The Neyman-Pearson Theory As Decision Theory, And As .
The Neyman-Pearson Theory as Decision Theory, and as Inference Theory; With a Criticismof the Lindley-Savage Argument for Bayesian TheoryAuthor(s): Allan BirnbaumSource: Synthese, Vol. 36, No. 1, Foundations of Probability and Statistics, Part I (Sep., 1977),pp. 19-49Published by: SpringerStable URL: http://www.jstor.org/stable/20115212 .Accessed: 03/10/2011 17:34Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at ms.jspJSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.Springer is collaborating with JSTOR to digitize, preserve and extend access to Synthese.http://www.jstor.org
ALLANTHEBIRNBAUM*NEYMAN-PEARSONASTHEORYDECISIONAND AS INFERENCETHEORY; WITH ATHEORY,CRITICISM OF THE LINDLEY-SAVAGEARGUMENTTHEORYFOR BAYESIAN1. INTRODUCTIONANDSUMMARYof a decision, whichis basic in the theories of Neymanand Savage, has been judged obscure or inappropriatePearson, Wald,of data in scientific research, by Fisher,when applied to interpretationsTheconceptand other writers. This point is basic for most statisticalTukey,is based on applicationsof methodsderivedin thewhichpractice,Cox,theory or analogousNeyman-Pearsonleast squares and maximumlikelihood.asof such methodsapplicationsTwo contrastinginterpretationsare formulated:to 'decibehavioral,applicableof the decisionconceptsions' in a concrete literal sense as in acceptancesampling; and evidential,asato 'decisions' suchin research context, whereapplicable'reject H{the pattern and strength of statistical evidencestatisticalconcerningis of central interest. Typicalstandard practiceis charachypothesesterized as based on the confidence concept of statistical evidence, which isdefined in terms of evidentialof the 'decisions' of decisioninterpretationsconcepts are illustrated by simple formal examples within geneticofand are traced in the heory is shown to have no direct cogency as a criticism oftheory. tion2. TWOsinceit is basedona behavioral,notanof decisions.INTERPRETATIONSOFDECISIONS'decision problems are the subject of major theories of modernandhave been developed with great precision and generality onstatistics,the mathematicalside. But in the view of many applied and theoreticalStatisticalSynthese 36 (1977) 19-49. All Rights Reserved.Copyright? 1977 byD. Reidel Publishing Company, Dordrecht,Holland.
20ALLANthestatisticians,remained obscurescope andor doubtfulBIRNBAUMinterpretationin connectionin typical scientific research situations.The reason for concern here is that mostofwithdecisiontheoriesinterpretationshasof dataapplied toresearch data have been given their most systematic mathematicaljusturntification withinthe Neyman-Pearsonandthatintheory;theoryhas been given itsmost systematic mathematicalwithin thedevelopment(non-Bayesian)statisticalstatistical methodsdecisioninitiated by Wald.theorystatistical hypotheseswhich mayIn thisthe alternativebe accepted'testing procedurein the formal modelwiththe respective'decisions'of aappearingdecisionproblem.each confidenceinterval which may be determinedSimilarly,by anestimation procedureis identified with one of the 'decisions' of a model.This leads to questionsabout the scope and interpretationof the 'decision' concept which have been discussed by a number of writers: In whatto regard the results of typical scientific datasense, if any, it is appropriateonstandardmethodsof testing and estimation asbasedstatisticalanalysisdecisions?shall treat this questionin a way which is self-contained,and moresomeinrespects than previous discussions. Our intention is tosystematicWein certain respects, withoutand clarify previous discussionsortoreviewsummarizeThethem.interested reader is urgedattemptingto read or re-read such earlier discussions,those of Tukeyparticularlyandbelow.others cited(1960), Cox (1958, p. 354),complement'decide' and 'decision' were used heavily by Neymanandin the series of joint papers which initiated their theory, notablyin the preliminarypaper of 1928, and in the 1933 paper inexploratorytermsThePearsonin aproblems of testing statistical hypothesis were first yregardedproblems.of statistical deciA frequently cited ('paradigm')type of applicationwhichsiontheoriesand of the Neyman-Pearsonsampling (Neyman and Pearson,theoryis that ofindustrial1936, p. 204; Wald,1950,ormustnottoAmanufacturerdecidewhetherpp. 2-3):place alampbatch of lamps on the market, on the basis of tests on a sample from thebatch.acceptance
THENEYMAN-PEARSONof decisionThe simplest modelsour present purposes of rTHEORY21are characterizedproblemsfully, forofsch?masthebyfollowing form:Hx,H2dx,d2a Probprobabilities:?[?i Hi], Prob[d2\H2]A simple hypothesisis any probability distribution which may be definedover the range of possible outcomes(the sample space) of an experimentor observationalprocedure.For example,the lamp manufacturerin the simplemay be thesis H1exactlylamps,and in the alternativethat the batch containssimple hypothesis H2exactly10% defectives,possibly because a batch is considered definitelyif it has 4% or fewer defectives,and is considered definitely bad if itgoodhas 10% or moredefectives.For a given batch,withholddi:his possible decisions are:the batch from the market;andthe batch on the market.d2:placeThe performanceof any decision function (that is any rule for using dataon a sample of lamps from the batch to arrive at a decision d\ or d2) iserror probcharacterizedand H2, by the respectivefully, under Hiaand ? definedin the schema.of a decision(An exampleis the rule: Place the batch on the market if and only if fewerare found in a random sample of 25 lamps.)than 3 defectivesabilitiesfunction hereConsiderthe interpretationof the decisions dx and d2 which appear inthe schema, in its applicationto the problem of the lamp manufacturer.Whenthe manufacturerheplaces a batch of lamps on the market,ansoorIfonemoreaction.he doesafter ons, aspossiblein favor of that action.the terms'decision'in a simpleandin ourexample,'action'referthen he hasto the behaviortakenofathedirect and literal way. We shall use the terminterpretation of the decision concept to refer to any comparaof a 'decision' appearingin ably simple, direct, and literal interpretationformal model of a decision problem.1manufacturerbehavioral
22ALLANBIRNBAUMin thebehavioralinterpretation must be criticized and rejected,aandwhensuchof manyschemaandstatisticians,investigatorsmodel are applied in a typical context of scientific research in connectionTheviewwithof data analysis. Convenientexamples may bewhichhavethestudies,general scientific ly characstandard methodsdrawnfrom geneticof extendingterizes a speciesor strain in classical Mendeliangenetics.2anConsiderinvestigator who judges that his linkage studies providethat two genetic loci lie on the same chromosomevery strong evidencereversethat future studies could conceivablyusualthe(withappreciationahis judgement);and who reports his conclusion,withsummarytogetherof it, basedinterpretationthedeterminedNeyman-Pearsonby applyingin a research1955, or Smith, 1953, pp. 180-3),of his dataand hisin part on use of a testtheory (as in Morton,journal.favoring the scientific hypothesis of linkage correspondsin some way to a 'decision' dx in a schema like that above, where now Hxno linkage. It is the nature ofis the statistical hypothesischaracterizingHis conclusionthis correspondence3.which we SIONTHEORYis often described(in ingsuch asHx (e.g. Neymanwhether or not to 'reject a statistical hypothesis'and Pearson,1928, p. 1; 1933, p. 291). This suggests the interpretationmostof testing as decisionwriters who formulate problemsgiven byTheof testingTHEto examinehypothesesandproblems:dx:reject Hxd2:do not reject//!.to the question: Whatis theleads immediatelythis e,'reject Hxinterpretationthat linkage was present?tigator of our example who concludedButif the geneticist uses typical terminologysuch as 'reject Hx,understandof no linkage,' neither he nor his colleagueshypothesisEventhethat
THETHEORYNEYMAN-PEARSON23sense which could behe ismaking a decision in any literal and unqualifiedawith that of thebehavioralclosely comparableinterpretationgivenin the example above.decisionlamp manufacturer'sterm 'reject' expresses here an interpretationthe decision-likeRather,of the statistical evidence, as giving appreciable but limited support to oneofThis evidentialstatistical hypotheses.of the alternativeinterpretationresults is in principle based on a complete schema of thethe experimentalindicated above, even when this is only implicit.In this essentialsuggested above betweenrespect, the identificationand isoftheschema is inadequate,and the single element dx'reject Hxkindmisleadingstatisticald\*:whenevidencetaken out of the contextare adequately(reject HxforH2,a, ?)(reject H2forHx,a, ?),of the schema.representedby symbolsSuch cases oflikeandd2 :each of whichof the complete schema which servesof statisticalfor the interpretationframe of referencecarries an indicationas the conceptualevidence here.The symbols d* and d2 represent in prototypetypical interpretationsin scientificand reports of data treated by standard statistical methodsresearchcontexts.interpretation of the decision conceptof models of decision problems; and we shallto refer to such applicationsto refer to suchuse the term confidence concept of statistical evidenceWeshall use the term evidentialof statistical evidence.interpretationsIn the view of this writer and some others, although typical applicationsin research are of the kind we haveof standard statistical methodsand interpretaillustrated, the central concepts guiding such applicationstions (for which we have introduced the terms in italics above) have notbeen defined within any precise systematic theory of statistical inference.these concepts exist and play their basic roles largely implicitlyRather,of stanand interpretationsin guiding applicationsand unsystematically,of new statistical methods.and in guiding the developmentdard methods,Weevenshall not offer any precise theoretical account of these concepts, norclaim that such an account can be given. Our aims are limited to
24ALLANthe existenceillustratingBIRNBAUMand widescope of the confidenceconcept,andclarifying some of its features.seems to be in part a primitiveThe alevidenceassociatedtheaboveconceptkind,which may(Conf):be expressedin the followingformulation:prototypicis not plausible unless it findsevidenceas against Hx with small probability(a)when Hx is true, and with much larger probability(1-/3) whenH2 is true.Aconcept of statistical'strong evidence forH2conThe following are simple examples of the texttheoftheceptThey iclinkageinterpretationsarein the first person becausestatistical evidenceexpressedthey illustrate in simple cases the writer's own practice and thinking concerningas an independentevidence, based in part on some experiencesomenew nasMendelianwell(Birnbaum,1972),theory and data analysisstatisticaland analysis of generalstatistical practiceandthese examples, and their interpretationsin followare typical of widespreadstatistical thought and practice,extensiveobservationthinking.In my viewing sections,that they are given here withwith the qualificationexplicit expression which is unusual. The interestedmake an independentjudgment about this.a degree and style ofreader will of courseto the usage of Savagefirst person form is somewhatanalogousdecisionisfrom the standpoint(1954) whose Bayesiantheorydevelopedof a generic rational person'you'. In a following section these examplesThewill be referredto in the courseof a critical discussiontions of Savage's and Wald'sdecisiontheories.Symbols of the form dx and d2 introduced aboveof some assumpare usedto presentthe examples.(1) I interpret(reject Hxas strongstatisticalfor H2,evidence(reject H2for Hi0.06,for H20.06,0.08)as against Hi.0.08)SimilarlyI interpret
THE NEYMAN-PEARSONas strong statisticalevidenceTHEORY25as against H2.for Hx(2) I interpret(reject Hxas conclusivefor H2,as against Hx. Here the zero value of theof the first kind indicates that the observationalresultsevidenceerror probabilityare incompatible0, 0.2)for H2with Hx.(3) I interpret(reject Hxfor H2,as very strong statistical0.01,evidence0.2)for H2as against Hx.(4) I interpret(reject H2for Hx,0, 0.2)as weakstatistical evidence forHx as against H2. Here the relatively large0.2 of the error probabilityof the second kind suggests relativethisevidenceagainst H2.skepticism concerningvalue(5) I interpret(reject Hxas worthlessfor H2,statistical0.5, 0.5)evidence.It is no morerelevantto the statisticalis the toss of a fair coin, since the errorhypotheses(0.5, 0.5) also represent amodel of a toss of a fair coin, withprobabilitiesone side labeled 'reject Hx and the other 'reject H2.If such a case aroseconsideredthanour comments wouldlead us to judgetesttoleast thebe worthless.adopted,The distinctionbetweenthe two interpretationsin practice,epitomized(as BernardNortonhas pointedordinary usages:3behavioral:'decideto' act in a certain way,out)the experiment,ofor at'decision' mayby contrastingbethe
26ALLANBIRNBAUMandevidential:that' a certain hypothesissupported by strong evidence.'decide-the differentConcerningtrue or wellis true or isidentification(pragmatist)with'decideto act asof 'decide that Aisis true or wellif Asupported'itwill be clear from discussion above and below that we rejectsupported',and regard conclusionsand statisticalany such simple identification,as having autonomousstatus and value.evidenceThewereconsiderationsthoughlessan inference we are 'deciding'a statementto makebe arguedthat in makingand that, therefore,the word decisiontype about the populationsprovidedtoo narrowly,the study of statisticaldecisionsembracesthat of inferences.interpretedis notprecedingformally by Cox(1958,emphasizedp. 354) as follows:clearlyitmightcertainpointhereis that oneofthe mainof statisticalgeneralproblemscan usefullybe madeand exactlywhattypes of statementdecidingdecisionstatisticaltheory, on the otheralreadythe possiblehand,inferenceof aTheconsistsinthey mean.are consideredInwhatdecisionsasspecified.betweenofthe two interpretationsanalysis of the distinctionsin'decisions' of decisionisthosesectionsbelowtheoryprovidedwhich treat certain assumptionsunderlying Savage's and Wald's decisionto regard evidentialtheories. In particular,it is shown that if one wishesFurtherthestatementsfor example,represented,(reject Hxdf:as 'decisions'forH2,0.05,in a formal modelby0.05)of a decisionthen certain basicproblem,areof statistical decisiontheoriesassumptionsincompatible with certainstatements.and meaningsof those evidentialbasic properties4. ENTIFICAMONGSEVERALSUPPORTOFCONCLUSIONSa conclusionin a scientificreached(1960) has emphasized,ourastwo loci As Tukeylinked,requires(a) statisticalhypothesesnot onlyevidenceof sufficientof interest.strengthconcerningthe statistical
THENEYMAN-PEARSONTHEORY27the investigator(or community of investigators) mustmodel, which(b) the adequacy of the mathematical-statisticalas the conceptualfor the interpretationframe of referenceIn additionto representstatisticalthe researchsituationjudgeservesof thein relevantevidence,respects; andand evidence of a concluwith other knowledge(c) the compatibilitysion that may be supported by statistical evidence provided by theevidencecurrent(for example,strong statisticalinvestigationnorepresentingagainst the statistical hypotheseslinkage).4prevent us from regarding a scientificimportant considerationsas being determinedin any simple or exclusive way by theconclusionstatistical evidence which may support it.The Neyman-Pearsontheory introduced a kind of formal symmetryof problemsof testing statistical hypotheses,into the formulationbyTheserequiring expliciterror probabilitiesthecomplementof alternativestatistical hypothesesandspecificationourof the second kind (e.g. H2 and ? inschema) toa in ourtraditionalandHxspecification(e.g. justschema).But inmanydefiniteearly and modern applications of statistical tests, there is ain the status of the alternativelack of symmetrystatisticalin the status orrelated to a lack of ecorrespondinghypothesespossiblesions. For exampleinmany cases one scientific hypothesisis regarded ashypotheseson the basis of currentor at least as acceptableknowledge,or plausible, unless and until sufficiently clear and strong evidence againstit appears. Clearly such considerationslie outside the scope of mathematand statisticalical statistical modelsin the sense discussedevidenceestablishedandabove, but rather in the scope of the scientific backgroundknowledgejudgment referred to in (b) and (c) above.In traditionalformulationsof testing problems which precededtheandtowhichcontinueinappear prominentlyNeyman-Pearsontheoryitmay be morestatistics, in various applicationsapplied and theoreticalor less plausibleto supposethat there is implicit, though not explicit,errorto alternativereferenceand correspondingstatistical abilities,implicit partinterpretationof a test statistic;and possiblyto supposealso that there is
28ALLANBIRNBAUMto possible alternativescientific hypothimplicit if not explicit referenceeses or possibletosuchconclusionscorrespondingimplicit statisticalnotdoesextend to tests inoftheThescopepresent paperhypotheses.toextentformulationsthethatsuch traditionalexceptthey may beanas being interpreted at least in principle withapplicationregarded into some alternativestatistiimplicit, if not explicit, referenceplausibleterms as 'standardcal hypotheses.Suchandstatistical methods''standard methodsthis paper, mustconfusion.as used throughoutof testing statistical hypotheses',to avoidbe understood with this important qualification5. THETHEORETICALNEYMAN-PEARSONAMBIGUITYOFTHETHEORYin its mathematicalThe Neyman-Pearsonform astheory is interpretablea special restricted part of general statistical decisiontheory, as we haveto the extraindicated above and will elaboratefurther below. Asand theory, which relate that mathematicalinterpretationsone may say that there are two Neyman-Pearsonform to applications,theories:mathematicalOneis based on behavioralhas beenelaboratedbehavioras mentionedof the decision concept, andinterpretationstermsinofhis concept of inductiveby Neymanabove. It is difficult or (in the view of the presentto discover or devise clear plausibleand some others) impossiblein typical scientific research situationsof this interpretationexamplesare applied. (The interested reader will make anwhere standard methodswriterindependentjudgement about this, and may wish to consider the extenof Neyman himself to the interpretationsive and important contributionsof scientific data in several research areas.)structure ofThe second theory which makes use of the mathematicalonisbasedevidentialof thethe Neyman-Pearsontheoryinterpretationsin that theory, and has as its central concept what we have'decisions'- acalled the confidenceconcept of statistical evidenceconcept whoseessentialrole is f standard methods,but a concept which has notinterpretationsin any systematicbeen elaboratedtheory of statistical inference.and
THEevenSinceNEYMAN-PEARSONthe existenceTHEORYofthis importantof the mathematical29distinctiontwobetweenstructure of the Neymaninterpretationsnornotisvery widelyclearly appreciated, much of thetheoryin the statisticalfoundliterature is notandmisunderstandingobscurityand obscuritysurprising. A simple step toward limiting this confusiontheoreticalPearsonwouldbe to makeconsistentview wheneveruse of terms whichkeepsuch as 'confidencethe distinctioninand 'evidential'ornecessary,concept'and to avoid unqualified use, when ambiguityinterpretation;and confusioncould result, of such standard terms as: the NeymanPearson'objectivist',theory (or approach, or school); and 'frequentist','behavioral''orthodox','classical', 'standard', and the like.seems to have someIn the many applications where each interpretationthe two interpretations mayrole, a sharp theoretical distinction betweenhave particular value in helping to clarify the purpose or purposes of theFor example,application and guide the adoption of appropriate methods.new knowledgeabout a genetic linkage may have immediate value as aof a particularbasis for the genetic counselingfamily. Here one can intwoofmodelsdecisionconsiderproblems as having some scopeprinciplein the literal'decisions'situation, one havinginterpretedsense (for example'do not have another child' or 'do'); and theother model having 'decisions' with evidential(for ticalpossiblehypothesesple concerningin the samebehavioralsions about geneticif variousEvenlinkage).details ofthe two modelsshould(forcorrespondexample the two decision functions adopted might, though they need not,in kind of interpretation),thein form though differentbe identicalpurposes and problems considered would be distinct, and hence properlyand treated by distinct theoretical concepts.characterizedIn other applicationswherethere is a problem of decisionsin thesense, one may seek conclusions(or strong statistical eviaasfordecisionsIn such cases, if somebasisdence)makingjudiciously.to be an accurate modelformal model of a decision problem is consideredbehavioralin the relevant respects, one mayas such is at(or statistical ationdecision problem and accurate model. On the other hand,that any formal model of the decision problem has sufficientofthe real situationconsiderconclusionsargue that tobest superfluofthe actualif it is not clearrealismto be
30ALLANBIRNBAUMor statisticalof new nce) may naturallysoughtmakingThe second exampleof the 1936 paper of Neymanand Pearsoninvolves explicit considerationof both conclusionsand related decisions,but is discussed so briefly and incompletelythat I am unable to interpret itthen developmentapplied,from the standpoint of the preceding paragraphs. No other examples ofwere discussedin the joint papers. Thus the joint papersapplicationsancontain no discussionofin which a scientific conclusionapplicationwasthe sole or primaryS. Pearsonconclusionsconclusions6. THEof an investigation. Variousdiscuss applications1937,1947,1962)object(notablyand decisionssoughtCONCEPTS(in the behavioralsense)as a basis for making decisions.OFTESTSOFNEYMANANDDECISIONSANDwritings of E.inwhich bothare of interest, withIN THE1933PAPERPEARSONThe1933 paper of Neymanand Pearson begins (pp. 141-2) with explicitabout the meaningsof concepts and methodsof testing.The authors discuss "What is the precise meaningof the words'anefficient test of a hypothesis?'There may be several meanings."concernin the precedingliteraconcept of an 'efficient test' had appearedof testing, but the term 'efficient' had beenintroducedintomathematicalstatistics by Fisher in connection with his theory of estimation in the early 1920's.NotureFisher'spower and conceptualtheory, with its striking mathematicalandinstoodtheofthe efforts of Neymanobscurities,depthsbackgroundato initiateand Pearsoncomparablysystematictheory of tests, as theyto their exploratoryindicated in the introductionpaper of 1928. Theirin an exact form (rather than by asymptoticplan to treat testing problemscaseforoftheapproximationslarge samples, as Fisher had done) wouldsome purelyeliminatetechnicaland thereby facilitatecomplicationsclarity concerningof tests.conceptssuch as 'efficient' or its analoguesin a theorythe side of applications,there was as much need for a systematictheory of tests as there had been for a moresystematictheory oftoinalternativeestimation,guide investigatorschoosing amongpossibleOn
THENEYMAN-PEARSONTHEORY31sensein problemsof increasing complexity,wherethe commonhad guidedtraditionalandfaltered.testing practice(NeymanPearson began their 1930 paper with discussion of Romanovsky's1928paper which had given new distributiontheory for several statistics for atestswhichstandardminingTheonout the open basic problem of "deterone to use in any given case.")appropriateaof 'an efficient test' which is cleardefinitionsuppliedtesting problem,which is the most1933 paperthe mathematicalpointingside, and is neutral in relation to the contrastingand evidentialof 'decision' discussed above.interpretationsAn efficient test is defined as one in which the error probabilities(suchas a and ? in our schema) are minimized(jointly in some appropriateevidential or behavioralof 'decisions' aresense). Whetherinterpretationsbehavioralseem to be aof error probabilitieswouldanNoof'efficienttest'has, even now,clearly appropriategoal.conceptbeen proposedin terms of the earlier tradition of formulatingtestingto error probabilitiesunder alternative(without referenceproblemsIn this sense one may say that it appearsto have beenhypotheses).in view,such minimizationformu'necessary' to make some change in the traditional mathematicalas a basis for introducinga concept of anlation of testing problems,'efficient test' which might guide applicationsand theoretical developments.In any case, Neymanand Pearson met a problem of broad theoreticaland practical scope by changing some of the terms of the problem,ashaveindoneall problem areas.6original investigatorsfrequentlysome changein the mathematicalformulationof testingAlthoughseems to have been necessary,in the sense just indicated, theproblemsof the Neyman-Pearsoninnovationtheoreticaltheory, the behavioralwasnotofsense: ntialhas been associated with typical applicationsofinterpretationtests in scientific research investigationsin all periods of their use (whichdates from 1710), without apparentthe mathematicaling 1933 whendiscontinuityduring the years followstructure of the Neyman-Pearsontheory became widely accepted as the new or improved mathematicalbasis for the theory of tests.This observation'What roles or functions wassuggests the questions:the behavioraltointendedserve?' and 'What functions hasinterpretationit served?' The joint papers suggest less than clear answers, while later
32ALLANBIRNBAUMand Pearsonclearersuggestseparatelyfor the respective authors.the 1933 paper begins, as we have noted, with concern aboutAlthoughof testing, it discussesthe meaningsof conceptsonly a eaningmeaning of 'a test' (or apapers writtenby Neymananswers which are differentis not discussedsuch as 'reject Hi)to nd evidentialbehavioralBehavioral:"Suchwhen".a ruleinterpretationswith regardsystematicallybut clear and contrastingappear:as to whethercase Htells us nothingin a particularis true. "or false when". "But.if we behave"rejected."then in the long run we shall reject H whenit is true not more,"accepted"to such a rule,accordingsay, than oncein a hundredthe frequencyconcerningEvidential:1. In the "methodtimes, and in addition we may have" analogousof rejectionsof H whenit is false."(p. 142.). in commonuse . If F wereof attackveryas an indicationbe consideredthat the hypothesis,H,generallyfalse, and vice versa."(p. 141.)2. "Let us now for a momentconsiderthe form in nTheexperience.of confidence;the followingWemayacceptor we may decideor wemayrejectto remain in doubt.position must be recognized.it is true; ifwe accept H0, we may be acceptingis true." (p. 146.)really some alternative Htattitudeauthors'towarda hypothesisBut whateverassurancesmall,wasthisprobablyare madeinwithvaryingconclusionisIf wereject H0, we may reject itit whenit is false, that is to say,is not madeinterpretationsfrom p. 142 gives approvinglytheevidentialquite clear. The precedingquotationa test in the new mathematicalofbehavioralinterpretationas against the traditional "method of attack . in commonformulation,use" (tradiBut theformulation, with evidentialinterpretation).from p. 146 (in a discussion not linked by the authors with thatquotationof a testthe evidentialof pp. 141-2) describes approvinglyinterpretationformulation.in the new mathematicaltional mathematicalisthis apparent discrepancyAn interpretation which would reconcileaastonotinintendedto regard the behavioralapplyinterpretationsensein any direct, literal, or concretesituation of scientific researchof thewith an evidentialincompatibleinterpretationasituation in a'decisions' in question; but rather intended to apply in suchway which is heuristic or hypothetical,serving to explain the inevitablywith the error probabilities,associatedabstracttheoretical meaning
THE NEYMAN-PEARSON THEORY AS DECISION THEORY, AND AS INFERENCE THEORY; WITH A CRITICISM OF THE LINDLEY-SAVAGE ARGUMENT FOR BAYESIAN THEORY 1. INTRODUCTION AND SUMMARY The concept of a decision, which is basic in the theories of Neyman Pearson, W
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Neyman's theory of confidence interval estimation was designed, as . the investigator has merely indeterminate knowledge of "prior" chances for the unknown quantities.' However, this criticism of Bayesian . In "In Defense of the Neyman-Pearson Theory of Confidence Inter- vals", D. Mayo ex
His favorite Polish poets were Adam Mickiewicz and Julian Tuwim. He often quoted them at social gatherings. I would probably not remember those early talks about Jerzy Neyman if I would not have taken an advanced statistics course. It was that course in which one day I learned about the Neyman-Pearson lemma and its importance in statistics.
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