Summary
Sampling
Preface xv Preface to the Second Edition xvii Preface to the First Edition xix 1 Introduction 1 1.1 Basic Ideas of Sampling and Estimation, 2 1.2 Sampling Units, 4 1.3 Sampling and Nonsampling Errors, 5 1.4 Models in Sampling, 5 1.5 Adaptive and Nonadaptive Designs, 6 1.6 Some Sampling History, 7 PART I BASIC SAMPLING 9 2 Simple Random Sampling 11 2.1 Selecting a Simple Random Sample, 11 2.2 Estimating the Population Mean, 13 2.3 Estimating the Population Total, 16 2.4 Some Underlying Ideas, 17 2.5 Random Sampling with Replacement, 19 2.6 Derivations for Random Sampling, 20 2.7 Model-Based Approach to Sampling, 22 2.8 Computing Notes, 26 Entering Data in R, 26 Sample Estimates, 27 Simulation, 28 Further Comments on the Use of Simulation, 32 Exercises, 35 3 Confidence Intervals 39 3.1 Confidence Interval for the Population Mean or Total, 39 3.2 Finite-Population Central Limit Theorem, 41 3.3 Sampling Distributions, 43 3.4 Computing Notes, 44 Confidence Interval Computation, 44 Simulations Illustrating the Approximate Normality of a Sampling Distribution with Small n and N , 45 Daily Precipitation Data, 46 Exercises, 50 4 Sample Size 53 4.1 Sample Size for Estimating a Population Mean, 54 4.2 Sample Size for Estimating a Population Total, 54 4.3 Sample Size for Relative Precision, 55 Exercises, 56 5 Estimating Proportions, Ratios, and Subpopulation Means 57 5.1 Estimating a Population Proportion, 58 5.2 Confidence Interval for a Proportion, 58 5.3 Sample Size for Estimating a Proportion, 59 5.4 Sample Size for Estimating Several Proportions Simultaneously, 60 5.5 Estimating a Ratio, 62 5.6 Estimating a Mean, Total, or Proportion of a Subpopulation, 62 Estimating a Subpopulation Mean, 63 Estimating a Proportion for a Subpopulation, 64 Estimating a Subpopulation Total, 64 Exercises, 65 6 Unequal Probability Sampling 67 6.1 Sampling with Replacement: The Hansen-Hurwitz Estimator, 67 6.2 Any Design: The Horvitz-Thompson Estimator, 69 6.3 Generalized Unequal-Probability Estimator, 72 6.4 Small Population Example, 73 6.5 Derivations and Comments, 75 6.6 Computing Notes, 78 Writing an R Function to Simulate a Sampling Strategy, 82 Comparing Sampling Strategies, 84 Exercises, 88 PART II MAKING THE BEST USE OF SURVEY DATA 91 7 Auxiliary Data and Ratio Estimation 93 7.1 Ratio Estimator, 94 7.2 Small Population Illustrating Bias, 97 7.3 Derivations and Approximations for the Ratio Estimator, 99 7.4 Finite-Population Central Limit Theorem for the Ratio Estimator, 101 7.5 Ratio Estimation with Unequal Probability Designs, 102 7.6 Models in Ratio Estimation, 105 Types of Estimators for a Ratio, 109 7.7 Design Implications of Ratio Models, 109 7.8 Computing Notes, 110 Exercises, 112 8 Regression Estimation 115 8.1 Linear Regression Estimator, 116 8.2 Regression Estimation with Unequal Probability Designs, 118 8.3 Regression Model, 119 8.4 Multiple Regression Models, 120 8.5 Design Implications of Regression Models, 123 Exercises, 124 9 The Sufficient Statistic in Sampling 125 9.1 The Set of Distinct, Labeled Observations, 125 9.2 Estimation in Random Sampling with Replacement, 126 9.3 Estimation in Probability-Proportional-to-Size Sampling, 127 9.4 Comments on the Improved Estimates, 128 10 Design and Model 131 10.1 Uses of Design and Model in Sampling, 131 10.2 Connections between the Design and Model Approaches, 132 10.3 Some Comments, 134 10.4 Likelihood Function in Sampling, 135 PART III SOME USEFUL DESIGNS 139 11 Stratified Sampling 141 11.1 Estimating the Population Total, 142 With Any Stratified Design, 142 With Stratified Random Sampling, 143 11.2 Estimating the Population Mean, 144 With Any Stratified Design, 144 With Stratified Random Sampling, 144 11.3 Confidence Intervals, 145 11.4 The Stratification Principle, 146 11.5 Allocation in Stratified Random Sampling, 146 11.6 Poststratification, 148 11.7 Population Model for a Stratified Population, 149 11.8 Derivations for Stratified Sampling, 149 Optimum Allocation, 149 Poststratification Variance, 150 11.9 Computing Notes, 151 Exercises, 155 12 Cluster and Systematic Sampling 157 12.1 Primary Units Selected by Simple Random Sampling, 159 Unbiased Estimator, 159 Ratio Estimator, 160 12.2 Primary Units Selected with Probabilities Proportional to Size, 161 Hansen-Hurwitz (PPS) Estimator, 161 Horvitz-Thompson Estimator, 161 12.3 The Basic Principle, 162 12.4 Single Systematic Sample, 162 12.5 Variance and Cost in Cluster and Systematic Sampling, 163 12.6 Computing Notes, 166 Exercises, 169 13 Multistage Designs 171 13.1 Simple Random Sampling at Each Stage, 173 Unbiased Estimator, 173 Ratio Estimator, 175 13.2 Primary Units Selected with Probability Proportional to Size, 176 13.3 Any Multistage Design with Replacement, 177 13.4 Cost and Sample Sizes, 177 13.5 Derivations for Multistage Designs, 179 Unbiased Estimator, 179 Ratio Estimator, 181 Probability-Proportional-to-Size Sampling, 181 More Than Two Stages, 181 Exercises, 182 14 Double or Two-Phase Sampling 183 14.1 Ratio Estimation with Double Sampling, 184 14.2 Allocation in Double Sampling for Ratio Estimation, 186 14.3 Double Sampling for Stratification, 186 14.4 Derivations for Double Sampling, 188 Approximate Mean and Variance: Ratio Estimation, 188 Optimum Allocation for Ratio Estimation, 189 Expected Value and Variance: Stratification, 189 14.5 Nonsampling Errors and Double Sampling, 190 Nonresponse, Selection Bias, or Volunteer Bias, 191 Double Sampling to Adjust for Nonresponse: Callbacks, 192 Response Modeling and Nonresponse Adjustments, 193 14.6 Computing Notes, 195 Exercises, 197 PART IV METHODS FOR ELUSIVE AND HARD-TO-DETECT POPULATIONS 199 15 Network Sampling and Link-Tracing Designs 201 15.1 Estimation of the Population Total or Mean, 202 Multiplicity Estimator, 202 Horvitz-Thompson Estimator, 204 15.2 Derivations and Comments, 207 15.3 Stratification in Network Sampling, 208 15.4 Other Link-Tracing Designs, 210 15.5 Computing Notes, 212 Exercises, 213 16 Detectability and Sampling 215 16.1 Constant Detectability over a Region, 215 16.2 Estimating Detectability, 217 16.3 Effect of Estimated Detectability, 218 16.4 Detectability with Simple Random Sampling, 219 16.5 Estimated Detectability and Simple Random Sampling, 220 16.6 Sampling with Replacement, 222 16.7 Derivations, 222 16.8 Unequal Probability Sampling of Groups with Unequal Detection Probabilities, 224 16.9 Derivations, 225 Exercises, 227 17 Line and Point Transects 229 17.1 Density Estimation Methods for Line Transects, 230 17.2 Narrow-Strip Method, 230 17.3 Smooth-by-Eye Method, 233 17.4 Parametric Methods, 234 17.5 Nonparametric Methods, 237 Estimating f (0) by the Kernel Method, 237 Fourier Series Method, 239 17.6 Designs for Selecting Transects, 240 17.7 Random Sample of Transects, 240 Unbiased Estimator, 241 Ratio Estimator, 243 17.8 Systematic Selection of Transects, 244 17.9 Selection with Probability Proportional to Length, 244 17.10 Note on Estimation of Variance for the Kernel Method, 246 17.11 Some Underlying Ideas about Line Transects, 247 Line Transects and Detectability Functions, 247 Single Transect, 249 Average Detectability, 249 Random Transect, 250 Average Detectability and Effective Area, 251 Effect of Estimating Detectability, 252 Probability Density Function of an Observed Distance, 253 17.12 Detectability Imperfect on the Line or Dependent on Size, 255 17.13 Estimation Using Individual Detectabilities, 255 Estimation of Individual Detectabilities, 256 17.14 Detectability Functions other than Line Transects, 257 17.15 Variable Circular Plots or Point Transects, 259 Exercise, 260 18 Capture-Recapture Sampling 263 18.1 Single Recapture, 264 18.2 Models for Simple Capture-Recapture, 266 18.3 Sampling Design in Capture-Recapture: Ratio Variance Estimator, 267 Random Sampling with Replacement of Detectability Units, 269 Random Sampling without Replacement, 270 18.4 Estimating Detectability with Capture-Recapture Methods, 271 18.5 Multiple Releases, 272 18.6 More Elaborate Models, 273 Exercise, 273 19 Line-Intercept Sampling 275 19.1 Random Sample of Lines: Fixed Direction, 275 19.2 Lines of Random Position and Direction, 280 Exercises, 282 PART V SPATIAL SAMPLING 283 20 Spatial Prediction or Kriging 285 20.1 Spatial Covariance Function, 286 20.2 Linear Prediction (Kriging), 286 20.3 Variogram, 289 20.4 Predicting the Value over a Region, 291 20.5 Derivations and Comments, 292 20.6 Computing Notes, 296 Exercise, 299 21 Spatial Designs 301 21.1 Design for Local Prediction, 302 21.2 Design for Prediction of Mean of Region, 302 22 Plot Shapes and Observational Methods 305 22.1 Observations from Plots, 305 22.2 Observations from Detectability Units, 307 22.3 Comparisons of Plot Shapes and Detectability Methods, 308 PART VI ADAPTIVE SAMPLING 313 23 Adaptive Sampling Designs 315 23.1 Adaptive and Conventional Designs and Estimators, 315 23.2 Brief Survey of Adaptive Sampling, 316 24 Adaptive Cluster Sampling 319 24.1 Designs, 321 Initial Simple Random Sample without Replacement, 322 Initial Random Sample with Replacement, 323 24.2 Estimators, 323 Initial Sample Mean, 323 Estimation Using Draw-by-Draw Intersections, 323 Estimation Using Initial Intersection Probabilities, 325 24.3 When Adaptive Cluster Sampling Is Better than Simple Random Sampling, 327 24.4 Expected Sample Size, Cost, and Yield, 328 24.5 Comparative Efficiencies of Adaptive and Conventional Sampling, 328 24.6 Further Improvement of Estimators, 330 24.7 Derivations, 333 24.8 Data for Examples and Figures, 336 Exercises, 337 25 Systematic and Strip Adaptive Cluster Sampling 339 25.1 Designs, 341 25.2 Estimators, 343 Initial Sample Mean, 343 Estimator Based on Partial Selection Probabilities, 344 Estimator Based on Partial Inclusion Probabilities, 345 25.3 Calculations for Adaptive Cluster Sampling Strategies, 347 25.4 Comparisons with Conventional Systematic and Cluster Sampling, 349 25.5 Derivations, 350 25.6 Example Data, 352 Exercises, 352 26 Stratified Adaptive Cluster Sampling 353 26.1 Designs, 353 26.2 Estimators, 356 Estimators Using Expected Numbers of Initial Intersections, 357 Estimator Using Initial Intersection Probabilities, 359 26.3 Comparisons with Conventional Stratified Sampling, 362 26.4 Further Improvement of Estimators, 364 26.5 Example Data, 367 Exercises, 367 Answers to Selected Exercises 369 References 375 Author Index 395 Subject Index 399
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