The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies

666 Pages·2011·15.55 MB·English

by  Bradley Huitema

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The Analysis of Covariance and
Alternatives
Statistical Methods for Experiments,
Quasi-Experiments, and Single-Case Studies
Second Edition
BRADLEYE.HUITEMA
DepartmentofPsychology
WesternMichiganUniversity
Kalamazoo,Michigan
AJOHNWILEYANDSONS,INC.,PUBLICATION
iii
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LibraryofCongressCataloging-in-PublicationData:
Huitema,BradleyE.,1938-
Theanalysisofcovarianceandalternatives/BradleyHuitema.–2nded.
p.cm.–(Wileyseriesinprobabilityandstatistics)
Includesbibliographicalreferencesandindex.
ISBN978-0-471-74896-0(cloth)
1. Analysisofcovariance. I. Title.
QA279.H832011
519.5(cid:2)38–dc22
2010054174
PrintedintheUnitedStatesofAmerica
oBookISBN:9781118067475
ePDFISBN:9781118067451
ePubISBN:9781118067468
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For
Betsy
Craig Laura
Alyssa Kathryn
Justin Brad
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Contents
Preface xv
PARTI BASICEXPERIMENTALDESIGNANDANALYSIS
1 ReviewofBasicStatisticalMethods 3
1.1 Introduction, 3
1.2 ElementaryStatisticalInference, 4
1.3 ElementaryStatisticalDecisionTheory, 7
1.4 EffectSize, 10
1.5 MeasuresofAssociation, 14
1.6 APracticalAlternativetoEffectSizesandMeasuresof
AssociationThatIsRelevanttotheIndividual:p(Y >Y ), 17
Tx Control
1.7 GeneralizationofResults, 19
1.8 ControlofNuisanceVariation, 20
1.9 Software, 22
1.10 Summary, 24
2 ReviewofSimpleCorrelatedSamplesDesignsand
AssociatedAnalyses 25
2.1 Introduction, 25
2.2 Two-LevelCorrelatedSamplesDesigns, 25
2.3 Software, 32
2.4 Summary, 32
3 ANOVABasicsforOne-FactorRandomizedGroup,Randomized
Block,andRepeatedMeasurementDesigns 35
3.1 Introduction, 35
3.2 One-FactorRandomizedGroupDesignandAnalysis, 35
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3.3 One-FactorRandomizedBlockDesignandAnalysis, 51
3.4 One-FactorRepeatedMeasurementDesignandAnalysis, 56
3.5 Summary, 60
PARTII ESSENTIALSOFREGRESSIONANALYSIS
4 SimpleLinearRegression 63
4.1 Introduction, 63
4.2 ComparisonofSimpleRegressionandANOVA, 63
4.3 RegressionEstimation,Inference,andInterpretation, 68
4.4 DiagnosticMethods:IstheModelApt?, 80
4.5 Summary, 82
5 EssentialsofMultipleLinearRegression 85
5.1 Introduction, 85
5.2 MultipleRegression:Two-PredictorCase, 86
5.3 GeneralMultipleLinearRegression:mPredictors, 105
5.4 AlternativestoOLSRegression, 115
5.5 Summary, 119
PARTIII ESSENTIALSOFSIMPLEANDMULTIPLEANCOVA
6 One-FactorAnalysisofCovariance 123
6.1 Introduction, 123
6.2 AnalysisofCovarianceModel, 127
6.3 ComputationandRationale, 128
6.4 AdjustedMeans, 133
6.5 ANCOVAExample1:TrainingEffects, 140
6.6 TestingHomogeneityofRegressionSlopes, 144
6.7 ANCOVAExample2:SexualActivityReducesLifespan, 148
6.8 Software, 150
6.9 Summary, 157
7 AnalysisofCovarianceThroughLinearRegression 159
7.1 Introduction, 159
7.2 SimpleAnalysisofVarianceThroughLinearRegression, 159
7.3 AnalysisofCovarianceThroughLinearRegression, 172
7.4 ComputationofAdjustedMeans, 177
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CONTENTS ix
7.5 SimilarityofANCOVAtoPartandPartialCorrelationMethods, 177
7.6 HomogeneityofRegressionTestThroughGeneralLinear
Regression, 178
7.7 Summary, 179
8 AssumptionsandDesignConsiderations 181
8.1 Introduction, 181
8.2 StatisticalAssumptions, 182
8.3 DesignandDataIssuesRelatedtotheInterpretation
ofANCOVA, 200
8.4 Summary, 213
9 MultipleComparisonTestsandConfidenceIntervals 215
9.1 Introduction, 215
9.2 OverviewofFourMultipleComparisonProcedures, 215
9.3 TestsonAllPairwiseComparisons:Fisher–Hayter, 216
9.4 AllPairwiseSimultaneousConfidenceIntervalsandTests:
Tukey–Kramer, 219
9.5 PlannedPairwiseandComplexComparisons:Bonferroni, 222
9.6 AnyorAllComparisons:Scheffe´, 225
9.7 IgnoreMultipleComparisonProcedures?, 227
9.8 Summary, 228
10 MultipleCovarianceAnalysis 229
10.1 Introduction, 229
10.2 MultipleANCOVAThroughMultipleRegression, 232
10.3 TestingHomogeneityofRegressionPlanes, 234
10.4 ComputationofAdjustedMeans, 236
10.5 MultipleComparisonProceduresforMultipleANCOVA, 237
10.6 Software:MultipleANCOVAandAssociatedTukey–Kramer
MultipleComparisonTestsUsingMinitab, 243
10.7 Summary, 246
PARTIV ALTERNATIVESFORASSUMPTIONDEPARTURES
11 Johnson–NeymanandPicked-PointsSolutions
forHeterogeneousRegression 249
11.1 Introduction, 249
11.2 J–NandPPAMethodsforTwoGroups,OneCovariate, 251
11.3 ACommonMethodThatShouldBeAvoided, 269
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11.4 Assumptions, 270
11.5 TwoGroups,MultipleCovariates, 272
11.6 MultipleGroups,OneCovariate, 277
11.7 AnyNumberofGroups,AnyNumberofCovariates, 278
11.8 Two-FactorDesigns, 278
11.9 InterpretationProblems, 279
11.10 MultipleDependentVariables, 281
11.11 NonlinearJohnson-NeymanAnalysis, 282
11.12 CorrelatedSamples, 282
11.13 RobustMethods, 282
11.14 Software, 283
11.15 Summary, 283
12 NonlinearANCOVA 285
12.1 Introduction, 285
12.2 DealingwithNonlinearity, 286
12.3 ComputationandExampleofFittingPolynomialModels, 288
12.4 Summary, 295
13 Quasi-ANCOVA:WhenTreatmentsAffectCovariates 297
13.1 Introduction, 297
13.2 Quasi-ANCOVAModel, 298
13.3 ComputationalExampleofQuasi-ANCOVA, 300
13.4 MultipleQuasi-ANCOVA, 304
13.5 ComputationalExampleofMultipleQuasi-ANCOVA, 304
13.6 Summary, 308
14 RobustANCOVA/RobustPickedPoints 311
14.1 Introduction, 311
14.2 RankANCOVA, 311
14.3 RobustGeneralLinearModel, 314
14.4 Summary, 320
15 ANCOVAforDichotomousDependentVariables 321
15.1 Introduction, 321
15.2 LogisticRegression, 323
15.3 LogisticModel, 324
15.4 DichotomousANCOVAThroughLogisticRegression, 325
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CONTENTS xi
15.5 HomogeneityofWithin-GroupLogisticRegression, 328
15.6 MultipleCovariates, 328
15.7 MultipleComparisonTests, 330
15.8 ContinuousVersusForcedDichotomyResults, 331
15.9 Summary, 331
16 DesignswithOrderedTreatmentsandNoCovariates 333
16.1 Introduction, 333
16.2 Qualitative,Quantitative,andOrderedTreatmentLevels, 333
16.3 ParametricMonotoneAnalysis, 337
16.4 NonparametricMonotoneAnalysis, 346
16.5 ReversedOrdinalLogisticRegression, 350
16.6 Summary, 353
17 ANCOVAforOrderedTreatmentsDesigns 355
17.1 Introduction, 355
17.2 GeneralizationoftheAbelson–TukeyMethodtoInclude
OneCovariate, 355
17.3 Abelson–Tukey:MultipleCovariates, 358
17.4 Rank-BasedANCOVAMonotoneMethod, 359
17.5 Rank-BasedMonotoneMethodwithMultipleCovariates, 362
17.6 ReversedOrdinalLogisticRegressionwithOneor
MoreCovariates, 362
17.7 RobustR-EstimateANCOVAMonotoneMethod, 363
17.8 Summary, 364
PARTV SINGLE-CASEDESIGNS
18 SimpleInterruptedTime-SeriesDesigns 367
18.1 Introduction, 367
18.2 LogicoftheTwo-PhaseDesign, 370
18.3 AnalysisoftheTwo-Phase(AB)Design, 371
18.4 TwoStrategiesforTime-SeriesRegressionIntervention
Analysis, 374
18.5 DetailsofStrategyII, 375
18.6 EffectSizes, 385
18.7 SampleSizeRecommendations, 389
18.8 WhentheModelIsTooSimple, 393
18.9 Summary, 394
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19 ExamplesofSingle-CaseABAnalysis 403
19.1 Introduction, 403
19.2 ExampleI:CancerDeathRatesintheUnitedKingdom, 403
19.3 ExampleII:FunctionalActivity, 411
19.4 ExampleIII:CerealSales, 414
19.5 ExampleIV:ParacetamolPoisoning, 424
19.6 Summary, 430
20 AnalysisofSingle-CaseReversalDesigns 433
20.1 Introduction, 433
20.2 StatisticalAnalysisofReversalDesigns, 434
20.3 ComputationalExample:PharmacyWaitTime, 441
20.4 Summary, 452
21 AnalysisofMultiple-BaselineDesigns 453
21.1 Introduction, 453
21.2 CaseIAnalysis:IndependenceofErrorsWithinandBetween
Series, 455
21.3 CaseIIAnalysis:AutocorrelatedErrorsWithinSeries,
IndependenceBetweenSeries, 461
21.4 CaseIIIAnalysis:IndependentErrorsWithinSeries,
Cross-CorrelationBetweenSeries, 461
21.5 InterventionVersusControlSeriesDesign, 467
21.6 Summary, 471
PARTVI ANCOVAEXTENSIONS
22 PowerEstimation 475
22.1 Introduction, 475
22.2 PowerEstimationforOne-FactorANOVA, 475
22.3 PowerEstimationforANCOVA, 480
22.4 PowerEstimationforStandardizedEffectSizes, 482
22.5 Summary, 482
23 ANCOVAforRandomized-BlockDesigns 483
23.1 Introduction, 483
23.2 ConventionalDesignandAnalysisExample, 484
23.3 CombinedAnalysis(ANCOVAandBlockingFactor), 486
23.4 Summary, 488
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CONTENTS xiii
24 Two-FactorDesigns 489
24.1 Introduction, 489
24.2 ANCOVAModelandComputationforTwo-FactorDesigns, 494
24.3 MultipleComparisonTestsforAdjustedMarginalMeans, 512
24.4 Two-FactorANOVAandANCOVAforRepeated-Measurement
Designs, 519
24.5 Summary, 530
25 RandomizedPretest–PosttestDesigns 531
25.1 Introduction, 531
25.2 ComparisonofThreeANOVAMethods, 531
25.3 ANCOVAforPretest–PosttestDesigns, 534
25.4 Summary, 539
26 MultipleDependentVariables 541
26.1 Introduction, 541
26.2 UncorrectedUnivariateANCOVA, 543
26.3 BonferroniMethod, 544
26.4 MultivariateAnalysisofCovariance(MANCOVA), 544
26.5 MANCOVAThroughMultipleRegressionAnalysis:Two
GroupsOnly, 553
26.6 IssuesAssociatedwithBonferroniFandMANCOVA, 554
26.7 AlternativestoBonferroniandMANCOVA, 555
26.8 ExampleAnalysesUsingMinitab, 557
26.9 Summary, 564
PARTVII QUASI-EXPERIMENTSANDMISCONCEPTIONS
27 NonrandomizedStudies:MeasurementErrorCorrection 567
27.1 Introduction, 567
27.2 EffectsofMeasurementError:Randomized-GroupCase, 568
27.3 EffectsofMeasurementErrorinExposureandCovariates:
NonrandomizedDesign, 569
27.4 MeasurementErrorCorrectionIdeas, 570
27.5 Summary, 573
28 DesignandAnalysisofObservationalStudies 575
28.1 Introduction, 575
28.2 DesignofNonequivalentGroup/ObservationalStudies, 579