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

668 Pages·2011·12.084 MB·English

by  Bradley E. Huitema(auth.), Walter A. Shewhart, Samuel S. Wilks(eds.)

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The Analysis of Covariance and
Alternatives
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WILEYSERIESINPROBABILITYANDSTATISTICS
EstablishedbyWALTERA.SHEWHARTandSAMUELS.WILKS
Editors:DavidJ.Balding,NoelA.C.Cressie,GarrettM.Fitzmaurice,
HarveyGoldstein,IainM.Johnstone,GeertMolenberghs,DavidW.Scott,
AdrianF.M.Smith,RueyS.Tsay,SanfordWeisberg
EditorsEmeriti:VicBarnett,J.StuartHunter,JosephB.Kadane,JozefL.Teugels
Acompletelistofthetitlesinthisseriesappearsattheendofthisvolume.
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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
10 9 8 7 6 5 4 3 2 1
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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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viii CONTENTS
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