Statistical Evidence: A Likelihood Paradigm

Abstract

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