Categorical Data Analysis

  1. Two-Variable Analysis
    1. Contingency Table Analysis
      1. Table Construction
        1. Joint Frequency Tables
          1. Marginal Distributions
            1. Conditional Distributions
            2. Independence Assessment
              1. Statistical Independence Concept
                1. Expected Frequencies Under Independence
                  1. Observed vs Expected Comparisons
                2. Tests of Independence
                  1. Pearson Chi-Square Test
                    1. Null and Alternative Hypotheses
                      1. Test Statistic Calculation
                        1. Degrees of Freedom Formula
                          1. Assumptions and Violations
                            1. Effect Size Interpretation
                            2. Likelihood Ratio Test
                              1. G-Test Statistic
                                1. Comparison with Pearson Test
                                  1. Asymptotic Equivalence
                                  2. Fisher's Exact Test
                                    1. Hypergeometric Distribution Basis
                                      1. Exact P-value Calculation
                                        1. Small Sample Applications
                                          1. Computational Considerations
                                          2. Monte Carlo Methods
                                            1. Simulation-Based P-values
                                              1. Applications to Large Tables
                                            2. Measures of Association
                                              1. Nominal Association Measures
                                                1. Phi Coefficient
                                                  1. Formula and Interpretation
                                                    1. Relationship to Chi-Square
                                                      1. Limitations
                                                      2. Cramer's V
                                                        1. Formula and Properties
                                                          1. Standardized Measure
                                                            1. Interpretation Guidelines
                                                            2. Contingency Coefficient
                                                              1. Formula and Properties
                                                                1. Upper Bound Limitations
                                                              2. Ordinal Association Measures
                                                                1. Concordant and Discordant Pairs
                                                                  1. Definition and Counting
                                                                    1. Tie Handling
                                                                    2. Gamma
                                                                      1. Formula and Interpretation
                                                                        1. Properties and Limitations
                                                                        2. Kendall's Tau-b
                                                                          1. Formula and Calculation
                                                                            1. Tie Corrections
                                                                            2. Kendall's Tau-c
                                                                              1. Square Table Applications
                                                                                1. Comparison with Tau-b
                                                                                2. Somers' d
                                                                                  1. Asymmetric Measure
                                                                                    1. Directional Interpretation
                                                                                3. Risk and Odds Measures
                                                                                  1. Risk Difference
                                                                                    1. Calculation and Interpretation
                                                                                      1. Confidence Intervals
                                                                                        1. Clinical Significance
                                                                                        2. Relative Risk
                                                                                          1. Definition and Formula
                                                                                            1. Interpretation Guidelines
                                                                                              1. Confidence Intervals
                                                                                                1. Cohort Study Applications
                                                                                                2. Odds Ratio
                                                                                                  1. Definition and Calculation
                                                                                                    1. Properties and Interpretation
                                                                                                      1. Confidence Intervals
                                                                                                        1. Case-Control Study Applications
                                                                                                          1. Cross-Product Ratio
                                                                                                          2. Number Needed to Treat
                                                                                                            1. Calculation from Risk Difference
                                                                                                              1. Clinical Interpretation

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                                                                                                          4. Single Variable Inference

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                                                                                                          6. Stratified Analysis