Hypothesis Testing and Model Selection in the Social Sciences

1. Hypothesis Testing and Model Selection 1.1. Introduction 1.2. Standard Procedure of Hypothesis Testing 1.3. Model Selection 1.4. Purpose and Plan of the Book 2. Hypothesis Testing: Criticisms and Alternatives 2.1. Hypothesis Testing and Its Discontents 2.2. Uses of Hypothesis Tests 2.3. Criticisms of Conventional Hypothesis Testing 2.4. Implications of the Criticisms 2.5. Alternatives to Conventional Tests 2.6. Examples 2.7. Summary and Conclusions Recommended Reading 3. The Classical Approach 3.1. Random Sampling and Classical Tests 3.2. Two Approaches to Hypothesis Tests 3.3. Confidence Intervals 3.4. Choosing a Significance Level 3.5. Comparison to Conventional Practice 3.6. Implications of Choosing an -level 3.7. Other Kinds of Errors 3.8. Example of Choosing an -level 3.9. Evaluation of Criticisms 3.10. Conclusions Recommended Reading 4. Bayesian Hypothesis Tests 4.1. Bayes's Theorem 4.2. Bayesian Estimation 4.3. Bayes Factors 4.4. Bayesian Confidence Intervals and Bayes Factors 4.5. Approaches to Bayesian Hypothesis Testing 4.6. The Unit Information Prior 4.7. Limits on Bayes Factors 4.8. Bayes Factors for Multiple Parameters 4.9. Conclusions Recommended Reading 5. The Akaike Information Criterion 5.1. Information 5.2. Prediction and Model Selection 5.3. The AIC 5.4. Consistency and Efficiency 5.5. Cross-Validation and the AIC 5.6. A Classical Perspective on the AIC 5.7. A Bayesian Perspective on the AIC 5.8. A General Class of Model Selection Criteria 5.9. Summary and Conclusions Recommended Reading 6. Three-Way Decisions 6.1. Substantive and Statistical Hypotheses 6.2. Bayes Factors for Directional Hypotheses 6.3. Bayes Factors for Three-Way Decisions 6.4. Summary and Conclusions Recommended Reading 7. Model Selection 7.1. Introduction 7.2. Bayesian Model Selection 7.3. The Value of Model Selection 7.4. The Risks of Model Selection 7.5. Examples of Model Selection 7.6. Conclusions Recommended Reading 8. Hypothesis Tests 8.1. Hypothesis Tests and the Strength of Evidence 8.2. When Should Hypotheses Be Tested? 8.3. The Role of Hypothesis Tests 8.4. Overfitting 8.5. Hypothesis Tests and the Development of Theory 8.6. Conclusions Recommended Reading References