Editing Statistical hypothesis test (section)

===Human sex ratio===
{{main|Human sex ratio}}
The earliest use of statistical hypothesis testing is generally credited to the question of whether male and female births are equally likely (null hypothesis), which was addressed in the 1700s by [[John Arbuthnot]] (1710),<ref>{{cite journal|author=John Arbuthnot|year=1710|title=An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes|url=http://www.york.ac.uk/depts/maths/histstat/arbuthnot.pdf|journal=[[Philosophical Transactions of the Royal Society of London]]|volume=27|issue=325–336|pages=186–190|doi=10.1098/rstl.1710.0011|doi-access=free|s2cid=186209819}}</ref> and later by [[Pierre-Simon Laplace]] (1770s).<ref>{{cite book|last1=Brian|first1=Éric|url=https://archive.org/details/descenthumansexr00bria|title=The Descent of Human Sex Ratio at Birth|last2=Jaisson|first2=Marie|publisher=Springer Science & Business Media|year=2007|isbn=978-1-4020-6036-6|pages=[https://archive.org/details/descenthumansexr00bria/page/n17 1]–25|chapter=Physico-Theology and Mathematics (1710–1794)|url-access=limited}}</ref>

Arbuthnot examined birth records in London for each of the 82 years from 1629 to 1710, and applied the [[sign test]], a simple [[non-parametric test]].<ref name="Conover1999">{{Citation|last=Conover|first=W.J.|title=Practical Nonparametric Statistics|pages=157–176|year=1999|chapter=Chapter 3.4: The Sign Test|edition=Third|publisher=Wiley|isbn=978-0-471-16068-7}}</ref><ref name="Sprent1989">{{Citation|last=Sprent|first=P.|title=Applied Nonparametric Statistical Methods|year=1989|edition=Second|publisher=Chapman & Hall|isbn=978-0-412-44980-2}}</ref><ref>{{cite book|last=Stigler|first=Stephen M.|title=The History of Statistics: The Measurement of Uncertainty Before 1900|publisher=Harvard University Press|year=1986|isbn=978-0-67440341-3|pages=[https://archive.org/details/historyofstatist00stig/page/225 225–226]}}</ref> In every year, the number of males born in London exceeded the number of females. Considering more male or more female births as equally likely, the probability of the observed outcome is 0.5<sup>82</sup>, or about 1 in 4,836,000,000,000,000,000,000,000; in modern terms, this is the ''p''-value. Arbuthnot concluded that this is too small to be due to chance and must instead be due to divine providence: "From whence it follows, that it is Art, not Chance, that governs." In modern terms, he rejected the null hypothesis of equally likely male and female births at the ''p''&nbsp;=&nbsp;1/2<sup>82</sup> significance level.

Laplace considered the statistics of almost half a million births. The statistics showed an excess of boys compared to girls.<ref name="Laplace 1778">{{cite journal|last=Laplace|first=P.|year=1778|title=Mémoire sur les probabilités|url=https://portal.getty.edu/books/bnf_bd6t54192707f|journal=Mémoires de l'Académie Royale des Sciences de Paris|pages=227–332}} Reprinted in {{cite book|last=Laplace|first=P.|title=Oeuvres complètes de Laplace|volume=9|pages=383–488|chapter=Mémoire sur les probabilités (XIX, XX)|chapter-url=http://gallica.bnf.fr/ark:/12148/bpt6k77597p/f386|publisher=Gauthier-Villars|year=1878–1912}} English translation: 
{{cite web|last=Laplace|first=P.|title=Mémoire sur les probabilités|translator-first=Richard J.|translator-last=Pulskam|date=August 21, 2010|url=http://cerebro.xu.edu/math/Sources/Laplace/memoir_probabilities.pdf
|archive-date=April 27, 2015|archive-url=https://web.archive.org/web/20150427142452/http://cerebro.xu.edu/math/Sources/Laplace/memoir_probabilities.pdf|url-status=dead}}</ref> He concluded by calculation of a ''p''-value that the excess was a real, but unexplained, effect.<ref>{{cite book|last=Stigler|first=Stephen M.|url=https://archive.org/details/historyofstatist00stig/page/134|title=The History of Statistics: The Measurement of Uncertainty before 1900|publisher=Belknap Press of Harvard University Press|year=1986|isbn=978-0-674-40340-6|location=Cambridge, Mass|page=[https://archive.org/details/historyofstatist00stig/page/134 134]}}</ref>