Editing Statistical hypothesis test (section)

==Alternatives==
{{main|Estimation statistics}}
{{See also|Confidence interval#Statistical hypothesis testing}}

A unifying position of critics is that statistics should not lead to an accept-reject conclusion or decision, but to an estimated value with an [[interval estimate]]; this data-analysis philosophy is broadly referred to as [[estimation statistics]]. Estimation statistics can be accomplished with either frequentist<ref>{{Cite journal |last=Ho |first=Joses |last2=Tumkaya |first2=Tayfun |last3=Aryal |first3=Sameer |last4=Choi |first4=Hyungwon |last5=Claridge-Chang |first5=Adam |date=June 19, 2019 |title=Moving beyond P values: data analysis with estimation graphics |url=https://www.nature.com/articles/s41592-019-0470-3 |journal=Nature Methods |language=en |volume=16 |issue=7 |pages=565–566 |doi=10.1038/s41592-019-0470-3 |issn=1548-7091}}</ref> or Bayesian methods.<ref name="Kruschke 2012">{{cite journal|last=Kruschke|first=J K|author-link=John K. Kruschke|title=Bayesian Estimation Supersedes the T Test|journal=Journal of Experimental Psychology: General|date=July 9, 2012 |volume=142|issue=2|pages=573–603|doi=10.1037/a0029146|pmid=22774788|s2cid=5610231 |url=https://jkkweb.sitehost.iu.edu/articles/Kruschke2012JEPG.pdf}}</ref><ref name="Kruschke 2018">{{cite journal|last=Kruschke|first=J K|author-link=John K. Kruschke|title=Rejecting or Accepting Parameter Values in Bayesian Estimation|journal=Advances in Methods and Practices in Psychological Science|date=May 8, 2018|volume=1|issue=2|pages=270–280|doi=10.1177/2515245918771304|s2cid=125788648 |url=https://jkkweb.sitehost.iu.edu/articles/Kruschke2018RejectingOrAcceptingParameterValuesWithSupplement.pdf}}</ref>

Critics of significance testing have advocated basing inference less on p-values and more on confidence intervals for effect sizes for importance, prediction intervals for confidence, replications and extensions for replicability, meta-analyses for generality :.<ref name=Armstrong1>{{cite journal|author=Armstrong, J. Scott|title=Significance tests harm progress in forecasting|journal=International Journal of Forecasting|volume=23|pages=321–327|year=2007|url=http://repository.upenn.edu/cgi/viewcontent.cgi?article=1104&context=marketing_papers|doi=10.1016/j.ijforecast.2007.03.004|issue=2|citeseerx=10.1.1.343.9516|s2cid=1550979}}</ref> But none of these suggested alternatives inherently produces a decision. Lehmann said that hypothesis testing theory can be presented in terms of conclusions/decisions, probabilities, or confidence intervals: "The distinction between the ... approaches is largely one of reporting and interpretation."<ref name=Lehmann97>{{cite journal|author=E. L. Lehmann|title=Testing Statistical Hypotheses: The Story of a Book|journal=Statistical Science|volume=12|issue=1|pages=48–52|year=1997|doi=10.1214/ss/1029963261|doi-access=free}}</ref>

[[Bayesian inference]] is one proposed alternative to significance testing. (Nickerson cited 10 sources suggesting it, including Rozeboom (1960)).<ref name="nickerson"/> For example, Bayesian [[parameter estimation]] can provide rich information about the data from which researchers can draw inferences, while using uncertain [[Prior probability|priors]] that exert only minimal influence on the results when enough data is available. Psychologist [[John K. Kruschke]] has suggested Bayesian estimation as an alternative for the [[Student's t-test|''t''-test]]<ref name="Kruschke 2012" /> and has also contrasted Bayesian estimation for assessing null values with Bayesian model comparison for hypothesis testing.<ref name="Kruschke 2018" /> Two competing models/hypotheses can be compared using [[Bayes factors]].<ref>{{cite report |last=Kass |first=R. E. |title=Bayes factors and model uncertainty |year=1993|url=http://www.stat.washington.edu/research/reports/1993/tr254.pdf |publisher=Department of Statistics, University of Washington}}</ref> Bayesian methods could be criticized for requiring information that is seldom available in the cases where significance testing is most heavily used. Neither the prior probabilities nor the [[probability distribution]] of the test statistic under the alternative hypothesis are often available in the social sciences.<ref name="nickerson"/>

Advocates of a Bayesian approach sometimes claim that the goal of a researcher is most often to [[objectivity (science)|objectively]] assess the [[probability]] that a [[hypothesis]] is true based on the data they have collected.<ref>{{Cite journal | last = Rozeboom | first = William W
 | title = The fallacy of the null-hypothesis significance test
 | journal = Psychological Bulletin | volume =  57
 | issue = 5 | pages = 416–428 | year = 1960
 | url = http://stats.org.uk/statistical-inference/Rozeboom1960.pdf | doi=10.1037/h0042040| pmid = 13744252
 | citeseerx = 10.1.1.398.9002
 }} "...the proper application of statistics to scientific inference is irrevocably committed to extensive consideration of inverse [AKA Bayesian] probabilities..."  It was acknowledged, with regret, that a priori probability distributions were available "only as a subjective feel, differing from one person to the next" "in the more immediate future, at least".</ref><ref>{{Cite journal | last = Berger | first = James
 | title = The Case for Objective Bayesian Analysis
 | journal = Bayesian Analysis | volume = 1  | issue = 3 | pages = 385–402 | year = 2006 | doi=10.1214/06-ba115| doi-access = free }}  In listing the competing definitions of "objective" Bayesian analysis, "A major goal of statistics (indeed science) is to find a completely coherent objective Bayesian methodology for learning from data."  The author expressed the view that this goal "is not attainable".</ref>  Neither [[Ronald Fisher|Fisher]]'s significance testing, nor [[Neyman–Pearson lemma|Neyman–Pearson]] hypothesis testing can provide this information, and do not claim to. The probability a hypothesis is true can only be derived from use of [[Bayes' Theorem]], which was unsatisfactory to both the Fisher and Neyman–Pearson camps due to the explicit use of [[subjectivity]] in the form of the [[prior probability]].<ref name="Neyman 289–337"/><ref>{{cite journal|last=Aldrich|first=J|title=R. A. Fisher on Bayes and Bayes' theorem|journal=Bayesian Analysis|year=2008|volume=3|issue=1|pages=161–170|doi=10.1214/08-BA306|df=mdy-all|doi-access=free}}</ref> Fisher's strategy is to sidestep this with the [[p-value|''p''-value]] (an objective ''index'' based on the data alone) followed by ''inductive inference'', while Neyman–Pearson devised their approach of ''inductive behaviour''.