Statistical Evidence: A Likelihood Paradigm

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ISBN 9780412044113
Cat# C4411



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  • Introduces a completely new paradigm and explains how to use it
  • Provides theory and methods for both measurement and graphical representation of statistical evidence
  • Helps resolve the frequentist versus Bayesian dilemma
  • Summary

    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.

    Table of Contents

    The First Principle
    The Law of Likelihood
    Three Questions
    Towards Verification
    Relativity of Evidence
    Strength of Evidence
    Testing Simple Hypotheses
    Composite Hypotheses
    Another Counterexample
    Irrelevance of the Sample Space
    The Likelihood Principle
    Evidence and Uncertainty
    Neyman-Pearson Theory
    Neyman-Pearson Statistical Theory
    Evidential Interpretation of Results of Neyman-Pearson Decision Procedures
    Neyman-Pearson Hypothesis Testing in Planning Experiments: Choosing the Sample Size
    Fisherian Theory
    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
    Paradigms for Statistics
    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
    Resolving the Old Paradoxes
    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?
    Looking at Likelihoods
    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
    Nuisance Parameters
    Orthogonal Parameters
    Marginal Likelihoods
    Conditional Likelihoods
    Estimated Likelihoods
    Profile Likelihoods
    Synthetic Conditional Likelihoods
    Bayesian Statistical Inference
    Bayesian Statistical Models
    Subjectivity in Bayesian Models
    The Trouble with Bayesian Statistics
    Are Likelihood Methods Bayesian?
    Objective Bayesian Inference
    Bayesian Integrated Likelihoods
    Appendix: The Paradox of the Ravens

    Editorial Reviews

    "...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 evidence…present 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 readability…provides 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