Statistical Inference

  1. Analysis of Variance (ANOVA)
    1. Introduction to ANOVA
      1. Purpose of ANOVA
        1. Comparing Multiple Means
          1. Why Not Multiple t-Tests
            1. Family-wise Error Rate Problem
            2. One-Way ANOVA
              1. Model and Assumptions
                1. Independence Assumption
                  1. Normality Assumption
                    1. Homogeneity of Variance Assumption
                      1. Fixed vs Random Effects
                      2. ANOVA Decomposition
                        1. Total Variation
                          1. Between-Group Variation
                            1. Within-Group Variation
                              1. Sum of Squares Decomposition
                                1. Total Sum of Squares (SST)
                                  1. Sum of Squares Between (SSB)
                                    1. Sum of Squares Within (SSW)
                                  2. Mean Squares and F-Statistic
                                    1. Mean Square Between (MSB)
                                      1. Mean Square Within (MSW)
                                        1. F-Statistic Calculation
                                          1. F-Distribution Properties
                                          2. ANOVA Table
                                            1. Structure and Components
                                              1. Degrees of Freedom
                                                1. P-value Calculation
                                                2. Post-Hoc Analysis
                                                  1. Need for Multiple Comparisons
                                                    1. Family-wise Error Rate
                                                      1. Tukey's Honestly Significant Difference
                                                        1. Bonferroni Method
                                                          1. Scheffé's Method
                                                            1. Fisher's LSD
                                                            2. Assumptions Checking
                                                              1. Residual Analysis
                                                                1. Tests for Normality
                                                                  1. Tests for Equal Variances
                                                                    1. Transformations
                                                                  2. Two-Way ANOVA
                                                                    1. Model and Design
                                                                      1. Two-Factor Design
                                                                        1. Balanced vs Unbalanced Designs
                                                                          1. Interaction Effects
                                                                          2. Main Effects
                                                                            1. Factor A Main Effect
                                                                              1. Factor B Main Effect
                                                                                1. Interpretation
                                                                                2. Interaction Effects
                                                                                  1. Definition and Interpretation
                                                                                    1. Testing for Interaction
                                                                                      1. Interaction Plots
                                                                                      2. ANOVA Table for Two-Way Design
                                                                                        1. Sources of Variation
                                                                                          1. Degrees of Freedom
                                                                                            1. F-Statistics for Each Effect
                                                                                            2. Simple Effects Analysis
                                                                                              1. When Interaction is Significant
                                                                                                1. Analyzing Effects at Each Level

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                                                                                            8. Categorical Data Analysis

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                                                                                            10. Simple Linear Regression Inference