Statistical Evidence

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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.

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The First Principle Introduction The Law of Likelihood Three Questions Towards Verification Relativity of Evidence Strength of Evidence Counterexamples Testing Simple Hypotheses Composite Hypotheses Another Counterexample Irrelevance of the Sample Space The Likelihood Principle Evidence and Uncertainty Summary Exercises Neyman-Pearson Theory Introduction Neyman-Pearson Statistical Theory Evidential Interpretation of Results of Neyman-Pearson Decision Procedures Neyman-Pearson Hypothesis Testing in Planning Experiments: Choosing the Sample Size Summary Exercises Fisherian Theory Introduction A Method for Measuring Statistical Evidence: The Test of Significance The Rationale for Significance Tests Troubles with p-Values Rejection Trials A Sample of Interpretations The Illogic of Rejection Trials Confidence Sets from Rejection Trials Alternative Hypothesis in Science Summary Paradigms for Statistics Introduction Three Paradigms An Alternative Paradigm Probabilities of Weak and Misleading Evidence: Normal Distribution Mean Understanding the Likelihood Paradigm Evidence about a Probability: Planning a Clinical Trial and Interpreting the Results Summary Exercises Resolving the Old Paradoxes Introduction Why is Power of Only 0.80 OK? Peeking at Data Repeated Tests Testing More than One Hypothesis What'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 Likelihoods Introduction Evidence about Hazard Rates in Two Factories Evidence about an Odds Ration A Standardized Mortality Rate Evidence about a Finite Population Total Determinants of Plans to Attend College Evidence about the Probabilities in a 2x2x2x2 Table Evidence from a Community Intervention Study of Hypertension Effects of Sugars on Growth of Pea Sections: Analysis of Variance Summary Exercises Nuisance Parameters Introduction Orthogonal Parameters Marginal Likelihoods Conditional Likelihoods Estimated Likelihoods Profile Likelihoods Synthetic Conditional Likelihoods Summary Exercises Bayesian Statistical Inference Introduction Bayesian Statistical Models Subjectivity in Bayesian Models The Trouble with Bayesian Statistics Are Likelihood Methods Bayesian? Objective Bayesian Inference Bayesian Integrated Likelihoods Summary Appendix: The Paradox of the Ravens

..."provides the explicit concept of evidence missing from the other approaches." -Aslib Book Guide "the book is well written and readable." --Hoben Thomas, Journal of Mathematical Psychology "This (hardback) book provides a very readable discussion of a possible alternative to both the Neyman-Pearson and the Fisherian approaches to the problem of interpreting data as evidencepresent this area of work in a accessible manner with a clear readable style. The main ideas are made easy to understand and well illustrated with some interesting examples, including in an appendix the paradox of the ravens. Diagrams and tables are well used in this respect and the number of formulae is kept low, which aids readabilityprovides a well-presented discussion of an interesting new way of looking at data which would be accessible to most with some understanding of statistics. For this reason I would recommend it to a library." --Thomas Chadwick, University of Newcastle, Biometrics

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