Sampling

by Thompson, Steven K.

• ISBN13: 9780470402313
• ISBN10: 0470402318
• Edition: 3rd
• Format: Hardcover
• Copyright: 2012-03-13
• Publisher: Wiley

Summary

The Third Edition retains the general organization of the prior two editions, but it incorporates new material throughout the text.  The book is organized into six parts: Part I covers basic sampling from simple random sampling to unequal probability sampling; Part II treats the use of auxiliary data with ratio and regression estimation and looks at the ideas of sufficient data, model, and design in practical sampling; Part III covers major useful designs such as stratified, cluster and systematic, multistage, and double and network sampling; Part IV examines detectability methods for elusive populations, and basic problems in detectability, visibility, and catchability are discussed; Part V concerns spatial sampling with the prediction methods of geostatistics, considerations of efficient spatial designs, and comparisons of different observational methods including plot shapes and detection aspects; and Part VI introduces adaptive sampling designs in which the sampling procedure depends on what is observed during the survey.  For this new edition, the author has focused on thoroughly updating the book with a special emphasis on the first 14 chapters since these topics are invariably covered in basic sampling courses.  The author has also implemented new approaches to explain the various techniques in the book, and as a result, new examples and explanations have been added throughout.  In an effort to improve the presentation and visualization of the book, new figures as well as replacement figures for previously existing figures have been added.  This book has continuously stood out from other sampling texts since the figures evoke the idea of each sampling design.  The new figures will help readers to better visualize and understand the underlying concepts such as the different sampling strategies.

Author Biography

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).

Table of Contents

Preface	p. xv
Preface to the Second Edition	p. xvii
Preface to the First Edition	p. xix
Introduction	p. 1
Basic Ideas of Sampling and Estimation	p. 2
Sampling Units	p. 4
Sampling and Nonsampling Errors	p. 5
Models in Sampling	p. 5
Adaptive and Nonadaptive Designs	p. 6
Some Sampling History	p. 7
Basic Sampling	p. 9
Simple Random Sampling	p. 11
Selecting a Simple Random Sample	p. 11
Estimating the Population Mean	p. 13
Estimating the Population Total	p. 16
Some Underlying Ideas	p. 17
Random Sampling with Replacement	p. 19
Derivations for Random Sampling	p. 20
Model-Based Approach to Sampling	p. 22
Computing Notes	p. 26
Entering Data in R	p. 26
Sample Estimates	p. 27
Simulation	p. 28
Further Comments on the Use of Simulation	p. 32
Exercises	p. 35
Confidence Intervals	p. 39
Confidence Interval for the Population Mean or Total	p. 39
Finite-Population Central Limit Theorem	p. 41
Sampling Distributions	p. 43
Computing Notes	p. 44
Confidence Interval Computation	p. 44
Simulations Illustrating the Approximate Normality of a Sampling Distribution with Small n and N	p. 45
Daily Precipitation Data	p. 46
Exercises	p. 50
Sample Size	p. 53
Sample Size for Estimating a Population Mean	p. 54
Sample Size for Estimating a Population Total	p. 54
Sample Size for Relative Precision	p. 55
Exercises	p. 56
Estimating Proportions, Ratios, and Subpopulation Means	p. 57
Estimating a Population Proportion	p. 58
Confidence Interval for a Proportion	p. 58
Sample Size for Estimating a Proportion	p. 59
Sample Size for Estimating Several Proportions Simultaneously	p. 60
Estimating a Ratio	p. 62
Estimating a Mean, Total, or Proportion of a Subpopulation	p. 62
Estimating a Subpopulation Mean	p. 63
Estimating a Proportion for a Subpopulation	p. 64
Estimating a Subpopulation Total	p. 64
Exercises	p. 65
Unequal Probability Sampling	p. 67
Sampling with Replacement: The Hansen-Hurwitz Estimator	p. 67
Any Design: The Horvitz-Thompson Estimator	p. 69
Generalized Unequal-Probability Estimator	p. 72
Small Population Example	p. 73
Derivations and Comments	p. 75
Computing Notes	p. 78
Writing an R Function to Simulate a Sampling Strategy	p. 82
Comparing Sampling Strategies	p. 84
Exercises	p. 88
Making The Best Use Of Survey Data	p. 91
Auxiliary Data and Ratio Estimation	p. 93
Ratio Estimator	p. 94
Small Population Illustrating Bias	p. 97
Derivations and Approximations for the Ratio Estimator	p. 99
Finite-Population Central Limit Theorem for the Ratio Estimator	p. 101
Ratio Estimation with Unequal Probability Designs	p. 102
Models in Ratio Estimation	p. 105
Types of Estimators for a Ratio	p. 109
Design Implications of Ratio Models	p. 109
Computing Notes	p. 110
Exercises	p. 112
Regression Estimation	p. 115
Linear Regression Estimator	p. 116
Regression Estimation with Unequal Probability Designs	p. 118
Regression Model	p. 119
Multiple Regression Models	p. 120
Design Implications of Regression Models	p. 123
Exercises	p. 124
The Sufficient Statistic in Sampling	p. 125
The Set of Distinct, Labeled Observations	p. 125
Estimation in Random Sampling with Replacement	p. 126
Estimation in Probability-Proportional-to-Size Sampling	p. 127
Comments on the Improved Estimates	p. 128
Design and Model	p. 131
Uses of Design and Model in Sampling	p. 131
Connections between the Design and Model Approaches	p. 132
Some Comments	p. 134
Likelihood Function in Sampling	p. 135
Some Useful Designs	p. 139
Stratified Sampling	p. 141
Estimating the Population Total	p. 142
With Any Stratified Design	p. 142
With Stratified Random Sampling	p. 143
Estimating the Population Mean	p. 144
With Any Stratified Design	p. 144
With Stratified Random Sampling	p. 144
Confidence Intervals	p. 145
The Stratification Principle	p. 146
Allocation in Stratified Random Sampling	p. 146
Poststratification	p. 148
Population Model for a Stratified Population	p. 149
Derivations for Stratified Sampling	p. 149
Optimum Allocation	p. 149
Poststratification Variance	p. 150
Computing Notes	p. 151
Exercises	p. 155
Cluster and Systematic Sampling	p. 157
Primary Units Selected by Simple Random Sampling	p. 159
Unbiased Estimator	p. 159
Ratio Estimator	p. 160
Primary Units Selected with Probabilities Proportional to Size	p. 161
Hansen-Hurwitz (PPS) Estimator	p. 161
Horvitz-Thompson Estimator	p. 161
The Basic Principle	p. 162
Single Systematic Sample	p. 162
Variance and Cost in Cluster and Systematic Sampling	p. 163
Computing Notes	p. 166
Exercises	p. 169
Multistage Designs	p. 171
Simple Random Sampling at Each Stage	p. 173
Unbiased Estimator	p. 173
Ratio Estimator	p. 175
Primary Units Selected with Probability Proportional to Size	p. 176
Any Multistage Design with Replacement	p. 177
Cost and Sample Sizes	p. 177
Derivations for Multistage Designs	p. 179
Unbiased Estimator	p. 179
Ratio Estimator	p. 181
Probability-Proportional-to-Size Sampling	p. 181
More Than Two Stages	p. 181
Exercises	p. 182
Double or Two-Phase Sampling	p. 183
Ratio Estimation with Double Sampling	p. 184
Allocation in Double Sampling for Ratio Estimation	p. 186
Double Sampling for Stratification	p. 186
Derivations for Double Sampling	p. 188
Approximate Mean and Variance: Ratio Estimation	p. 188
Optimum Allocation for Ratio Estimation	p. 189
Expected Value and Variance: Stratification	p. 189
Nonsampling Errors and Double Sampling	p. 190
Nonresponse, Selection Bias, or Volunteer Bias	p. 191
Double Sampling to Adjust for Nonresponse: Callbacks	p. 192
Response Modeling and Nonresponse Adjustments	p. 193
Computing Notes	p. 195
Exercises	p. 197
Methods For Elusive And Hard-To-Detect Populations	p. 199
Network Sampling and Link-Tracing Designs	p. 201
Estimation of the Population Total or Mean	p. 202
Multiplicity Estimator	p. 202
Horvitz-Thompson Estimator	p. 204
Derivations and Comments	p. 207
Stratification in Network Sampling	p. 208
Other Link-Tracing Designs	p. 210
Computing Notes	p. 212
Exercises	p. 213
Detectability and Sampling	p. 215
Constant Detectability over a Region	p. 215
Estimating Detectability	p. 217
Effect of Estimated Detectability	p. 218
Detectability with Simple Random Sampling	p. 219
Estimated Detectability and Simple Random Sampling	p. 220
Sampling with Replacement	p. 222
Derivations	p. 222
Unequal Probability Sampling of Groups with Unequal Detection Probabilities	p. 224
Derivations	p. 225
Exercises	p. 227
Line and Point Transects	p. 229
Density Estimation Methods for Line Transects	p. 230
Narrow-Strip Method	p. 230
Smooth-by-Eye Method	p. 233
Parametric Methods	p. 234
Nonparametric Methods	p. 237
Estimating f (0) by the Kernel Method	p. 237
Fourier Series Method	p. 239
Designs for Selecting Transects	p. 240
Random Sample of Transects	p. 240
Unbiased Estimator	p. 241
Ratio Estimator	p. 243
Systematic Selection of Transects	p. 244
Selection with Probability Proportional to Length	p. 244
Note on Estimation of Variance for the Kernel Method	p. 246
Some Underlying Ideas about Line Transects	p. 247
Line Transects and Detectability Functions	p. 247
Single Transect	p. 249
Average Detectability	p. 249
Random Transect	p. 250
Average Detectability and Effective Area	p. 251
Effect of Estimating Detectability	p. 252
Probability Density Function of an Observed Distance	p. 253
Detectability Imperfect on the Line or Dependent on Size	p. 255
Estimation Using Individual Detectabilities	p. 255
Estimation of Individual Detectabilities	p. 256
Detectability Functions other than Line Transects	p. 257
Variable Circular Plots or Point Transects	p. 259
Exercise	p. 260
Capture-Recapture Sampling	p. 263
Single Recapture	p. 264
Models for Simple Capture-Recapture	p. 266
Sampling Design in Capture-Recapture: Ratio Variance Estimator	p. 267
Random Sampling with Replacement of Detectability Units	p. 269
Random Sampling without Replacement	p. 270
Estimating Detectability with Capture-Recapture Methods	p. 271
Multiple Releases	p. 272
More Elaborate Models	p. 273
Exercise	p. 273
Line-Intercept Sampling	p. 275
Random Sample of Lines: Fixed Direction	p. 275
Lines of Random Position and Direction	p. 280
Exercises	p. 282
Spatial Sampling	p. 283
Spatial Prediction or Kriging	p. 285
Spatial Covariance Function	p. 286
Linear Prediction (Kriging)	p. 286
Variogram	p. 289
Predicting the Value over a Region	p. 291
Derivations and Comments	p. 292
Computing Notes	p. 296
Exercise	p. 299
Spatial Designs	p. 301
Design for Local Prediction	p. 302
Design for Prediction of Mean of Region	p. 302
Plot Shapes and Observational Methods	p. 305
Observations from Plots	p. 305
Observations from Detectability Units	p. 307
Comparisons of Plot Shapes and Detectability Methods	p. 308
Adaptive Sampling	p. 313
Adaptive Sampling Designs	p. 315
Adaptive and Conventional Designs and Estimators	p. 315
Brief Survey of Adaptive Sampling	p. 316
Adaptive Cluster Sampling	p. 319
Designs	p. 321
Initial Simple Random Sample without Replacement	p. 322
Initial Random Sample with Replacement	p. 323
Estimators	p. 323
Initial Sample Mean	p. 323
Estimation Using Draw-by-Draw Intersections	p. 323
Estimation Using Initial Intersection Probabilities	p. 325
When Adaptive Cluster Sampling Is Better than Simple Random Sampling	p. 327
Expected Sample Size, Cost, and Yield	p. 328
Comparative Efficiencies of Adaptive and Conventional Sampling	p. 328
Further Improvement of Estimators	p. 330
Derivations	p. 333
Data for Examples and Figures	p. 336
Exercises	p. 337
Systematic and Strip Adaptive Cluster Sampling	p. 339
Designs	p. 341
Estimators	p. 343
Initial Sample Mean	p. 343
Estimator Based on Partial Selection Probabilities	p. 344
Estimator Based on Partial Inclusion Probabilities	p. 345
Calculations for Adaptive Cluster Sampling Strategies	p. 347
Comparisons with Conventional Systematic and Cluster Sampling	p. 349
Derivations	p. 350
Example Data	p. 352
Exercises	p. 352
Stratified Adaptive Cluster Sampling	p. 353
Designs	p. 353
Estimators	p. 356
Estimators Using Expected Numbers of Initial Intersections	p. 357
Estimator Using Initial Intersection Probabilities	p. 359
Comparisons with Conventional Stratified Sampling	p. 362
Further Improvement of Estimators	p. 364
Example Data	p. 367
Exercises	p. 367
Answers to Selected Exercises	p. 369
References	p. 375
Author Index	p. 395
Subject Index	p. 399
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