Statistical Inference

  1. Hypothesis Testing Framework
    1. The Logic of Hypothesis Testing
      1. Scientific Method and Statistical Testing
        1. Proof by Contradiction Analogy
          1. Role of Sampling Distributions
            1. Evidence vs Proof
            2. Formulating Hypotheses
              1. The Null Hypothesis
                1. Definition and Characteristics
                  1. Status Quo Hypothesis
                    1. Examples and Notation
                    2. The Alternative Hypothesis
                      1. Definition and Characteristics
                        1. Research Hypothesis
                          1. Examples and Notation
                          2. Types of Alternative Hypotheses
                            1. One-Tailed Tests
                              1. Left-Tailed Tests
                                1. Right-Tailed Tests
                                  1. When to Use
                                  2. Two-Tailed Tests
                                    1. Non-Directional Alternatives
                                      1. When to Use
                                  3. Components of Hypothesis Testing
                                    1. The Test Statistic
                                      1. Definition and Purpose
                                        1. Standardization
                                          1. Distribution Under Null Hypothesis
                                          2. The Significance Level
                                            1. Definition and Interpretation
                                              1. Choosing Alpha
                                                1. Common Values and Conventions
                                                  1. Type I Error Rate
                                                  2. The Rejection Region
                                                    1. Critical Region Definition
                                                      1. Determining Critical Values
                                                        1. One-Tailed vs Two-Tailed Regions
                                                          1. Relationship to Significance Level
                                                          2. The P-value
                                                            1. Definition and Calculation
                                                              1. Interpretation and Meaning
                                                                1. P-value vs Significance Level
                                                                  1. Reporting P-values
                                                                2. Decision Making in Hypothesis Testing
                                                                  1. Decision Rules
                                                                    1. P-value Approach
                                                                      1. Critical Value Approach
                                                                        1. Equivalence of Methods
                                                                        2. Stating Conclusions
                                                                          1. Statistical Conclusion
                                                                            1. Practical Conclusion
                                                                              1. Strength of Evidence
                                                                            2. Errors in Hypothesis Testing
                                                                              1. Type I Error
                                                                                1. Definition and Consequences
                                                                                  1. Probability of Type I Error
                                                                                    1. Controlling Type I Error
                                                                                    2. Type II Error
                                                                                      1. Definition and Consequences
                                                                                        1. Probability of Type II Error
                                                                                          1. Factors Affecting Type II Error
                                                                                          2. The Relationship Between Error Types
                                                                                            1. Trade-offs Between Alpha and Beta
                                                                                              1. Sample Size Effects
                                                                                            2. Statistical Power
                                                                                              1. Definition of Power
                                                                                                1. Factors Affecting Power
                                                                                                  1. Effect Size
                                                                                                    1. Sample Size
                                                                                                      1. Significance Level
                                                                                                        1. Population Variability
                                                                                                        2. Power Calculations
                                                                                                          1. A Priori Power Analysis
                                                                                                            1. Post Hoc Power Analysis
                                                                                                              1. Power Curves
                                                                                                              2. Increasing Statistical Power
                                                                                                                1. Design Considerations
                                                                                                                  1. Sample Size Planning
                                                                                                                2. Effect Size and Practical Significance
                                                                                                                  1. Statistical vs Practical Significance
                                                                                                                    1. Measures of Effect Size
                                                                                                                      1. Interpreting Effect Sizes
                                                                                                                        1. Reporting Effect Sizes
                                                                                                                        2. Multiple Testing Issues
                                                                                                                          1. Family-wise Error Rate
                                                                                                                            1. False Discovery Rate
                                                                                                                              1. Bonferroni Correction
                                                                                                                                1. Other Multiple Comparison Procedures

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                                                                                                                              4. Interval Estimation and Confidence Intervals

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                                                                                                                              6. One-Sample Parametric Tests