Sampling
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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
