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Full Description
Statistics is more topical than ever. Numerous decisions depend on statistical considerations: just think of the Corona crisis or decisions about approving new drugs or other products. If researchers announce they have proved some fact using statistical tests, can we then always be sure that their claim is correct? How, and more importantly why, does statistics work? What can we expect from statistics and what not? 'Fact or Fluke?' is not a textbook that explains statistical tests to the reader; instead, it discusses what comes before those tests: the philosophy behind the statistics. Should one carry out tests, or are there other ways to look at statistics?
Ronald Meester and Klaas Slooten use a variety of examples - from court cases to theoretical physics - to present different views on statistics and provide arguments for what they think is the best point of view. This book is meant for anyone who is in some way concerned with, or interested in, statistical evidence: scientific researchers, students, teachers, mathematicians, philosophers, lawyers, managers, and no doubt many others.
Contents
Preface, Prologue, Part I Classical Statistics 1. Significance Testing 1.1 Testing the Null Hypothesis and Statistical Significance 1.2 The Logic of Significance Testing: In the Words of Fisher 1.3 Significance Testing Ignores the Context 1.4 Back to Sally Clark 2. p-Values 2.1 What Is a p-value? 2.2 The Main Problem with p-Values 2.3 Publication Bias 2.4 One-Tailed Versus Two-Tailed: A Paradox 2.5 The p-Value in Adaptive Sampling Studies 2.6 More on Adaptive Sampling Studies 3. Confidence Intervals 3.1 What Is a Confidence Interval? 3.2 Confidence Intervals, p-Values, and Effect Size 3.3 Dependence on the Experimental Setup 3.4 Strange (and Amusing) Confidence Intervals Part II A Bayesian Approach 4. What Is Statistical Evidence? 4.1 The Likelihood Ratio 4.2 Likelihood Ratios for an Unknown Probability of Success 4.3 The Likelihood Ratio Solves Problems with p-Values 74.4 The Interpretation of the Likelihood Ratio 4.5 p-Values versus Likelihood Ratios 4.6 Likelihood Ratios and Power 5. Evidence and Belief 5.1 Alternative Hypotheses and Context 5.2 A Return to Ioannidis' Argument 5.3 An Anecdotal Cards Example 5.4 A Philosophical Interlude 5.5 Worked-Out Examples - Credibility Intervals 5.6 Laypersons and the Prior 5.7 Objective Bayes? 5.8 A Few Conclusions 6. The Likelihood Ratio and the Experimental Setup 6.1 Error Probabilities and Misleading Evidence 6.2 How Often Does Misleading Evidence Occur? 6.3 Likelihood Ratios and Designing an Experimental Setup 6.4 Conclusions Part III Statistics in Practice 7. Two Worked-Out Examples 7.1 Face Masks 7.2 The Lucia de Berk Case 8. Sometimes p-Values Can Be Justified 8.1 Elementary Particles in Theoretical Physics 8.2 Model Validation, Appendix, Bibliography, Index
