Sampling Theory

  1. Probability Sampling Methods
    1. Principles of Probability Sampling
      1. Randomization Importance
        1. Equal Probability of Selection
          1. Known Selection Probabilities
            1. Representativeness Concepts
              1. Statistical Inference Foundation
              2. Simple Random Sampling
                1. Definition and Assumptions
                  1. Sampling with Replacement
                    1. Sampling without Replacement
                      1. Selection Methods
                        1. Lottery Method
                          1. Random Number Tables
                            1. Computer-Generated Random Numbers
                              1. Systematic Random Selection
                              2. Advantages and Limitations
                                1. Estimation Procedures
                                  1. Population Mean Estimation
                                    1. Population Total Estimation
                                      1. Population Proportion Estimation
                                        1. Variance Estimation
                                      2. Systematic Sampling
                                        1. Definition and Procedure
                                          1. Sampling Interval Determination
                                            1. Random Start Selection
                                              1. Linear Systematic Sampling
                                                1. Circular Systematic Sampling
                                                  1. Advantages and Disadvantages
                                                    1. Periodicity Effects
                                                      1. Identifying Periodic Patterns
                                                        1. Impact on Estimates
                                                          1. Mitigation Strategies
                                                          2. Estimation in Systematic Sampling
                                                            1. Treating as Simple Random Sample
                                                              1. Alternative Variance Estimators
                                                            2. Stratified Random Sampling
                                                              1. Rationale for Stratification
                                                                1. Variance Reduction
                                                                  1. Subgroup Representation
                                                                    1. Administrative Convenience
                                                                    2. Strata Definition
                                                                      1. Stratification Criteria
                                                                        1. Homogeneity within Strata
                                                                          1. Heterogeneity between Strata
                                                                            1. Number of Strata Considerations
                                                                            2. Sample Size Allocation
                                                                              1. Proportional Allocation
                                                                                1. Optimal Allocation
                                                                                  1. Neyman Allocation
                                                                                    1. Disproportional Allocation
                                                                                      1. Power Allocation
                                                                                      2. Estimation Procedures
                                                                                        1. Stratified Mean Estimation
                                                                                          1. Stratified Total Estimation
                                                                                            1. Stratified Proportion Estimation
                                                                                              1. Weighted Estimation Methods
                                                                                                1. Variance Estimation
                                                                                                2. Advantages and Limitations
                                                                                                  1. Post-Stratification
                                                                                                  2. Cluster Sampling
                                                                                                    1. Rationale for Clustering
                                                                                                      1. Cost Efficiency
                                                                                                        1. Administrative Convenience
                                                                                                          1. Natural Groupings
                                                                                                            1. Geographic Considerations
                                                                                                            2. Cluster Definition
                                                                                                              1. Cluster Size Considerations
                                                                                                                1. Cluster Homogeneity
                                                                                                                  1. Intracluster Correlation
                                                                                                                  2. Single-Stage Cluster Sampling
                                                                                                                    1. Selection of Clusters
                                                                                                                      1. Complete Enumeration within Clusters
                                                                                                                        1. Estimation Procedures
                                                                                                                        2. Multi-Stage Cluster Sampling
                                                                                                                          1. Two-Stage Sampling
                                                                                                                            1. Three-Stage and Higher
                                                                                                                              1. Primary Sampling Units
                                                                                                                                1. Secondary Sampling Units
                                                                                                                                  1. Ultimate Sampling Units
                                                                                                                                  2. Probability Proportional to Size Sampling
                                                                                                                                    1. PPS Selection Methods
                                                                                                                                      1. Cumulative Size Method
                                                                                                                                        1. Systematic PPS Selection
                                                                                                                                          1. Applications and Advantages
                                                                                                                                          2. Estimation in Cluster Sampling
                                                                                                                                            1. Unbiased Estimators
                                                                                                                                              1. Design Effect
                                                                                                                                                1. Effective Sample Size
                                                                                                                                                2. Advantages and Limitations
                                                                                                                                                  1. Cost Benefits
                                                                                                                                                    1. Precision Considerations
                                                                                                                                                      1. Design Effect Impact
                                                                                                                                                    2. Complex Sample Designs
                                                                                                                                                      1. Stratified Cluster Sampling
                                                                                                                                                        1. Multi-Stage Stratified Sampling
                                                                                                                                                          1. Unequal Probability Sampling
                                                                                                                                                            1. Design Considerations
                                                                                                                                                              1. Estimation Challenges
                                                                                                                                                              2. Comparison of Probability Sampling Designs
                                                                                                                                                                1. Precision Comparisons
                                                                                                                                                                  1. Cost Efficiency Analysis
                                                                                                                                                                    1. Design Effect Considerations
                                                                                                                                                                      1. Suitability for Different Populations
                                                                                                                                                                        1. Selection Criteria

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                                                                                                                                                                      1. Foundations of Sampling Theory

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                                                                                                                                                                      3. Non-Probability Sampling Methods