Sampling Theory

Sampling theory is the statistical study of selecting a subset of individuals (a sample) from within a population to estimate the characteristics of the whole population. Rather than studying every single member, which is often impractical or impossible, this theory provides the principles and techniques—such as random, stratified, and cluster sampling—for drawing a representative sample. It allows researchers to make valid inferences and generalizations about the larger group while also providing the mathematical tools to quantify the degree of uncertainty, known as sampling error, associated with those conclusions.

1. Foundations of Sampling Theory
   1. Purpose and Rationale of Sampling
      1. Cost Reduction and Resource Efficiency
      2. Feasibility in Large Population Studies
      3. Enabling Destructive Testing Procedures
      4. Achieving Timely Data Collection
      5. Enhancing Data Quality and Manageability
      6. Practical Constraints and Limitations
   2. Core Concepts and Definitions
      1. Population Concepts
         1. Target Population
         2. Sampled Population
         3. Finite vs Infinite Populations
      2. Sample Characteristics
         1. Sample Definition
         2. Sample Size
         3. Sample Selection Process
      3. Sampling Unit
         1. Elementary Units
         2. Listing Units
         3. Observation Units
      4. Sampling Frame
         1. Frame Construction Principles
         2. Frame Coverage Issues
         3. Frame Errors and Deficiencies
         4. Multiple Frame Approaches
      5. Parameters and Statistics
         1. Population Parameters
         2. Sample Statistics
         3. Estimators and Estimates
      6. Census vs Sample Survey
         1. Complete Enumeration
         2. Partial Enumeration
         3. Trade-offs and Decision Criteria
   3. Types of Errors in Sampling
      1. Sampling Error
         1. Definition and Nature
         2. Sources of Sampling Error
         3. Quantifying Sampling Error
         4. Standard Error Concepts
      2. Non-sampling Error
         1. Coverage Error
            1. Undercoverage
            2. Overcoverage
            3. Multiple Coverage
            4. Effects on Population Estimates
         2. Nonresponse Error
            1. Unit Nonresponse
            2. Item Nonresponse
            3. Nonresponse Bias
            4. Response Rate Calculations
         3. Measurement Error
            1. Interviewer Effects
            2. Respondent Effects
            3. Instrument Effects
            4. Mode Effects
         4. Processing Error
            1. Data Entry Errors
            2. Coding Errors
            3. Editing Errors
            4. Weighting Errors
      3. Total Survey Error Framework
         1. Error Components Integration
         2. Mean Squared Error Decomposition
         3. Bias-Variance Trade-offs