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Statistical Evidence
A Likelihood Paradigm




ISBN 9780412044113
Published June 1, 1997 by Chapman and Hall/CRC
191 Pages

 
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Book Description

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
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

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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