Editing Frequentist probability (section)

{{Short description|Interpretation of probability}}
{{Redirect|Statistical probability| the TV series episode|Statistical Probabilities}}
{{Use dmy dates|date=March 2020}}
[[Image:John Venn.jpg|thumb|upright=0.9|[[John Venn]], who provided a thorough exposition of frequentist probability in his book, ''The Logic of Chance''<ref name=Venn-1888/>]]

'''Frequentist probability''' or '''frequentism''' is an [[interpretation of probability]]; it defines an event's [[probability]] (the ''long-run probability'') as the [[limit of a sequence|limit]] of its [[Empirical probability|relative frequency]] in infinitely many [[Experiment (probability theory)|trials]].<ref>
{{cite book
 | last=Kaplan | first=D.
 | year=2014
 | title=Bayesian Statistics for the Social Sciences
 | publisher=Guilford Publications
 | series=Methodology in the Social Sciences
 | isbn=978-1-4625-1667-4
 | url=https://books.google.com/books?id=JFwKBAAAQBAJ&pg=PA4
 | access-date=2022-04-23
 | page=4
}}
</ref>
Probabilities can be found (in principle) by a repeatable objective process, as in repeated [[sampling (statistics)|sampling]] from the same [[population (statistics)|population]], and are thus ideally devoid of subjectivity. The continued use of frequentist methods in scientific inference, however, has been called into question.<ref>
{{cite journal
 |last = Goodman |first = Steven N.
 |year=1999
 |title = Toward evidence-based medical statistics. 1:&nbsp;The {{nobr|{{mvar|p}} value}} fallacy
 |journal = [[Annals of Internal Medicine]]
 |volume = 130 |issue = 12 |pages = 995–1004
 |pmid = 10383371 |s2cid = 7534212
 |doi = 10.7326/0003-4819-130-12-199906150-00008
}}
</ref><ref>
{{cite journal
 |last1 = Morey    |first1 = Richard D.    |last2 = Hoekstra |first2 = Rink
 |last3 = Rouder   |first3 = Jeffrey N.    |last4 = Lee      |first4 = Michael D.
 |last5 = Wagenmakers |first5 = Eric-Jan
 |year = 2016
 |title = The fallacy of placing confidence in confidence intervals
 |journal = Psychonomic Bulletin & Review
 |volume=23 |issue=1 |pages=103–123
 |doi = 10.3758/s13423-015-0947-8
 |pmid=26450628 |pmc=4742505
}}
</ref><ref>
{{cite journal
 |last = Matthews  |first = Robert
 |year = 2021
 |title = The {{mvar|p}}-value statement, five years on
 |journal = Significance
 |volume = 18  |issue = 2  |pages = 16–19
 |s2cid = 233534109
 |doi = 10.1111/1740-9713.01505
}}
</ref>

The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the [[Classical definition of probability|classical interpretation]]. In the classical interpretation, probability was defined in terms of the [[principle of indifference]], based on the natural symmetry of a problem, so, for example, the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. This classical interpretation stumbled at any statistical problem that has no natural symmetry for reasoning.