EvidenceFisherNeyman-PearsonLikelihood RatiosBayesianEvidence Fisher Neyman-Pearson Likelihood Ratios BayesianThe Nature of EvidenceBret [email protected] of Botany and of StatisticsUniversity of Wisconsin—MadisonBotany 940—January 31, 2006Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianDefinitions of EvidenceWhat is evidence?According to The Merriam Webster Dictionary,Evidence is PROOF or TESTIMONY; matter submitted incourt to determine the truth of alleged facts,A statistical definition according to Goodman and Royall (1988),Evidence is a property of data that makes us alter our beliefsabout how the world around us is working.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianDefinitions of EvidenceWhat is evidence?According to The Merriam Webster Dictionary,Evidence is PROOF or TESTIMONY; matter submitted incourt to determine the truth of alleged facts,A statistical definition according to Goodman and Royall (1988),Evidence is a property of data that makes us alter our beliefsabout how the world around us is working.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianDefinitions of EvidenceWhat is evidence?According to The Merriam Webster Dictionary,Evidence is PROOF or TESTIMONY; matter submitted incourt to determine the truth of alleged facts,A statistical definition according to Goodman and Royall (1988),Evidence is a property of data that makes us alter our beliefsabout how the world around us is working.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianThe Debate in Statistics over EvidenceThe debate over what statistical inference methods oughtto be used in science extends back to the 1920s.The debate continues today.However, almost all introductory courses in statistics forscientists do not discuss the debate within the statisticscommunity about the related philosophical issues.You may be surprised that the primary inferentialprocedures taught in most statistics courses is acombination of two schools of thought, and was dislikedgreatly by the founders of each school.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianThe Debate in Statistics over EvidenceThe debate over what statistical inference methods oughtto be used in science extends back to the 1920s.The debate continues today.However, almost all introductory courses in statistics forscientists do not discuss the debate within the statisticscommunity about the related philosophical issues.You may be surprised that the primary inferentialprocedures taught in most statistics courses is acombination of two schools of thought, and was dislikedgreatly by the founders of each school.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianThe Debate in Statistics over EvidenceThe debate over what statistical inference methods oughtto be used in science extends back to the 1920s.The debate continues today.However, almost all introductory courses in statistics forscientists do not discuss the debate within the statisticscommunity about the related philosophical issues.You may be surprised that the primary inferentialprocedures taught in most statistics courses is acombination of two schools of thought, and was dislikedgreatly by the founders of each school.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianTestingNow you have the chance to tell me how to carry out astatistical test....Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianSchools of ThoughtI will describe four separate schools of thought on how to dostatistical inference.1Fisher and Significance tests;2Neyman and Pearson and Hypothesis tests;3Likelihood Ratios;4Bayesian Inference.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianThe Fisher SchoolEvery experiment may be said to exist only in order togive the facts a chance of disproving the nullhypothesis. — R. A. FISHER (1937).According to Fisher, the necessary elements of asignificance test werea null hypothesis;and a test statistic with a null distribution.This results in a p-value.The p-value is interpreted as the probability of obtainingdata at least as extreme as the observed data assumingthat the null hypothesis is true.Data for which the p-value is less than an arbitrarythreshold such as 0.05 is called significant.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianThe Neyman-Pearson SchoolAccording to Neyman and Pearson, the necessaryelements of a hypothesis test werenull and alternative hypotheses;a test statistic with a null distribution;and a rejection region.The decision to accept or reject the null hypothesis in favorof the alternative hypothesis is based on whether or not thetest statistic falls into the rejection region.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianA Revealing Quote...no test based upon a theory of probability can byitself provide any valuable evidence of the truth orfalsehood of a hypothesis.But we may look at the purpose of tests from anotherviewpoint. Without hoping to know whether eachseparate hypothesis is true or false, we may search forrules to govern our behavior with regard to them, infollowing which we insure that, in the long run ofexperience, we shall not often be wrong.— J. NEYMAN AND E. PEARSON (1933)Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianDiscussion of QuoteNeyman and Pearson regarded hypothesis testing as aprocess which guaranteed a long-run error rate of rejectingfalse null hypotheses.The price of this objective method to make decisions is thatwe abandon our ability to measure evidence or judge truthin individual experiments.As the inability to make judgments in individualexperiments is clearly undesirable, standard practiceevolved to “fix” the Neyman-Pearson procedure.Fisher’s p-value was added as a measure of the strengthof evidence against the null hypothesis.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianThe Combined ApproachThe combined approach became standard practice despitethe vehement arguments against each other’s methodsfrom the founders of each school.The combined method is lauded by many as beingscientific because of its objectivity.However, the combined method is an automatic procedurefor drawing inferences that does not allow for the inclusionof judgment or knowledge of the underlying scientificprocesses.There is no mechanism to include any prior evidence.Evidence Fisher Neyman-Pearson Likelihood Ratios BayesianP-values as Measures of EvidenceOver the decades, many authors have criticized p-values andhypothesis
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