A First Course in Design and Analysis of Experiments

2010·4 MB·English

by  A First Course in Design and Analysis of Experiments

A First Course in
Design and Analysis
of Experiments

A First Course in
Design and Analysis
of Experiments
Gary W. Oehlert
University of Minnesota
CoverdesignbyVictoriaTomaselli
CoverillustrationbyPeterHamlin
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Design-ExpertisaregisteredtrademarkofStat-Ease,Inc.
LibraryofCongressCataloging-in-PublicationData.
Oehlert,GaryW.
Afirstcourseindesignandanalysisofexperiments/GaryW.Oehlert.
p. cm.
Includesbibligraphicalreferencesandindex.
ISBN0-7167-3510-5
1. ExperimentalDesign I.Title
QA279.O342000
519.5—dc21 99-059934
Copyright c 2010GaryW.Oehlert. Allrightsreserved.
(cid:13)
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For Becky
who helped me all the way through
and for Christie and Erica
who put up with a lot while it was getting done

Contents
Preface xvii
1 Introduction 1
1.1 WhyExperiment? . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ComponentsofanExperiment . . . . . . . . . . . . . . . 4
1.3 TermsandConcepts . . . . . . . . . . . . . . . . . . . . . 5
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 MoreAboutExperimentalUnits . . . . . . . . . . . . . . 8
1.6 MoreAboutResponses . . . . . . . . . . . . . . . . . . . 10
2 RandomizationandDesign 13
2.1 RandomizationAgainstConfounding . . . . . . . . . . . 14
2.2 RandomizingOtherThings . . . . . . . . . . . . . . . . . 16
2.3 PerformingaRandomization . . . . . . . . . . . . . . . . 17
2.4 RandomizationforInference . . . . . . . . . . . . . . . . 19
2.4.1 Thepairedt-test . . . . . . . . . . . . . . . . . . 20
2.4.2 Two-samplet-test . . . . . . . . . . . . . . . . . 25
2.4.3 Randomizationinferenceandstandardinference . 26
2.5 FurtherReadingandExtensions . . . . . . . . . . . . . . 27
2.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 CompletelyRandomizedDesigns 31
3.1 StructureofaCRD . . . . . . . . . . . . . . . . . . . . . 31
3.2 PreliminaryExploratoryAnalysis . . . . . . . . . . . . . 33
3.3 ModelsandParameters . . . . . . . . . . . . . . . . . . . 34
viii CONTENTS
3.4 EstimatingParameters . . . . . . . . . . . . . . . . . . . 39
3.5 ComparingModels: TheAnalysisofVariance . . . . . . . 44
3.6 MechanicsofANOVA . . . . . . . . . . . . . . . . . . . 45
3.7 WhyANOVAWorks . . . . . . . . . . . . . . . . . . . . 52
3.8 BacktoModelComparison . . . . . . . . . . . . . . . . . 52
3.9 Side-by-SidePlots . . . . . . . . . . . . . . . . . . . . . 54
3.10 Dose-ResponseModeling . . . . . . . . . . . . . . . . . . 55
3.11 FurtherReadingandExtensions . . . . . . . . . . . . . . 58
3.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 LookingforSpecificDifferences—Contrasts 65
4.1 ContrastBasics . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 InferenceforContrasts . . . . . . . . . . . . . . . . . . . 68
4.3 OrthogonalContrasts . . . . . . . . . . . . . . . . . . . . 71
4.4 PolynomialContrasts . . . . . . . . . . . . . . . . . . . . 73
4.5 FurtherReadingandExtensions . . . . . . . . . . . . . . 75
4.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5 MultipleComparisons 77
5.1 ErrorRates . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 Bonferroni-BasedMethods . . . . . . . . . . . . . . . . . 81
5.3 TheScheffe´ MethodforAllContrasts . . . . . . . . . . . 85
5.4 PairwiseComparisons. . . . . . . . . . . . . . . . . . . . 87
5.4.1 Displayingtheresults . . . . . . . . . . . . . . . 88
5.4.2 TheStudentizedrange . . . . . . . . . . . . . . . 89
5.4.3 Simultaneousconfidenceintervals . . . . . . . . . 90
5.4.4 Strongfamilywiseerrorrate . . . . . . . . . . . . 92
5.4.5 Falsediscoveryrate . . . . . . . . . . . . . . . . 96
5.4.6 Experimentwiseerrorrate . . . . . . . . . . . . . 97
5.4.7 Comparisonwiseerrorrate . . . . . . . . . . . . . 98
5.4.8 Pairwisetestingreprise . . . . . . . . . . . . . . 98
5.4.9 Pairwisecomparisonsmethodsthatdonotcontrol
combinedTypeIerrorrates . . . . . . . . . . . . 98
5.4.10 Confidentdirections . . . . . . . . . . . . . . . . 100
CONTENTS ix
5.5 ComparisonwithControlortheBest . . . . . . . . . . . . 101
5.5.1 Comparisonwithacontrol . . . . . . . . . . . . . 101
5.5.2 Comparisonwiththebest . . . . . . . . . . . . . 104
5.6 RealityCheckonCoverageRates . . . . . . . . . . . . . 105
5.7 AWarningAboutConditioning. . . . . . . . . . . . . . . 106
5.8 SomeControversy. . . . . . . . . . . . . . . . . . . . . . 106
5.9 FurtherReadingandExtensions . . . . . . . . . . . . . . 107
5.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6 CheckingAssumptions 111
6.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2 Transformations . . . . . . . . . . . . . . . . . . . . . . . 113
6.3 AssessingViolationsofAssumptions. . . . . . . . . . . . 114
6.3.1 Assessingnonnormality . . . . . . . . . . . . . . 115
6.3.2 Assessingnonconstantvariance . . . . . . . . . . 118
6.3.3 Assessingdependence . . . . . . . . . . . . . . . 120
6.4 FixingProblems . . . . . . . . . . . . . . . . . . . . . . . 124
6.4.1 Accommodatingnonnormality . . . . . . . . . . 124
6.4.2 Accommodatingnonconstantvariance . . . . . . 126
6.4.3 Accommodatingdependence . . . . . . . . . . . 133
6.5 EffectsofIncorrectAssumptions . . . . . . . . . . . . . . 134
6.5.1 Effectsofnonnormality . . . . . . . . . . . . . . 134
6.5.2 Effectsofnonconstantvariance . . . . . . . . . . 136
6.5.3 Effectsofdependence . . . . . . . . . . . . . . . 138
6.6 ImplicationsforDesign . . . . . . . . . . . . . . . . . . . 140
6.7 FurtherReadingandExtensions . . . . . . . . . . . . . . 141
6.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7 PowerandSampleSize 149
7.1 ApproachestoSampleSizeSelection . . . . . . . . . . . 149
7.2 SampleSizeforConfidenceIntervals. . . . . . . . . . . . 151
7.3 PowerandSampleSizeforANOVA . . . . . . . . . . . . 153
7.4 PowerandSampleSizeforaContrast . . . . . . . . . . . 158
7.5 MoreaboutUnitsandMeasurementUnits . . . . . . . . . 158
x CONTENTS
7.6 AllocationofUnitsforTwoSpecialCases . . . . . . . . . 160
7.7 FurtherReadingandExtensions . . . . . . . . . . . . . . 161
7.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8 FactorialTreatmentStructure 165
8.1 FactorialStructure. . . . . . . . . . . . . . . . . . . . . . 165
8.2 FactorialAnalysis: MainEffectandInteraction . . . . . . 167
8.3 AdvantagesofFactorials . . . . . . . . . . . . . . . . . . 170
8.4 VisualizingInteraction . . . . . . . . . . . . . . . . . . . 171
8.5 ModelswithParameters. . . . . . . . . . . . . . . . . . . 175
8.6 TheAnalysisofVarianceforBalancedFactorials . . . . . 179
8.7 GeneralFactorialModels . . . . . . . . . . . . . . . . . . 182
8.8 AssumptionsandTransformations . . . . . . . . . . . . . 185
8.9 SingleReplicates . . . . . . . . . . . . . . . . . . . . . . 186
8.10 PoolingTermsintoError . . . . . . . . . . . . . . . . . . 191
8.11 Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 197
9 ACloserLookatFactorialData 203
9.1 ContrastsforFactorialData . . . . . . . . . . . . . . . . . 203
9.2 ModelingInteraction . . . . . . . . . . . . . . . . . . . . 209
9.2.1 Interactionplots . . . . . . . . . . . . . . . . . . 209
9.2.2 One-cellinteraction . . . . . . . . . . . . . . . . 210
9.2.3 Quantitativefactors . . . . . . . . . . . . . . . . 212
9.2.4 Tukeyone-degree-of-freedomfornonadditivity . . 217
9.3 FurtherReadingandExtensions . . . . . . . . . . . . . . 220
9.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 222
10 FurtherTopicsinFactorials 225
10.1 UnbalancedData . . . . . . . . . . . . . . . . . . . . . . 225
10.1.1 Sumsofsquaresinunbalanceddata . . . . . . . . 226
10.1.2 Buildingmodels . . . . . . . . . . . . . . . . . . 227
10.1.3 Testinghypotheses . . . . . . . . . . . . . . . . . 230
10.1.4 Emptycells . . . . . . . . . . . . . . . . . . . . . 233
10.2 MultipleComparisons . . . . . . . . . . . . . . . . . . . 234