Sampling: Design and Analysis

609 Pages·2009·4.96 MB·English

by  Sharon L. Lohr

BrooksCole:Lohr November11,2009 22:19
Sampling:
Design and Analysis
Second Edition
SharonL.Lohr
ArizonaStateUniversity
i
BrooksCole:Lohr November11,2009 22:19
Sampling: Design and Analysis, Second
Edition
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Sharon L. Lohr
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BrooksCole:Lohr November11,2009 22:19
Contents
Preface ix
1
Introduction 1
CHAPTER
1.1 ASampleControversy 1
1.2 RequirementsofaGoodSample 3
1.3 SelectionBias 5
1.4 MeasurementError 9
1.5 QuestionnaireDesign 11
1.6 SamplingandNonsamplingErrors 16
1.7 Exercises 19
2
Simple Probability Samples 25
CHAPTER
2.1 TypesofProbabilitySamples 25
2.2 FrameworkforProbabilitySampling 28
2.3 SimpleRandomSampling 33
2.4 SamplingWeights 39
2.5 ConfidenceIntervals 40
2.6 SampleSizeEstimation 46
2.7 SystematicSampling 50
2.8 RandomizationTheoryResultsforSimpleRandomSampling 51
2.9 APredictionApproachforSimpleRandomSampling 54
2.10 WhenShouldaSimpleRandomSampleBeUsed? 58
2.11 ChapterSummary 59
2.12 Exercises 61
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iv
Contents
3
Stratified Sampling 73
CHAPTER
3.1 WhatIsStratifiedSampling? 73
3.2 TheoryofStratifiedSampling 77
3.3 SamplingWeightsinStratifiedRandomSampling 82
3.4 AllocatingObservationstoStrata 85
3.5 DefiningStrata 91
3.6 Model-BasedInferenceforStratifiedSampling 95
3.7 QuotaSampling 96
3.8 ChapterSummary 99
3.9 Exercises 101
4
Ratio and Regression Estimation 117
CHAPTER
4.1 RatioEstimationinaSimpleRandomSample 118
4.2 EstimationinDomains 133
4.3 RegressionEstimationinSimpleRandomSampling 138
4.4 Poststratification 142
4.5 RatioEstimationwithStratifiedSamples 144
4.6 Model-BasedTheoryforRatioandRegressionEstimation 146
4.7 ChapterSummary 154
4.8 Exercises 155
5
Cluster Sampling with Equal Probabilities 165
CHAPTER
5.1 NotationforClusterSampling 168
5.2 One-StageClusterSampling 170
5.3 Two-StageClusterSampling 182
5.4 DesigningaClusterSample 191
5.5 SystematicSampling 196
5.6 Model-BasedInferenceinClusterSampling 200
5.7 ChapterSummary 205
5.8 Exercises 207
BrooksCole:Lohr November11,2009 22:19
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Contents
6
Sampling with Unequal Probabilities 219
CHAPTER
6.1 SamplingOnePrimarySamplingUnit 221
6.2 One-StageSamplingwithReplacement 225
6.3 Two-StageSamplingwithReplacement 235
6.4 Unequal-ProbabilitySamplingWithoutReplacement 238
6.5 ExamplesofUnequal-ProbabilitySamples 249
6.6 RandomizationTheoryResultsandProofs 254
6.7 ModelsandUnequal-ProbabilitySampling 262
6.8 ChapterSummary 265
6.9 Exercises 267
7
Complex Surveys 281
CHAPTER
7.1 AssemblingDesignComponents 281
7.2 SamplingWeights 285
7.3 EstimatingaDistributionFunction 288
7.4 PlottingDatafromaComplexSurvey 294
7.5 DesignEffects 309
7.6 TheNationalCrimeVictimizationSurvey 312
7.7 SamplingandDesignofExperiments 317
7.8 ChapterSummary 319
7.9 Exercises 320
8
Nonresponse 329
CHAPTER
8.1 EffectsofIgnoringNonresponse 330
8.2 DesigningSurveystoReduceNonsamplingErrors 332
8.3 CallbacksandTwo-PhaseSampling 336
8.4 MechanismsforNonresponse 338
8.5 WeightingMethodsforNonresponse 340
8.6 Imputation 346
8.7 ParametricModelsforNonresponse 351
BrooksCole:Lohr November11,2009 22:19
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Contents
8.8 WhatIsanAcceptableResponseRate? 354
8.9 ChapterSummary 356
8.10 Exercises 357
9
Variance Estimation in Complex Surveys 365
CHAPTER
9.1 Linearization(TaylorSeries)Methods 366
9.2 RandomGroupMethods 370
9.3 ResamplingandReplicationMethods 373
9.4 GeneralizedVarianceFunctions 386
9.5 ConfidenceIntervals 388
9.6 ChapterSummary 392
9.7 Exercises 394
10
Categorical DataAnalysis in Complex Surveys 401
CHAPTER
10.1 Chi-SquareTestswithMultinomialSampling 401
10.2 EffectsofSurveyDesignonChi-SquareTests 407
10.3 Correctionstoχ2 Tests 411
10.4 LoglinearModels 417
10.5 ChapterSummary 421
10.6 Exercises 422
11
Regression with Complex Survey Data 429
CHAPTER
11.1 Model-BasedRegressioninSimpleRandomSamples 430
11.2 RegressioninComplexSurveys 434
11.3 UsingRegressiontoCompareDomainMeans 445
11.4 ShouldWeightsBeUsedinRegression? 447
11.5 MixedModelsforClusterSamples 453
11.6 LogisticRegression 455
11.7 GeneralizedRegressionEstimationforPopulationTotals 457
11.8 ChapterSummary 461
11.9 Exercises 462
BrooksCole:Lohr November11,2009 22:19
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Contents
12
Two-Phase Sampling 469
CHAPTER
12.1 TheoryforTwo-PhaseSampling 472
12.2 Two-PhaseSamplingwithStratification 473
12.3 RatioandRegressionEstimationinTwo-PhaseSamples 477
12.4 JackknifeVarianceEstimationforTwo-PhaseSampling 481
12.5 DesigningaTwo-PhaseSample 482
12.6 ChapterSummary 485
12.7 Exercises 486
13
Estimating Population Size 495
CHAPTER
13.1 Capture–RecaptureEstimation 495
13.2 MultipleRecaptureEstimation 501
13.3 ChapterSummary 505
13.4 Exercises 505
14
Rare Populations and SmallArea Estimation 511
CHAPTER
14.1 SamplingRarePopulations 512
14.2 SmallAreaEstimation 518
14.3 ChapterSummary 522
14.4 Exercises 523
15
Survey Quality 527
CHAPTER
15.1 CoverageError 529
15.2 NonresponseError 533
15.3 MeasurementError 535
15.4 SensitiveQuestions 540
15.5 ProcessingError 542
15.6 TotalSurveyQuality 543
15.7 ChapterSummary 545
15.8 Exercises 546
BrooksCole:Lohr November11,2009 22:19
viii
Contents
A
Probability Concepts Used in Sampling 549
APPENDIX
A.1 Probability 549
A.2 RandomVariablesandExpectedValue 552
A.3 ConditionalProbability 556
A.4 ConditionalExpectation 558
References 563
Author Index 587
Subject Index 592
BrooksCole:Lohr November11,2009 22:19
Preface
S
urveysandsamplessometimesseemtosurroundyou.Manygivevaluableinforma-
tion;some,unfortunately,aresopoorlyconceivedandimplementedthatitwouldbe
betterforscienceandsocietyiftheyweresimplynotdone.Thisbookconcentrateson
thestatisticalaspectsoftakingandanalyzingasample.Itgivesyouguidanceonhow
totellwhenasampleisvalidornot,andhowtodesignandanalyzemanydifferent
formsofsamplesurveys.
Muchresearchhasbeendoneontheoreticalandappliedaspectsofsurveysam-
plingsincethepublicationofthefirsteditionofthisbook.Thesecondeditionincor-
poratessomeofthisrecentresearch,containsnewtopicssuchastotalsurveydesign
and statistical issues in Internet surveys, and expands coverage of weighting, cali-
bration, two-phase sampling, and sampling for rare events.The order of topics has
beenstreamlinedtobemoreintuitive,chaptersummarieshavebeenaddedforquick
review,andexercisesetsarenowbettercategorizedbyproblemtype.SAS®software
is now used for calculations, with downloadable SAS code provided on the book’s
companionwebsite.
Sixmainfeaturesdistinguishthisbookfromothertextsaboutsamplingmethods.
■ Thebookisaccessibletostudentswithawiderangeofstatisticalbackgrounds,
andisflexibleforcontentandlevel.Byappropriatechoiceofsections,thisbook
can be used for a first-year graduate course for statistics students or for a class
withstudentsfrombusiness,sociology,psychology,orbiologywhowanttolearn
about designing and analyzing data from sample surveys. It is also useful for a
persondoingsurveyresearchwhowantstolearnmoreaboutthestatisticalaspects
ofsurveysandrecentdevelopments.
■ Ihavetriedtouserealdataasmuchaspossible—theAcmeWidgetCompanynever
appearsinthisbook.Theexamplesandexercisescomefromsocialsciences,engi-
neering,agriculture,ecology,medicine,andavarietyofotherdisciplines,andare
selected to illustrate the wide applicability of sampling methods.A number of
data sets have extra variables not specifically referenced in the text; an instruc-
tor can use these for additional exercises or variations. The exercises also give
the instructor much flexibility for course level. Some emphasize mastering the
mechanics, but many encourage the student to think about the sampling issues
involvedandtounderstandthestructureofsampledesignsatadeeperlevel,while
othersareopen-endedandencouragefurtherexplorationoftheideas.
■ Ihaveincorporatedmodel-basedaswellasrandomization-basedtheoryintothe
text, with the goal of placing sampling methods within the framework used in
other areas of statistics. Many of the important results in the last twenty-plus
yearsofsamplingresearchhaveinvolvedmodels,andanunderstandingofboth
approachesisessentialforthesurveypractitioner.Themodel-basedapproachis
introducedinSection2.9andfurtherdevelopedinsuccessivechapters;however,
thosesectionscouldbediscussedatanytimelaterinthecourse.
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