Statistical Evidence

NOTE EDITORE

Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.

SOMMARIO

The First PrincipleIntroductionThe Law of LikelihoodThree QuestionsTowards VerificationRelativity of EvidenceStrength of EvidenceCounterexamplesTesting Simple HypothesesComposite HypothesesAnother CounterexampleIrrelevance of the Sample SpaceThe Likelihood PrincipleEvidence and UncertaintySummary ExercisesNeyman-Pearson TheoryIntroductionNeyman-Pearson Statistical TheoryEvidential Interpretation of Results of Neyman-Pearson Decision ProceduresNeyman-Pearson Hypothesis Testing in Planning Experiments: Choosing the Sample SizeSummaryExercisesFisherian TheoryIntroductionA Method for Measuring Statistical Evidence: The Test of SignificanceThe Rationale for Significance TestsTroubles with p-ValuesRejection TrialsA Sample of InterpretationsThe Illogic of Rejection TrialsConfidence Sets from Rejection TrialsAlternative Hypothesis in ScienceSummaryParadigms for StatisticsIntroductionThree ParadigmsAn Alternative ParadigmProbabilities of Weak and Misleading Evidence: Normal Distribution MeanUnderstanding the Likelihood ParadigmEvidence about a Probability: Planning a Clinical Trial and Interpreting the ResultsSummaryExercisesResolving the Old ParadoxesIntroductionWhy is Power of Only 0.80 OK?Peeking at Data Repeated TestsTesting More than One HypothesisWhat's Wrong with One-SIded Tests?Must the Significance Level be Predetermined?And is the Strength of Evidence Limited by the Researcher's Expectations?Summary Looking at LikelihoodsIntroductionEvidence about Hazard Rates in Two FactoriesEvidence about an Odds RationA Standardized Mortality RateEvidence about a Finite Population TotalDeterminants of Plans to Attend College Evidence about the Probabilities in a 2x2x2x2 TableEvidence from a Community Intervention Study of HypertensionEffects of Sugars on Growth of Pea Sections: Analysis of VarianceSummaryExercisesNuisance ParametersIntroductionOrthogonal ParametersMarginal LikelihoodsConditional LikelihoodsEstimated LikelihoodsProfile LikelihoodsSynthetic Conditional LikelihoodsSummaryExercisesBayesian Statistical InferenceIntroductionBayesian Statistical ModelsSubjectivity in Bayesian ModelsThe Trouble with Bayesian StatisticsAre Likelihood Methods Bayesian?Objective Bayesian InferenceBayesian Integrated LikelihoodsSummary Appendix: The Paradox of the Ravens

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780412044113
• Collana: Chapman & Hall/CRC Monographs on Statistics and Applied Probability
• Dimensioni: 9.25 x 6.25 in Ø 1.00 lb
• Formato: Copertina rigida
• Pagine Arabe: 191