Editing Sampling (statistics) (section)

==History==
Random sampling by using lots is an old idea, mentioned several times in the Bible. In 1786, Pierre Simon [[Laplace]] estimated the population of France by using a sample, along with [[ratio estimator]]. He also computed probabilistic estimates of the error. These were not expressed as modern [[confidence interval]]s but as the sample size that would be needed to achieve a particular upper bound on the sampling error with probability 1000/1001. His estimates used [[Bayes' theorem]] with a uniform [[prior probability]] and assumed that his sample was random. [[Alexander Ivanovich Chuprov]] introduced sample surveys to [[Imperial Russia]] in the 1870s.<ref>{{Cite journal |author1-link=Eugene Seneta |last=Seneta |first=E. |date=1985 |title=A Sketch of the History of Survey Sampling in Russia |url=https://www.jstor.org/stable/2981944 |journal=Journal of the Royal Statistical Society. Series A (General) |volume=148 |issue=2 |pages=118–125 |doi=10.2307/2981944|jstor=2981944 }}</ref>

In the US, the 1936 ''[[Literary Digest]]'' prediction of a Republican win in the [[U.S. presidential election, 1936|presidential election]] went badly awry, due to severe [[bias]] [https://www.wsj.com/articles/SB115974322285279370]. More than two million people responded to the study with their names obtained through magazine subscription lists and telephone directories. It was not appreciated that these lists were heavily biased towards Republicans and the resulting sample, though very large, was deeply flawed.<ref>David S. Moore and George P. McCabe. "''Introduction to the Practice of Statistics''".</ref><ref>{{Cite book |last1 = Freedman |first1=David |author-link1=David Freedman (statistician)| last2 = Pisani | first2 = Robert | last3 = Purves | first3 = Roger |title=Statistics | url=http://www.wwnorton.com/college/titles/math/stat4/comment.htm%7C <!-- place = [[New York City|New York]] |publisher = [[W. W. Norton & Company|Norton]] | year = 2007 | edition = 4th | isbn = 0-393-92972-8 -->}}</ref>

[[Elections in Singapore]] have adopted this practice since the [[2015 Singaporean general election|2015 election]], also known as the sample counts, whereas according to the [[Elections Department Singapore|Elections Department]] (ELD), their country's election commission, sample counts help reduce speculation and misinformation, while helping election officials to check against the election result for that electoral division. While the reported sample counts yield a fairly accurate indicative result with a 4% [[margin of error]] at a 95% [[confidence interval]], ELD reminded the public that sample counts are separate from official results, and only the [[returning officer]] will declare the official results once vote counting is complete.<ref>{{cite web |title=SAMPLE COUNT - Elections Department Singapore |url=https://www.eld.gov.sg/mediarelease/SampleCount_Generic.pdf |access-date=3 September 2023}}</ref><ref>{{cite web |last1=Ho |first1=Timothy |title=Presidential Election 2023: How Accurate Will The Sample Count Be Tonight? |url=https://dollarsandsense.sg/presidential-election-2023-accurate-will-sample-count-tonight/#:~:text=The%20sample%20count%20will%20give,margin%20of%20the%20sample%20count. |website=DollarsAndSense.sg |access-date=3 September 2023 |date=1 September 2023}}</ref>