Editing P-value (section)

{{short description|Function of the observed sample results}}
{{distinguish|text=the [[P-factor]]}}
{{DISPLAYTITLE:''p''-value}}
In [[statistical hypothesis testing|null-hypothesis significance testing]], the '''''p''-value'''{{NoteTag|1=Italicisation, capitalisation and hyphenation of the term vary. For example, [[AMA style]] uses "''P'' value", [[APA style]] uses "''p'' value", and the [[American Statistical Association]] uses "''p''-value". In all cases, the "p" stands for probability.<ref>{{cite web | title = ASA House Style | url = http://magazine.amstat.org/wp-content/uploads/STATTKadmin/style%5B1%5D.pdf | work = Amstat News | publisher = American Statistical Association }}</ref>}} is the probability of obtaining test results at least as extreme as the [[Realization (probability)|result actually observed]], under the assumption that the [[null hypothesis]] is correct.<ref>{{cite web | vauthors = Aschwanden C |author-link = Christie Aschwanden| title = Not Even Scientists Can Easily Explain P-values | url = https://fivethirtyeight.com/features/not-even-scientists-can-easily-explain-p-values/ | website = FiveThirtyEight | access-date = 11 October 2019 | archive-url = https://web.archive.org/web/20190925221600/https://fivethirtyeight.com/features/not-even-scientists-can-easily-explain-p-values/ | archive-date = 25 September 2019 | date = 2015-11-24 }}</ref><ref name="ASA">{{cite journal | vauthors = Wasserstein RL, Lazar NA |date= 7 March 2016 |title = The ASA's Statement on p-Values: Context, Process, and Purpose |journal= The American Statistician |volume = 70 |issue = 2 |pages = 129–133 |doi= 10.1080/00031305.2016.1154108 |doi-access = free }}</ref> A very small ''p''-value means that such an extreme observed [[Outcome (probability)|outcome]] would be very unlikely ''under the null hypothesis''. Even though reporting ''p''-values of statistical tests is common practice in [[academic publishing|academic publications]] of many quantitative fields, misinterpretation and [[misuse of p-values]] is widespread and has been a major topic in mathematics and [[metascience]].<ref>{{cite journal | vauthors = Hubbard R, Lindsay RM |title=Why ''P'' Values Are Not a Useful Measure of Evidence in Statistical Significance Testing |journal=[[Theory & Psychology]] |year=2008 |volume=18 |issue=1 |pages=69–88 |doi=10.1177/0959354307086923 |s2cid=143487211 }}</ref><ref>{{cite journal | vauthors = Munafò MR, Nosek BA, Bishop DV, Button KS, Chambers CD, du Sert NP, Simonsohn U, Wagenmakers EJ, Ware JJ, Ioannidis JP | display-authors = 6 | title = A manifesto for reproducible science | journal = Nature Human Behaviour | volume = 1 | pages = 0021 | date = January 2017 | issue = 1 | pmid = 33954258 | pmc = 7610724 | doi = 10.1038/s41562-016-0021 | s2cid = 6326747 | doi-access = free | author-link1 = John Ioannidis }}</ref> 

In 2016, the [[American Statistical Association]] (ASA) made a formal statement that "''p''-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone" and that "a ''p''-value, or statistical significance, does not measure the size of an effect or the importance of a result" or "evidence regarding a model or hypothesis".<ref>{{Cite journal |last1=Wasserstein |first1=Ronald L. |last2=Lazar |first2=Nicole A. |date=2016-04-02 |title=The ASA Statement on p -Values: Context, Process, and Purpose |journal=The American Statistician |language=en |volume=70 |issue=2 |pages=129–133 |doi=10.1080/00031305.2016.1154108 |s2cid=124084622 |issn=0003-1305 |doi-access=free }}</ref> That said, a 2019 task force by ASA has issued a statement on statistical significance and replicability, concluding with: "''p''-values and significance tests, when properly applied and interpreted, increase the rigor of the conclusions drawn from data".<ref name="ASA2019">{{cite journal | last1=Benjamini | first1=Yoav | last2=De Veaux | first2=Richard D. | last3=Efron | first3=Bradley | last4=Evans | first4=Scott | last5=Glickman | first5=Mark | last6=Graubard | first6=Barry I. | last7=He | first7=Xuming | last8=Meng | first8=Xiao-Li | last9=Reid | first9=Nancy M. | last10=Stigler | first10=Stephen M. | last11=Vardeman | first11=Stephen B. | last12=Wikle | first12=Christopher K. | last13=Wright | first13=Tommy | last14=Young | first14=Linda J. | last15=Kafadar | first15=Karen | title=ASA President's Task Force Statement on Statistical Significance and Replicability | journal=Chance | publisher=Informa UK Limited | volume=34 | issue=4 | date=2021-10-02 | issn=0933-2480 | doi=10.1080/09332480.2021.2003631 | pages=10–11 | doi-access=free }}</ref>