Sampling

Steven K. Thompson, PhD, is Shrum Chair in Science and Professor of Statistics at the Simon Fraser University. During his career, he has served on the faculties of the Pennsylvania State University, the University of Auckland, and the University of Alaska. He is also the coauthor of Adaptive Sampling (Wiley).

• Preface xv Preface to the Second Edition xviiPreface to the First Edition xix1 Introduction 11.1 Basic Ideas of Sampling and Estimation, 21.2 Sampling Units, 41.3 Sampling and Nonsampling Errors, 51.4 Models in Sampling, 51.5 Adaptive and Nonadaptive Designs, 61.6 Some Sampling History, 7PART I BASIC SAMPLING 92 Simple Random Sampling 112.1 Selecting a Simple Random Sample, 112.2 Estimating the Population Mean, 132.3 Estimating the Population Total, 162.4 Some Underlying Ideas, 172.5 Random Sampling with Replacement, 192.6 Derivations for Random Sampling, 202.7 Model-Based Approach to Sampling, 222.8 Computing Notes, 26Entering Data in R, 26Sample Estimates, 27Simulation, 28Further Comments on the Use of Simulation, 32Exercises, 353 Confidence Intervals 393.1 Confidence Interval for the Population Mean or Total, 393.2 Finite-Population Central Limit Theorem, 413.3 Sampling Distributions, 433.4 Computing Notes, 44Confidence Interval Computation, 44Simulations Illustrating the Approximate Normality of a Sampling Distribution with Small n and N, 45Daily Precipitation Data, 46Exercises, 504 Sample Size 534.1 Sample Size for Estimating a Population Mean, 544.2 Sample Size for Estimating a Population Total, 544.3 Sample Size for Relative Precision, 55Exercises, 565 Estimating Proportions, Ratios, and Subpopulation Means 575.1 Estimating a Population Proportion, 585.2 Confidence Interval for a Proportion, 585.3 Sample Size for Estimating a Proportion, 595.4 Sample Size for Estimating Several Proportions Simultaneously, 605.5 Estimating a Ratio, 625.6 Estimating a Mean, Total, or Proportion of a Subpopulation, 62Estimating a Subpopulation Mean, 63Estimating a Proportion for a Subpopulation, 64Estimating a Subpopulation Total, 64Exercises, 656 Unequal Probability Sampling 676.1 Sampling with Replacement: The Hansen–Hurwitz Estimator, 676.2 Any Design: The Horvitz–Thompson Estimator, 696.3 Generalized Unequal-Probability Estimator, 726.4 Small Population Example, 736.5 Derivations and Comments, 756.6 Computing Notes, 78Writing an R Function to Simulate a Sampling Strategy, 82Comparing Sampling Strategies, 84Exercises, 88PART II MAKING THE BEST USE OF SURVEY DATA 917 Auxiliary Data and Ratio Estimation 937.1 Ratio Estimator, 947.2 Small Population Illustrating Bias, 977.3 Derivations and Approximations for the Ratio Estimator, 997.4 Finite-Population Central Limit Theorem for the Ratio Estimator, 1017.5 Ratio Estimation with Unequal Probability Designs, 1027.6 Models in Ratio Estimation, 105Types of Estimators for a Ratio, 1097.7 Design Implications of Ratio Models, 1097.8 Computing Notes, 110Exercises, 1128 Regression Estimation 1158.1 Linear Regression Estimator, 1168.2 Regression Estimation with Unequal Probability Designs, 1188.3 Regression Model, 1198.4 Multiple Regression Models, 1208.5 Design Implications of Regression Models, 123Exercises, 1249 The Sufficient Statistic in Sampling 1259.1 The Set of Distinct, Labeled Observations, 1259.2 Estimation in Random Sampling with Replacement, 1269.3 Estimation in Probability-Proportional-to-Size Sampling, 1279.4 Comments on the Improved Estimates, 12810 Design and Model 13110.1 Uses of Design and Model in Sampling, 13110.2 Connections between the Design and Model Approaches, 13210.3 Some Comments, 13410.4 Likelihood Function in Sampling, 135PART III SOME USEFUL DESIGNS 13911 Stratified Sampling 14111.1 Estimating the Population Total, 142With Any Stratified Design, 142With Stratified Random Sampling, 14311.2 Estimating the Population Mean, 144With Any Stratified Design, 144With Stratified Random Sampling, 14411.3 Confidence Intervals, 14511.4 The Stratification Principle, 14611.5 Allocation in Stratified Random Sampling, 14611.6 Poststratification, 14811.7 Population Model for a Stratified Population, 14911.8 Derivations for Stratified Sampling, 149Optimum Allocation, 149Poststratification Variance, 15011.9 Computing Notes, 151Exercises, 15512 Cluster and Systematic Sampling 15712.1 Primary Units Selected by Simple Random Sampling, 159Unbiased Estimator, 159Ratio Estimator, 16012.2 Primary Units Selected with Probabilities Proportional to Size, 161Hansen–Hurwitz (PPS) Estimator, 161Horvitz–Thompson Estimator, 16112.3 The Basic Principle, 16212.4 Single Systematic Sample, 16212.5 Variance and Cost in Cluster and Systematic Sampling, 16312.6 Computing Notes, 166Exercises, 16913 Multistage Designs 17113.1 Simple Random Sampling at Each Stage, 173Unbiased Estimator, 173Ratio Estimator, 17513.2 Primary Units Selected with Probability Proportional to Size, 17613.3 Any Multistage Design with Replacement, 17713.4 Cost and Sample Sizes, 17713.5 Derivations for Multistage Designs, 179Unbiased Estimator, 179Ratio Estimator, 181Probability-Proportional-to-Size Sampling, 181More Than Two Stages, 181Exercises, 18214 Double or Two-Phase Sampling 18314.1 Ratio Estimation with Double Sampling, 18414.2 Allocation in Double Sampling for Ratio Estimation, 18614.3 Double Sampling for Stratification, 18614.4 Derivations for Double Sampling, 188Approximate Mean and Variance: Ratio Estimation, 188Optimum Allocation for Ratio Estimation, 189Expected Value and Variance: Stratification, 18914.5 Nonsampling Errors and Double Sampling, 190Nonresponse, Selection Bias, or Volunteer Bias, 191Double Sampling to Adjust for Nonresponse: Callbacks, 192Response Modeling and Nonresponse Adjustments, 19314.6 Computing Notes, 195Exercises, 197PART IV METHODS FOR ELUSIVE AND HARD-TO-DETECT POPULATIONS 19915 Network Sampling and Link-Tracing Designs 20115.1 Estimation of the Population Total or Mean, 202Multiplicity Estimator, 202Horvitz–Thompson Estimator, 20415.2 Derivations and Comments, 20715.3 Stratification in Network Sampling, 20815.4 Other Link-Tracing Designs, 21015.5 Computing Notes, 212Exercises, 21316 Detectability and Sampling 21516.1 Constant Detectability over a Region, 21516.2 Estimating Detectability, 21716.3 Effect of Estimated Detectability, 21816.4 Detectability with Simple Random Sampling, 21916.5 Estimated Detectability and Simple Random Sampling, 22016.6 Sampling with Replacement, 22216.7 Derivations, 22216.8 Unequal Probability Sampling of Groups with Unequal Detection Probabilities, 22416.9 Derivations, 225Exercises, 22717 Line and Point Transects 22917.1 Density Estimation Methods for Line Transects, 23017.2 Narrow-Strip Method, 23017.3 Smooth-by-Eye Method, 23317.4 Parametric Methods, 23417.5 Nonparametric Methods, 237Estimating f (0) by the Kernel Method, 237Fourier Series Method, 23917.6 Designs for Selecting Transects, 24017.7 Random Sample of Transects, 240Unbiased Estimator, 241Ratio Estimator, 24317.8 Systematic Selection of Transects, 24417.9 Selection with Probability Proportional to Length, 24417.10 Note on Estimation of Variance for the Kernel Method, 24617.11 Some Underlying Ideas about Line Transects, 247Line Transects and Detectability Functions, 247Single Transect, 249Average Detectability, 249Random Transect, 250Average Detectability and Effective Area, 251Effect of Estimating Detectability, 252Probability Density Function of an Observed Distance, 25317.12 Detectability Imperfect on the Line or Dependent on Size, 25517.13 Estimation Using Individual Detectabilities, 255Estimation of Individual Detectabilities, 25617.14 Detectability Functions other than Line Transects, 25717.15 Variable Circular Plots or Point Transects, 259Exercise, 26018 Capture–Recapture Sampling 26318.1 Single Recapture, 26418.2 Models for Simple Capture–Recapture, 26618.3 Sampling Design in Capture–Recapture: Ratio Variance Estimator, 267Random Sampling with Replacement of Detectability Units, 269Random Sampling without Replacement, 27018.4 Estimating Detectability with Capture–Recapture Methods, 27118.5 Multiple Releases, 27218.6 More Elaborate Models, 273Exercise, 27319 Line-Intercept Sampling 27519.1 Random Sample of Lines: Fixed Direction, 27519.2 Lines of Random Position and Direction, 280Exercises, 282PART V SPATIAL SAMPLING 28320 Spatial Prediction or Kriging 28520.1 Spatial Covariance Function, 28620.2 Linear Prediction (Kriging), 28620.3 Variogram, 28920.4 Predicting the Value over a Region, 29120.5 Derivations and Comments, 29220.6 Computing Notes, 296Exercise, 29921 Spatial Designs 30121.1 Design for Local Prediction, 30221.2 Design for Prediction of Mean of Region, 30222 Plot Shapes and Observational Methods 30522.1 Observations from Plots, 30522.2 Observations from Detectability Units, 30722.3 Comparisons of Plot Shapes and Detectability Methods, 308PART VI ADAPTIVE SAMPLING 31323 Adaptive Sampling Designs 31523.1 Adaptive and Conventional Designs and Estimators, 31523.2 Brief Survey of Adaptive Sampling, 31624 Adaptive Cluster Sampling 31924.1 Designs, 321Initial Simple Random Sample without Replacement, 322Initial Random Sample with Replacement, 32324.2 Estimators, 323Initial Sample Mean, 323Estimation Using Draw-by-Draw Intersections, 323Estimation Using Initial Intersection Probabilities, 32524.3 When Adaptive Cluster Sampling Is Better than Simple Random Sampling, 32724.4 Expected Sample Size, Cost, and Yield, 32824.5 Comparative Efficiencies of Adaptive and ConventionalSampling, 32824.6 Further Improvement of Estimators, 33024.7 Derivations, 33324.8 Data for Examples and Figures, 336Exercises, 33725 Systematic and Strip Adaptive Cluster Sampling 33925.1 Designs, 34125.2 Estimators, 343Initial Sample Mean, 343Estimator Based on Partial Selection Probabilities, 344Estimator Based on Partial Inclusion Probabilities, 34525.3 Calculations for Adaptive Cluster Sampling Strategies, 34725.4 Comparisons with Conventional Systematic and Cluster Sampling, 34925.5 Derivations, 35025.6 Example Data, 352Exercises, 35226 Stratified Adaptive Cluster Sampling 35326.1 Designs, 35326.2 Estimators, 356Estimators Using Expected Numbers of Initial Intersections, 357Estimator Using Initial Intersection Probabilities, 35926.3 Comparisons with Conventional Stratified Sampling, 36226.4 Further Improvement of Estimators, 36426.5 Example Data, 367Exercises, 367Answers to Selected Exercises 369References 375Author Index 395Subject Index 399