Editing P-value (section)

== Usage ==
The ''p''-value is widely used in [[statistical hypothesis testing]], specifically in null hypothesis significance testing. In this method, before conducting the study, one first chooses a model (the [[null hypothesis]]) and the alpha level ''α'' (most commonly 0.05). After analyzing the data, if the ''p''-value is less than ''α'', that is taken to mean that the observed data is sufficiently inconsistent with the [[null hypothesis]] for the null hypothesis to be rejected. However, that does not prove that the null hypothesis is false. The ''p''-value does not, in itself, establish probabilities of hypotheses. Rather, it is a tool for deciding whether to reject the null hypothesis.<ref name="nature506">{{cite journal | vauthors = Nuzzo R | title = Scientific method: statistical errors | journal = Nature | volume = 506 | issue = 7487 | pages = 150–152 | date = February 2014 | pmid = 24522584 | doi = 10.1038/506150a | doi-access = free | bibcode = 2014Natur.506..150N | author1-link = Regina Nuzzo }}</ref>

=== Misuse ===
{{Main|Misuse of p-values}}
According to the ASA, there is widespread agreement that ''p''-values are often misused and misinterpreted.<ref name="ASA" /> One practice that has been particularly criticized is accepting the alternative hypothesis for any ''p''-value nominally less than 0.05 without other supporting evidence. Although ''p''-values are helpful in assessing how incompatible the data are with a specified statistical model, contextual factors must also be considered, such as "the design of a study, the quality of the measurements, the external evidence for the phenomenon under study, and the validity of assumptions that underlie the data analysis".<ref name="ASA" /> Another concern is that the ''p''-value is often misunderstood as being the probability that the null hypothesis is true.<ref name="ASA" /><ref>{{cite journal | vauthors = Colquhoun D | title = An investigation of the false discovery rate and the misinterpretation of p-values | journal = Royal Society Open Science | volume = 1 | issue = 3 | pages = 140216 | date = November 2014 | pmid = 26064558 | pmc = 4448847 | doi = 10.1098/rsos.140216 | arxiv = 1407.5296 | bibcode = 2014RSOS....140216C }}</ref>

Some statisticians have proposed abandoning ''p''-values and focusing more on other inferential statistics,<ref name="ASA" /> such as [[confidence intervals]],<ref>{{cite journal | vauthors = Lee DK | title = Alternatives to P value: confidence interval and effect size | journal = Korean Journal of Anesthesiology | volume = 69 | issue = 6 | pages = 555–562 | date = December 2016 | pmid = 27924194 | pmc = 5133225 | doi = 10.4097/kjae.2016.69.6.555 }}</ref><ref>{{cite journal | vauthors = Ranstam J | title = Why the P-value culture is bad and confidence intervals a better alternative | journal = Osteoarthritis and Cartilage | volume = 20 | issue = 8 | pages = 805–808 | date = August 2012 | pmid = 22503814 | doi = 10.1016/j.joca.2012.04.001 | doi-access = free }}</ref> [[Likelihood principle#The law of likelihood|likelihood ratios]],<ref>{{cite journal | vauthors = Perneger TV | title = Sifting the evidence. Likelihood ratios are alternatives to P values | journal = BMJ | volume = 322 | issue = 7295 | pages = 1184–1185 | date = May 2001 | pmid = 11379590 | pmc = 1120301 | doi = 10.1136/bmj.322.7295.1184 }}</ref><ref>{{cite book | vauthors = Royall R |chapter=The Likelihood Paradigm for Statistical Evidence |title = The Nature of Scientific Evidence |pages=119–152 |doi = 10.7208/chicago/9780226789583.003.0005 |language=en |year=2004 |isbn= 9780226789576 }}</ref> or [[Bayes factors]],<ref>{{cite web | vauthors = Schimmack U |title=Replacing p-values with Bayes-Factors: A Miracle Cure for the Replicability Crisis in Psychological Science |url = https://replicationindex.wordpress.com/2015/04/30/replacing-p-values-with-bayes-factors-a-miracle-cure-for-the-replicability-crisis-in-psychological-science/ |website=Replicability-Index |access-date=7 March 2017 |date=30 April 2015 }}</ref><ref>{{cite journal | vauthors = Marden JI |title = Hypothesis Testing: From p Values to Bayes Factors |journal = Journal of the American Statistical Association |date=December 2000 |volume=95|issue=452 |pages=1316–1320 |doi = 10.2307/2669779 |jstor=2669779 }}</ref><ref>{{cite journal | vauthors = Stern HS | title = A Test by Any Other Name: P Values, Bayes Factors, and Statistical Inference | journal = Multivariate Behavioral Research | volume = 51 | issue = 1 | pages = 23–29 | date = 16 February 2016 | pmid = 26881954 | pmc = 4809350 | doi = 10.1080/00273171.2015.1099032 }}</ref> but there is heated debate on the feasibility of these alternatives.<ref>{{cite journal | vauthors = Murtaugh PA | title = In defense of P values | journal = Ecology | volume = 95 | issue = 3 | pages = 611–617 | date = March 2014 | pmid = 24804441 | doi = 10.1890/13-0590.1 | bibcode = 2014Ecol...95..611M | url = https://zenodo.org/record/894459 }}</ref><ref>{{cite web |url = https://fivethirtyeight.com/features/statisticians-found-one-thing-they-can-agree-on-its-time-to-stop-misusing-p-values/ |title = Statisticians Found One Thing They Can Agree On: It's Time To Stop Misusing P-Values
| vauthors = Aschwanden C |author-link = Christie Aschwanden |website=FiveThirtyEight |date= 7 March 2016 }}</ref> Others have suggested to remove fixed significance thresholds and to interpret ''p''-values as continuous indices of the strength of evidence against the null hypothesis.<ref>{{cite journal | vauthors = Amrhein V, Korner-Nievergelt F, Roth T | title = The earth is flat (''p'' > 0.05): significance thresholds and the crisis of unreplicable research | journal = PeerJ | volume = 5 | pages = e3544 | year = 2017 | pmid = 28698825 | pmc = 5502092 | doi = 10.7717/peerj.3544 | author1-link = Valentin Amrhein | doi-access = free }}</ref><ref>{{cite journal | vauthors = Amrhein V, Greenland S | title = Remove, rather than redefine, statistical significance | journal = Nature Human Behaviour | volume = 2 | issue = 1 | pages = 4 | date = January 2018 | pmid = 30980046 | doi = 10.1038/s41562-017-0224-0 | s2cid = 46814177 | author1-link = Valentin Amrhein }}</ref> Yet others suggested to report alongside ''p''-values the prior probability of a real effect that would be required to obtain a false positive risk (i.e. the probability that there is no real effect) below a pre-specified threshold (e.g. 5%).<ref>{{cite journal | vauthors = Colquhoun D | title = The reproducibility of research and the misinterpretation of ''p''-values | journal = Royal Society Open Science | volume = 4 | issue = 12 | pages = 171085 | date = December 2017 | pmid = 29308247 | pmc = 5750014 | doi = 10.1098/rsos.171085 }}</ref>

That said, in 2019 a task force by ASA had convened to consider the use of statistical methods in scientific studies, specifically hypothesis tests and ''p''-values, and their connection to replicability.<ref name="ASA2019" /> It states that "Different measures of uncertainty can complement one another; no single measure serves all purposes", citing ''p''-value as one of these measures. They also stress that ''p''-values can provide valuable information when considering the specific value as well as when compared to some threshold. In general, it stresses that "''p''-values and significance tests, when properly applied and interpreted, increase the rigor of the conclusions drawn from data".