Sampling: Design and Analysis

Front Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Contents......Page 4
Preface......Page 10
1.1 A Sample Controversy......Page 14
1.2 Requirements of a Good Sample......Page 16
1.3 Selection Bias......Page 18
1.4 Measurement Error......Page 22
1.5 Questionnaire Design......Page 24
1.6 Sampling and Nonsampling Errors......Page 29
Key Terms......Page 31
1.7 Exercises......Page 32
2.1 Types of Probability Samples......Page 38
2.2 Framework for Probability Sampling......Page 41
2.3 Simple Random Sampling......Page 46
2.4 Sampling Weights......Page 52
2.5 Confidence Intervals......Page 53
2.6 Sample Size Estimation......Page 59
2.7 Systematic Sampling......Page 63
2.8 Randomization Theory Results for Simple Random Sampling......Page 64
2.9 A Prediction Approach for Simple Random Sampling......Page 67
2.10 When Should a Simple Random Sample Be Used?......Page 71
2.11 Chapter Summary......Page 72
Key Terms......Page 73
2.12 Exercises......Page 74
3.1 What Is Stratified Sampling?......Page 86
3.2 Theory of Stratified Sampling......Page 90
3.3 Sampling Weights in Stratified Random Sampling......Page 95
3.4.1 Proportional Allocation......Page 98
3.4.2 Optimal Allocation......Page 100
3.4.3 Allocation for Specified Precision within Strata......Page 103
3.5 Defining Strata......Page 104
3.6 Model-Based Inference for Stratified Sampling......Page 108
3.7 Quota Sampling......Page 109
3.8 Chapter Summary......Page 112
For Further Reading......Page 113
3.9 Exercises......Page 114
CHAPTER 4 Ratio and Regression Estimation......Page 130
4.1 Ratio Estimation in a Simple Random Sample......Page 131
4.1.1 Why Use Ratio Estimation?......Page 132
4.1.2 Bias and Mean Squared Error of Ratio Estimators......Page 135
4.1.3 Ratio Estimation with Proportions......Page 142
4.1.4 Ratio Estimation Using Weight Adjustments......Page 144
4.2 Estimation in Domains......Page 146
4.3.1 Using a Straight-Line Model......Page 151
4.3.2 Difference Estimation......Page 154
4.4 Poststratification......Page 155
4.5 Ratio Estimation with Stratified Samples......Page 157
4.6 Model-Based Theory for Ratio and Regression Estimation......Page 159
4.6.1 A Model for Ratio Estimation......Page 160
4.6.2 A Model for Regression Estimation......Page 164
4.6.3 Differences Between Model-Based and Design-Based Estimators......Page 166
Key Terms......Page 167
4.8 Exercises......Page 168
CHAPTER 5 Cluster Sampling with Equal Probabilities......Page 178
5.1 Notation for Cluster Sampling......Page 181
5.2.1 Clusters of Equal Sizes: Estimation......Page 183
5.2.2 Clusters of Equal Sizes: Theory......Page 186
5.2.3 Clusters of Unequal Sizes......Page 191
5.3 Two-Stage Cluster Sampling......Page 195
5.4.1 Choosing the psu Size......Page 204
5.4.2 Choosing Subsampling Sizes......Page 206
5.4.3 Choosing the Sample Size (Number of psus)......Page 208
5.5 Systematic Sampling......Page 209
5.6 Model-Based Inference in Cluster Sampling......Page 213
5.6.1 Estimation Using Models......Page 214
5.7 Chapter Summary......Page 218
5.8 Exercises......Page 220
CHAPTER 6 Sampling with Unequal Probabilities......Page 232
6.1 Sampling One Primary Sampling Unit......Page 234
6.2.1 Selecting Primary Sampling Units......Page 238
6.2.2 Theory of Estimation......Page 241
6.2.3 Designing the Selection Probabilities......Page 244
6.2.4 Weights in Unequal-Probability Sampling with Replacement......Page 247
6.3 Two-Stage Sampling with Replacement......Page 248
6.4 Unequal-Probability Sampling Without Replacement......Page 251
6.4.1 The Horvitz–Thompson Estimator for One-Stage Sampling......Page 253
6.4.2 Selecting the psus......Page 257
6.4.3 The Horvitz–Thompson Estimator for Two-Stage Sampling......Page 258
6.4.4 Weights in Unequal-Probability Samples......Page 259
6.5 Examples of Unequal-Probability Samples......Page 262
6.6 Randomization Theory Results and Proofs......Page 267
6.7 Models and Unequal-Probability Sampling......Page 275
6.8 Chapter Summary......Page 278
Key Terms......Page 279
6.9 Exercises......Page 280
7.1.1 Building Blocks for Surveys......Page 294
7.1.3 Simplicity in Survey Design......Page 297
7.2.1 Constructing Sampling Weights......Page 298
7.2.2 Self-Weighting and Non-Self-Weighting Samples......Page 300
7.3 Estimating a Distribution Function......Page 301
7.4.1 Univariate Plots......Page 307
7.4.2 Bivariate Plots......Page 317
7.5 Design Effects......Page 322
7.5.2 Design Effects and Sample Sizes......Page 324
7.6 The National Crime Victimization Survey......Page 325
7.7 Sampling and Design of Experiments......Page 330
Key Terms......Page 332
7.9 Exercises......Page 333
CHAPTER 8 Nonresponse......Page 342
8.1 Effects of Ignoring Nonresponse......Page 343
8.2 Designing Surveys to Reduce Nonsampling Errors......Page 345
8.3 Callbacks and Two-Phase Sampling......Page 349
8.4 Mechanisms for Nonresponse......Page 351
8.5.1 Weighting Class Adjustment......Page 353
8.5.2 Poststratification......Page 355
8.5.3 Advantages and Disadvantages of Weighting Adjustments......Page 358
8.6 Imputation......Page 359
8.6.2 Cell Mean Imputation......Page 360
8.6.3 Hot-Deck Imputation......Page 361
8.6.4 Regression Imputation......Page 362
8.6.6 Multiple Imputation......Page 363
8.7 Parametric Models for Nonresponse......Page 364
8.8 What Is an Acceptable Response Rate?......Page 367
Key Terms......Page 369
8.10 Exercises......Page 370
CHAPTER 9 Variance Estimation in Complex Surveys......Page 378
9.1 Linearization (Taylor Series) Methods......Page 379
9.2.1 Replicating the Survey Design......Page 383
9.2.2 Dividing the Sample into Random Groups......Page 384
9.3.1 Balanced Repeated Replication (BRR)......Page 386
9.3.2 Jackknife......Page 393
9.3.3 Bootstrap......Page 397
9.4 Generalized Variance Functions......Page 399
9.5.1 Confidence Intervals for Smooth Functions of Population Totals......Page 401
9.5.2 Confidence Intervals for Population Quantiles......Page 402
9.6 Chapter Summary......Page 405
For Further Reading......Page 406
9.7 Exercises......Page 407
10.1 Chi-Square Tests with Multinomial Sampling......Page 414
10.1.1 Testing Independence of Factors......Page 416
10.1.2 Testing Homogeneity of Proportions......Page 417
10.1.3 Testing Goodness of Fit......Page 418
10.2 Effects of Survey Design on Chi-Square Tests......Page 420
10.2.1 Contingency Tables for Data from Complex Surveys......Page 421
10.2.2 Effects on Hypothesis Tests and Confidence Intervals......Page 422
10.3.1 Wald Tests......Page 424
10.3.2 Rao–Scott Tests......Page 426
10.3.3 Model-Based Methods for χ[sup(2)] Tests......Page 429
10.4.1 Loglinear Models with Multinomial Sampling......Page 430
10.4.2 Loglinear Models in a Complex Survey......Page 432
10.5 Chapter Summary......Page 434
10.6 Exercises......Page 435
CHAPTER 11 Regression with Complex Survey Data......Page 442
11.1 Model-Based Regression in Simple Random Samples......Page 443
11.2 Regression in Complex Surveys......Page 447
11.2.1 Point Estimation......Page 448
11.2.2 Standard Errors......Page 451
11.2.3 Multiple Regression......Page 454
11.2.4 Regression Using Weights versus Weighted Least Squares......Page 456
11.2.5 Software for Regression in Complex Surveys......Page 457
11.3 Using Regression to Compare Domain Means......Page 458
11.4 Should Weights Be Used in Regression?......Page 460
11.5 Mixed Models for Cluster Samples......Page 466
11.6 Logistic Regression......Page 468
11.7 Generalized Regression Estimation for Population Totals......Page 470
For Further Reading......Page 474
11.9 Exercises......Page 475
CHAPTER 12 Two-Phase Sampling......Page 482
12.1 Theory for Two-Phase Sampling......Page 485
12.2 Two-Phase Sampling with Stratification......Page 486
12.3.1 Two-Phase Sampling with Ratio Estimation......Page 490
12.3.2 Generalized Regression Estimation in Two-Phase Sampling......Page 492
12.4 Jackknife Variance Estimation for Two-Phase Sampling......Page 494
12.5 Designing a Two-Phase Sample......Page 495
12.5.1 Two-Phase Sampling with Stratification......Page 496
Key Terms......Page 498
12.7 Exercises......Page 499
13.1 Capture–Recapture Estimation......Page 508
13.1.1 Contingency Tables for Capture–Recapture Experiments......Page 510
13.1.2 Confidence Intervals for N......Page 511
13.1.3 Using Capture–Recapture on Lists......Page 512
13.2 Multiple Recapture Estimation......Page 514
13.4 Exercises......Page 518
CHAPTER 14 Rare Populations and Small Area Estimation......Page 524
14.1 Sampling Rare Populations......Page 525
14.1.2 Two-Phase Sampling......Page 526
14.1.4 Multiple Frame Surveys......Page 527
14.1.5 Network or Multiplicity Sampling......Page 529
14.1.7 Sequential Sampling......Page 530
14.2 Small Area Estimation......Page 531
14.2.1 Direct Estimators......Page 532
14.2.2 Synthetic and Composite Estimators......Page 533
14.2.3 Model-Based Estimators......Page 534
14.3 Chapter Summary......Page 535
14.4 Exercises......Page 536
CHAPTER 15 Survey Quality......Page 540
15.1.1 Measuring Coverage and Coverage Bias......Page 542
15.1.2 Coverage and Survey Mode......Page 544
15.1.3 Improving Coverage......Page 545
15.2 Nonresponse Error......Page 546
15.3 Measurement Error......Page 548
15.3.1 Measuring and Modeling Measurement Error......Page 550
15.3.2 Reducing Measurement Error......Page 552
15.4.1 Nonresponse and Measurement Error......Page 553
15.4.2 Randomized Response......Page 554
15.5 Processing Error......Page 555
15.6 Total Survey Quality......Page 556
For Further Reading......Page 558
15.8 Exercises......Page 559
A.1: Probability......Page 562
A.2: Random Variables and Expected Value......Page 565
A.3: Conditional Probability......Page 569
A.4: Conditional Expectation......Page 571
References......Page 576
Author Index......Page 600
Subject Index......Page 605