Statistical Inference

  1. Non-parametric Methods
    1. Introduction to Non-parametric Inference
      1. When to Use Non-parametric Methods
        1. Distribution-Free Methods
          1. Advantages and Limitations
            1. Robustness vs Efficiency
            2. Rank-Based Methods
              1. Concept of Ranks
                1. Handling Tied Observations
                  1. Rank Statistics Properties
                  2. One-Sample Non-parametric Tests
                    1. Sign Test
                      1. Assumptions and Procedure
                        1. Test Statistic and Distribution
                          1. Exact vs Normal Approximation
                            1. Applications and Examples
                            2. Wilcoxon Signed-Rank Test
                              1. Assumptions and Procedure
                                1. Test Statistic and Distribution
                                  1. Comparison with Sign Test
                                    1. Efficiency Relative to t-Test
                                  2. Two-Sample Non-parametric Tests
                                    1. Wilcoxon Rank-Sum Test (Mann-Whitney U)
                                      1. Independent Samples
                                        1. Assumptions and Procedure
                                          1. Test Statistic and Distribution
                                            1. Exact vs Normal Approximation
                                              1. Efficiency Relative to t-Test
                                              2. Wilcoxon Signed-Rank Test for Paired Data
                                                1. Paired Samples
                                                  1. Assumptions and Procedure
                                                    1. Comparison with Paired t-Test
                                                  2. Multi-Sample Non-parametric Tests
                                                    1. Kruskal-Wallis Test
                                                      1. Non-parametric Alternative to One-Way ANOVA
                                                        1. Assumptions and Procedure
                                                          1. Test Statistic and Distribution
                                                            1. Post-Hoc Comparisons
                                                            2. Friedman Test
                                                              1. Non-parametric Alternative to Repeated Measures ANOVA
                                                                1. Randomized Block Design
                                                                  1. Assumptions and Procedure
                                                                2. Non-parametric Correlation
                                                                  1. Spearman's Rank Correlation
                                                                    1. Definition and Calculation
                                                                      1. Interpretation
                                                                        1. Testing for Significance
                                                                        2. Kendall's Tau
                                                                          1. Definition and Calculation
                                                                            1. Comparison with Spearman's
                                                                          2. Bootstrap Methods
                                                                            1. Bootstrap Principle
                                                                              1. Bootstrap Sampling
                                                                                1. Bootstrap Confidence Intervals
                                                                                  1. Bootstrap Hypothesis Tests
                                                                                    1. Parametric vs Non-parametric Bootstrap

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                                                                                  11. Introduction to Bayesian Inference

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                                                                                  1. Foundations of Statistical Inference