Sampling: Design and Analysis

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
Symbols and Acronyms
1. Introduction
	1.1. Guidance from Samples
	1.2. Populations and Representative Samples
	1.3. Selection Bias
		1.3.1. Convenience Samples
		1.3.2. Purposive or Judgment Samples
		1.3.3. Self-Selected Samples
		1.3.4. Undercoverage
		1.3.5. Overcoverage
		1.3.6. Nonresponse
		1.3.7. What Good Are Samples with Selection Bias?
	1.4. Measurement Error
	1.5. Questionnaire Design
	1.6. Sampling and Nonsampling Errors
	1.7. Why Use Sampling?
		1.7.1. Advantages of Taking a Census
		1.7.2. Advantages of Taking a Sample Instead of a Census
	1.8. Chapter Summary
	1.9. Exercises
2. Simple Probability Samples
	2.1. Types of Probability Samples
	2.2. Framework for Probability Sampling
	2.3. Simple Random Sampling
	2.4. Sampling Weights
	2.5. Confidence Intervals
	2.6. Using Statistical Software to Analyze Survey Data
	2.7. Determining the Sample Size
	2.8. Systematic Sampling
	2.9. Randomization Theory for Simple Random Sampling*
	2.10. Model-Based Theory for Simple Random Sampling*
	2.11. When Should a Simple Random Sample Be Used?
	2.12. Chapter Summary
	2.13. Exercises
3. Stratified Sampling
	3.1. What Is Stratified Sampling?
	3.2. Theory of Stratified Sampling
	3.3. Sampling Weights in Stratified Random Sampling
	3.4. Allocating Observations to Strata
		3.4.1. Proportional Allocation
		3.4.2. Optimal Allocation
		3.4.3. Allocation for Specified Precision within Strata
		3.4.4. Which Allocation to Use?
		3.4.5. Determining the Total Sample Size
	3.5. Defining Strata
	3.6. Model-Based Theory for Stratified Sampling*
	3.7. Chapter Summary
	3.8. Exercises
4. Ratio and Regression Estimation
	4.1. Ratio Estimation in Simple Random Sampling
		4.1.1. Why Use Ratio Estimation?
		4.1.2. Bias and Mean Squared Error of Ratio Estimators
		4.1.3. Ratio Estimation with Proportions
		4.1.4. Ratio Estimation Using Weight Adjustments
		4.1.5. Advantages of Ratio Estimation
	4.2. Regression Estimation in Simple Random Sampling
	4.3. Estimation in Domains
	4.4. Poststratification
	4.5. Ratio Estimation with Stratified Sampling
	4.6. Model-Based Theory for Ratio and Regression Estimation*
		4.6.1. A Model for Ratio Estimation
		4.6.2. A Model for Regression Estimation
		4.6.3. Differences between Model-Based and Design-Based Estimators
	4.7. Chapter Summary
	4.8. Exercises
5. Cluster Sampling with Equal Probabilities
	5.1. Notation for Cluster Sampling
	5.2. One-Stage Cluster Sampling
		5.2.1. Clusters of Equal Sizes: Estimation
		5.2.2. Clusters of Equal Sizes: Theory
		5.2.3. Clusters of Unequal Sizes
	5.3. Two-Stage Cluster Sampling
	5.4. Designing a Cluster Sample
		5.4.1. Choosing the psu Size
		5.4.2. Choosing Subsampling Sizes
		5.4.3. Choosing the Sample Size (Number of psus)
	5.5. Systematic Sampling
	5.6. Model-Based Theory for Cluster Sampling*
		5.6.1. Estimation Using Models
		5.6.2. Design Using Models
	5.7. Chapter Summary
	5.8. Exercises
6. Sampling with Unequal Probabilities
	6.1. Sampling One Primary Sampling Unit
	6.2. One-Stage Sampling with Replacement
		6.2.1. Selecting Primary Sampling Units
		6.2.2. Theory of Estimation
		6.2.3. Designing the Selection Probabilities
		6.2.4. Weights in Unequal-Probability Sampling with Replacement
	6.3. Two-Stage Sampling with Replacement
	6.4. Unequal-Probability Sampling without Replacement
		6.4.1. The Horvitz–Thompson Estimator for One-Stage Sampling
		6.4.2. Selecting the psus
		6.4.3. The Horvitz–Thompson Estimator for Two-Stage Sampling
		6.4.4. Weights in Unequal-Probability Samples
	6.5. Examples of Unequal-Probability Samples
	6.6. Randomization Theory Results and Proofs*
	6.7. Model-Based Inference with Unequal-Probability Samples*
	6.8. Chapter Summary
	6.9. Exercises
7. Complex Surveys
	7.1. Assembling Design Components
		7.1.1. Building Blocks for Surveys
		7.1.2. Ratio Estimation in Complex Surveys
		7.1.3. Simplicity in Survey Design
	7.2. Sampling Weights
		7.2.1. Constructing Sampling Weights
		7.2.2. Self-Weighting and Non-Self-Weighting Samples
	7.3. Estimating Distribution Functions and Quantiles
	7.4. Design Effects
	7.5. The National Health and Nutrition Examination Survey
	7.6. Graphing Data from a Complex Survey
		7.6.1. Univariate Plots
		7.6.2. Bivariate Plots
	7.7. Chapter Summary
	7.8. Exercises
8. Nonresponse
	8.1. Effects of Ignoring Nonresponse
	8.2. Designing Surveys to Reduce Nonresponse
	8.3. Two-Phase Sampling
	8.4. Response Propensities and Mechanisms for Nonresponse
		8.4.1. Auxiliary Information for Treating Nonresponse
		8.4.2. Methods to Adjust for Nonresponse
		8.4.3. Response Propensities
		8.4.4. Types of Missing Data
	8.5. Adjusting Weights for Nonresponse
		8.5.1. Weighting Class Adjustments
		8.5.2. Regression Models for Response Propensities
	8.6. Poststratification
		8.6.1. Poststratification Using Weights
		8.6.2. Raking Adjustments
		8.6.3. Steps for Constructing Final Survey Weights
		8.6.4. Advantages and Disadvantages of Weighting Adjustments
	8.7. Imputation
		8.7.1. Deductive Imputation
		8.7.2. Cell Mean Imputation
		8.7.3. Hot-Deck Imputation
		8.7.4. Regression Imputation and Chained Equations
		8.7.5. Imputation from Another Data Source
		8.7.6. Multiple Imputation
		8.7.7. Advantages and Disadvantages of Imputation
	8.8. Response Rates and Nonresponse Bias Assessments
		8.8.1. Calculating and Reporting Response Rates
		8.8.2. What Is an Acceptable Response Rate?
		8.8.3. Nonresponse Bias Assessments
	8.9. Chapter Summary
	8.10. Exercises
9. Variance Estimation in Complex Surveys
	9.1. Linearization (Taylor Series) Methods
	9.2. Random Group Methods
		9.2.1. Replicating the Survey Design
		9.2.2. Dividing the Sample into Random Groups
	9.3. Resampling and Replication Methods
		9.3.1. Balanced Repeated Replication (BRR)
		9.3.2. Jackknife
		9.3.3. Bootstrap
		9.3.4. Creating and Using Replicate Weights
	9.4. Generalized Variance Functions
	9.5. Confidence Intervals
		9.5.1. Confidence Intervals for Smooth Functions of Population Totals
		9.5.2. Confidence Intervals for Population Quantiles
	9.6. Chapter Summary
	9.7. Exercises
10. Categorical Data Analysis in Complex Surveys
	10.1. Chi-Square Tests with Multinomial Sampling
		10.1.1. Testing Independence of Factors
		10.1.2. Testing Homogeneity of Proportions
		10.1.3. Testing Goodness of Fit
	10.2. Effects of Survey Design on Chi-Square Tests
		10.2.1. Contingency Tables for Data from Complex Surveys
		10.2.2. Effects on Hypothesis Tests and Confidence Intervals
	10.3. Corrections to Chi-Square Tests
		10.3.1. Wald Tests
		10.3.2. Rao–Scott Tests
		10.3.3. Model-Based Methods for Chi-Square Tests
	10.4. Loglinear Models
		10.4.1. Loglinear Models with Multinomial Sampling
		10.4.2. Loglinear Models in a Complex Survey
	10.5. Chapter Summary
	10.6. Exercises
11. Regression with Complex Survey Data
	11.1. Model-Based Regression in Simple Random Samples
	11.2. Regression with Complex Survey Data
		11.2.1. Point Estimation
		11.2.2. Standard Errors
		11.2.3. Multiple Regression
		11.2.4. Regression Using Weights versus Weighted Least Squares
	11.3. Using Regression to Compare Domain Means
	11.4. Interpreting Regression Coefficients from Survey Data
		11.4.1. Purposes of Regression Analyses
		11.4.2. Model-Based and Design-Based Inference
		11.4.3. Survey Weights and Regression
		11.4.4. Survey Design and Standard Errors
		11.4.5. Mixed Models for Cluster Samples
	11.5. Logistic Regression
	11.6. Calibration to Population Totals
	11.7. Chapter Summary
	11.8. Exercises
12. Two-Phase Sampling
	12.1. Theory for Two-Phase Sampling
	12.2. Two-Phase Sampling with Stratification
	12.3. Ratio and Regression Estimation in Two-Phase Samples
		12.3.1. Two-Phase Sampling with Ratio Estimation
		12.3.2. Generalized Regression Estimation in Two-Phase Sampling
	12.4. Jackknife Variance Estimation for Two-Phase Sampling
	12.5. Designing a Two-Phase Sample
		12.5.1. Two-Phase Sampling with Stratification
		12.5.2. Optimal Allocation for Ratio Estimation
	12.6. Chapter Summary
	12.7. Exercises
13. Estimating the Size of a Population
	13.1. Capture–Recapture Estimation
		13.1.1. Contingency Tables for Capture–Recapture Experiments
		13.1.2. Confidence Intervals for
		13.1.3. Using Capture–Recapture on Lists
	13.2. Multiple Recapture Estimation
	13.3. Chapter Summary
	13.4. Exercises
14. Rare Populations and Small Area Estimation
	14.1. Sampling Rare Populations
		14.1.1. Stratified Sampling with Disproportional Allocation
		14.1.2. Two-Phase Sampling
		14.1.3. Unequal-Probability Sampling
		14.1.4. Multiple Frame Surveys
		14.1.5. Network or Multiplicity Sampling
		14.1.6. Snowball Sampling
		14.1.7. Sequential Sampling
	14.2. Small Area Estimation
		14.2.1. Direct Estimators
		14.2.2. Synthetic and Composite Estimators
		14.2.3. Model-Based Estimators
	14.3. Chapter Summary
	14.4. Exercises
15. Nonprobability Samples
	15.1. Types of Nonprobability Samples
		15.1.1. Administrative Records
		15.1.2. Quota Samples
		15.1.3. Judgment Samples
		15.1.4. Convenience Samples
	15.2. Selection Bias and Mean Squared Error
		15.2.1. Random Variables Describing Participation in a Sample
		15.2.2. Bias and Mean Squared Error of a Sample Mean
	15.3. Reducing Bias of Estimates from Nonprobability Samples
		15.3.1. Weighting
		15.3.2. Estimate the Values of the Missing Units
		15.3.3. Measures of Uncertainty for Nonprobability Samples
	15.4. Nonprobability versus Low-Response Probability Samples
	15.5. Chapter Summary
	15.6. Exercises
16. Survey Quality
	16.1. Coverage Error
		16.1.1. Measuring Coverage and Coverage Bias
		16.1.2. Coverage and Survey Mode
		16.1.3. Improving Coverage
	16.2. Nonresponse Error
	16.3. Measurement Error
		16.3.1. Measuring and Modeling Measurement Error
		16.3.2. Reducing Measurement Error
		16.3.3. Sensitive Questions
		16.3.4. Randomized Response
	16.4. Processing Error
	16.5. Total Survey Quality
	16.6. Chapter Summary
	16.7. Exercises
A. Probability Concepts Used in Sampling
	A.1. Probability
		A.1.1. Simple Random Sampling with Replacement
		A.1.2. Simple Random Sampling without Replacement
	A.2. Random Variables and Expected Value
	A.3. Conditional Probability
	A.4. Conditional Expectation
	A.5. Exercises
Bibliography
Index