Categorical Data Analysis

  1. Single Variable Inference
    1. Confidence Intervals for Proportions
      1. Large Sample Methods
        1. Wald Interval
          1. Formula and Assumptions
            1. Coverage Properties
              1. Limitations
              2. Wilson Score Interval
                1. Derivation and Formula
                  1. Improved Coverage Properties
                    1. Computational Methods
                    2. Agresti-Coull Interval
                      1. Modified Wald Approach
                        1. Practical Implementation
                      2. Exact Methods
                        1. Clopper-Pearson Interval
                          1. Beta Distribution Approach
                            1. Conservative Nature
                            2. Small Sample Considerations
                              1. Rule of Thumb Guidelines
                                1. Method Selection Criteria
                              2. Hypothesis Testing for Single Proportions
                                1. Large Sample Tests
                                  1. One-Sample Z-Test
                                    1. Null and Alternative Hypotheses
                                      1. Test Statistic
                                        1. Assumptions and Conditions
                                          1. P-value Calculation
                                          2. Continuity Correction
                                            1. When to Apply
                                              1. Effect on Results
                                            2. Exact Tests
                                              1. Binomial Test
                                                1. Exact P-value Calculation
                                                  1. One-Tailed and Two-Tailed Tests
                                                    1. Small Sample Applications
                                                2. Goodness-of-Fit Testing
                                                  1. Pearson Chi-Square Test
                                                    1. Test Statistic Formula
                                                      1. Expected Frequency Calculation
                                                        1. Degrees of Freedom
                                                          1. Assumptions and Conditions
                                                            1. Interpretation Guidelines
                                                            2. Likelihood Ratio Test
                                                              1. G-Statistic
                                                                1. Comparison with Pearson Chi-Square
                                                                  1. Asymptotic Properties
                                                                  2. Exact Goodness-of-Fit Tests
                                                                    1. Multinomial Exact Tests
                                                                      1. Small Sample Applications

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                                                                  3. Probability Foundations for Categorical Data

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                                                                  5. Two-Variable Analysis