQBAJ?hl=de&gbpv=1&dq=%22population%22%20%22support%22%20of%20a%20random%20variable&pg=PA141</ref> of the population distribution is a '''finite population''' with population size <math>N</math>. A population with infinitely many values in the support is called '''infinite population'''.

A common aim of statistical analysis is to produce [[information]] about some chosen population.<ref>{{cite book | last1 = Yates | first1 = Daniel S. | last2 = Moore | first2 = David S | last3 = Starnes | first3 = Daren S. | year = 2003 | title = The Practice of Statistics | edition = 2nd | publisher = [[W. H. Freeman and Company|Freeman]] | location = New York | url = http://bcs.whfreeman.com/yates2e/ | isbn = 978-0-7167-4773-4 | url-status = dead | archive-url = https://web.archive.org/web/20050209001108/HTTP://bcs.whfreeman.com/yates2e/ | archive-date = 2005-02-09 }}</ref>
In [[statistical inference]], a subset of the population (a statistical ''[[sample (statistics)|sample]]'') is chosen to represent the population in a statistical analysis.<ref>{{Cite web|title=Glossary of statistical terms: Sample|website=[[Statistics.com]]|url=http://www.statistics.com/glossary&term_id=281|access-date=22 February 2016}}</ref> Moreover, the statistical sample must be [[Unbiased estimator|unbiased]] and [[Accuracy (statistics)|accurately]] model the population. The ratio of the size of this statistical sample to the size of the population is called a ''[[sampling fraction]]''. It is then possible to [[Estimation theory|estimate]] the ''[[population parameter]]s'' using the appropriate [[sample statistics]].<ref>{{Cite book |last1=Levy |first1=Paul S. |url=https://books.google.com/books?id=XU9ZmLe5k1IC |title=Sampling of Populations: Methods and Applications |last2=Lemeshow |first2=Stanley |date=2013-06-07 |publisher=John Wiley & Sons |isbn=978-1-118-62731-0 |language=en}}</ref>

For finite populations, sampling from the population typically removes the sampled value from the population [[urn model|due to drawing samples without replacement]]. This introduces a violation of the typical [[Independent and identically distributed random variables|independent and identically distribution assumption]] so that sampling from finite populations requires "[[finite population correction|finite population corrections]]" (which can be derived from the [[hypergeometric distribution]]). As a rough rule of thumb,<ref>Hahn, G. J., Meeker, W. Q. (2011). Statistical Intervals: A Guide for Practitioners. Deutschland: Wiley. Page 19. https://www.google.de/books/edition/Statistical_Intervals/ADGuRxqt5z4C?hl=de&gbpv=1&dq=infinite%20population&pg=PA19</ref> if the sampling fraction is below 10% of the population size, then finite population corrections can approximately be neglected.