Experimental Design Techniques in Statistical Practice: A Practical Software-Based Approach

410 Pages·1998·22.753 MB·English

by  W.P. Gardiner, G Gettinby

Experimental Design Techniques
in Statistical Practice:
apractical software-based approach
"Talking ofeducation, peoplehavenowa-days" (said he)"got a strange opinion
that everything shouldbetaught bylectures. Now,Icannot seethat lectures can
dosomuchgoodasreadingthebooksfromwhichthelecturesaretaken. Iknow
nothing that can be best taught by lectures, except where experiments are tobe
shewn. Youmayteachchymestrybylectures- Youmightteachmakingofshoes
bylectures!"
JamesBoswell: LifeofSamuelJohnson, 1766 (1709-1784)
Thedirectioninwhicheducationstartsamanwilldeterminehisfuturelife.
Plato: TheRepublic, BookV
(427-347Be)
THE AUTHORS
BillGardiner
Dr BillGardiner graduated with first class honours in mathematics at the Universityof
Strathclyde and later with a Ph.D. in statistics and mathematical modelling. He has
devoted his professional life to high quality teaching of statistics to under-graduates
across a range of disciplines and also to postgraduate MSc students in industrial
mathematics He has provided consultancy support for over 16 years to biologists,
chemists and health providers Much ofhis work has involved the use ofexperimental
designs within practical problems which, with histeaching and consultancy experience,
culminated in the writing of this book together with George Gettinby He currently
lectures at Glasgow Caledonian University, where he emphasises the importance and
practical benefits ofstatistical data analysis as a fundamental and integral part ofdata
interpretation for students of all disciplines He has also recently published work on
unbalanced experimental designs and two introductory statistics books for bioscientists
and chemists.Thispresent textbook covers both elementary and advanced methods and
reflects Dr Gardiner's successful teaching style in practice, where the emphasis is on
usingsoftwareasanaidto statisticalanalysisanddecision-making
George Gettinby
George Gettinby is Professor and Chairman in the Department of Statistics and
Modelling Scienceat the University ofStrathclyde, Glasgow. He graduated inapplied
mathematics at Queens University Belfast and obtained a DPhil for his thesis on
mathematical and statistical modelling at the University of Ulster He subsequently
qualifiedasa chartered statistician. Overthe last twenty years he hasbeen anadviserto
international agencies, industry and governmental bodies on the design and analysis of
studies using experimental design methods. His research and teaching interests have
focused on the use of statistical and mathematical models for the study of the
environmentandthe control ofdiseases Hisindustrialinterests have centred around the
research, development and manufacture ofhuman and animalmedicines.In recent years
hehastaught manyshort courses forindustrythat promote the useofstatisticalmethods
for assessingthe quality ofproducts. He is a member ofthe Royal Statistical Society,
Professional Statisticians in Industry and the UK Medicines Commission In 1997 he
waselectedaFellowoftheRoyalSocietyofEdinburgh.
Experimental Design Techniques
in Statistical Practice:
a practical software-based approach
William P. Gardiner, Bsc, PhD
LecturerinStatistics
Glasgow Caledonian University
and
George Gettinby, BSc, Dphil, CStat
ProfessorofStatistics andModelling Science
UniversityofStrathclyde
Glasgow
Horwood Publishing
Chichester
First publishedin 1998by
HORWOODPUBLISHINGLIMITED
InternationalPublishers
ColiHouse, Westergate, Chichester, West Sussex,P020 6QL
England
COPYRIGHTNOTICE
All Rights Reserved,Nopart ofthis publication maybe reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise, without the permission of
HorwoodPublishing,InternationalPublishers,ColiHouse,Westergate,Chichester,
WestSussex,England
©W.P.Gardiner& G.Gettinby,1998
British LibraryCataloguingin Publication Data
AcataloguerecordofthisbookisavailablefromtheBritishLibrary
ISBN1-898563-35-7
PrintedandboundinGreatBritainbyMPGBooksLtd,Bodmin,Cornwall
Table ofContents
Authors' Preface xiii
Glossary xv
Chapter1 Introduction
1.1 Introduction 1
1.2 Informationonthe Statistical Software 2
1.2.1 SAS 3
1.2.2 Minitab 4
1.3 SummarisingExperimentalData 6
1.3.1 GraphicalPresentations 6
1.3.2 NumericalSummaries 8
1.4 TheNormalDistributionWithinData Analysis 11
1.5 Outliers inData 12
lA Appendix: IntroductorySoftware Information 14
Chapter2 InferentialDataAnalysis for Simple Experiments
2.1 Introduction 19
2.2 Basic ConceptsofInferentialData Analysis 19
2.3 Inference Methodsfor Two SampleStudies 23
2.3.1 HypothesisTest forDifferenceinMean Responses 24
2.3.2 Confidence Interval forDifferenceinMean Responses 27
2.3.3 HypothesisTest forVariability 28
2.3.4 Confidence Interval forthe Ratio ofTwo Variances 29
2.3.5 Non-parametricMethods 30
2.4 Inference Methodsfor Paired SampleStudies 30
2.4.1 HypothesisTest forMean DifferenceinResponses 31
2.4.2 Confidence IntervalforMean Difference 33
2.4.3 HypothesisTest for Variability 34
2.4.4 Non-parametricMethods 36
2.5 Sample SizeEstimationinDesignPlanning 36
2.5.1 Sample SizeEstimation for Two SampleStudies 36
2.5.2 Sample SizeEstimation forPaired SampleStudies 38
2.6 Validityand GoodStatistical Practice 39
2.7 Protocols 40
2.8 Commonly Occurring DesignMistakes 41
Problems 42
2A.l Appendix: SoftwareInformationfor Two SampleStudies 44
2A.2 Appendix: SoftwareInformation forPaired Sample Studies .47
Chapter3 One FactorDesigns
3.1 Introduction 51
3.2 CompletelyRandomisedDesign 53
3.2.1 Design Structure 53
3.2.2 Modelforthe MeasuredResponse 54
3.2.3 Assumptions 55
3.2.4 ExploratoryData Analysis 56
3.3 ANOVAPrincipleforthe CompletelyRandomisedDesign 57
vi TableofContents
3.3.1 Hypotheses 57
3.3.2 ANOVATable 57
3.3.3 TreatmentTestStatistic 58
3.4 Follow-upAnalysisProcedures 59
3.4.1 MainEffectsPlot 60
3.4.2 StandardError Plot 60
3.4.3 MultipleComparisons 61
3.4.4 LinearContrasts 64
3.4.5 OrthogonalPolynomials 67
3.4.6 TreatmentEffectEstimation 67
3.4.7 ModelFit 69
3.5 DiagnosticCheckingofModelAssumptions 69
3.5.1 GraphicalChecks 70
3.5.2 StatisticalChecks 73
3.6 PowerAnalysisinDesignPlanning 74
3.6.1 PowerEstimation 75
3.6.2 SampleSizeEstimation 76
3.7 Non-parametricAlternativetotheANOVABasedTreatmentTests 77
3.7.1 TheKruskal-WallisTestofTreatmentDifferences 77
3.7.2 MultipleComparisonAssociatedwiththeKruskal-WallisTest 78
3.7.3 LinearContrasts 79
3.8 DataTransformations 80
Problems 82
3A Appendix:SoftwareInformationforCompletelyRandomisedDesign 84
Chapter4 One FactorBlocking Designs
4.1 Introduction 89
4.2 RandomisedBlockDesign 89
4.2.1 DesignStructure 90
4.2.2 ModelfortheMeasuredResponse 90
4.2.3 Assumptions 91
4.2.4 ExploratoryDataAnalysis 91
4.3 ANOVAPrinciplefortheRandomisedBlockDesign 92
4.3.1 Hypotheses 92
4.3.2 ANOVATable 92
4.3.3 Test Statistics 93
4.4 Follow-upAnalysisProceduresforRandomisedBlockDesigns 95
4.5 AdditionalAspectsofBlockingDesigns 97
4.5.1 PowerAnalysis 97
4.5.2 MissingObservations 98
4.5.3 Efficiency 98
4.6 Non-parametricAlternativeto ANOVABasedTreatmentTests 98
4.6.1 FriedmanTestofTreatmentDifferences 99
4.6.2 MultipleComparisonAssociatedwithFriedman'sTest 99
4.7 IncompleteBlockDesigns 100
4.7.1 BalancedIncompleteBlockDesign 101
4.7.2 ANOVAPrinciple 102
4.7.3 Follow-upAnalysisProcedures 103
4.7.4 OtherIncompleteDesigns 104
4.8 LatinSquareDesign 104
4.8.1 DesignStructure 104
TableofContents vii
4.8.2 ModelfortheMeasuredResponse 105
4.8.3 ANOVAPrinciple 106
4.8.4 Follow-upAnalysisProcedures 108
4.8.5 MissingObservations 110
4.8.6 Efficiency 111
Problems 111
4Al Appendix:SoftwareInformationforRandomisedBlockDesign 114
4A2 Appendix:SoftwareInformationforBalancedIncompleteBlockDesign 116
4A3 Appendix:SoftwareInformationforLatinSquareDesign 117
Chapter5 FactorialExperimentalDesigns
5.1 Introduction 119
5.2 TwoFactor FactorialDesignwithnReplicationsper Cell 120
5.2.1 DesignStructure 121
5.2.2 ModelfortheMeasuredResponse 123
5.2.3 Exploratory DataAnalysis 124
5.3 ANOVAPrincipleforthe TwoFactorFactorialDesign 124
5.3.1 Hypotheses 125
5.3.2 ANOVATable 125
5.3.3 Test Statistics 125
5.4 Follow-upAnalysisProcedures forFactorialDesignsofModelIType 127
5.4.1 SignificantInteraction 128
5.4.2 Non-significantInteractionbut SignificantFactor Effect.. 130
5.4.3 LinearContrasts 130
5.4.4 OrthogonalPolynomials 130
5.4.5 Estimation 131
5.4.6 DiagnosticChecking 132
5.5 OverviewofDataAnalysisforTwoFactor FactorialDesigns 134
5.6 Power AnalysisinTwoFactor FactorialDesigns 134
5.7 Non-parametric InferenceforaTwoFactor FactorialDesign 135
5.8 RandomEffects-ModelII/MixedModelExperiments 136
5.8.1 AdditionalEffectAssumptions 137
5.8.2 EMSExpressionsandTest StatisticDerivation 138
5.8.3 AnalysisComponentsforModelswithRandomEffects 140
5.8.4 Power AnalysisforRandomEffects 140
5.9 UnbalancedTwoFactor FactorialDesign 141
5.9.1 TypeIto IVSumsofSquares 142
5.9.2 TypeIto IIIHypotheses 144
5.10 ThreeFactor FactorialDesignwithnReplicationsperCell 147
5.10.1 ModelfortheMeasuredResponse 148
5.10.2 ANOVAPrincipleandTest Statistics 148
5.10.3 OverviewofDataAnalysisforThreeFactor FactorialDesigns 152
5.10.4 PoolingofFactor Effects 155
5.10.5 UnbalancedApproaches 156
5.11 AnalysisofCovariance 156
Problems 156
5Al Appendix:SoftwareInformationforTwoFactor FactorialDesigns 162
5A2 Appendix:SoftwareInformationforThreeFactor FactorialDesigns 164
viii TableofContents
Chapter6 HierarchicalDesigns
6.1 Introduction 166
6.2 TwoFactorNested Design 166
6.2.1 DesignStructure 166
6.2.2 ModelfortheMeasuredResponse 168
6.2.3 ExploratoryDataAnalysis 169
6.3 ANaVAPrincipleforthe TwoFactorNestedDesign 169
6.3.1 Hypotheses 169
6.3.2 ANaVATable 170
6.3.3 TestStatistics 170
6.4 Follow-upAnalysis 172
6.4.1 AnalysisofFactor Effects 172
6.4.2 MixedModel- SignificantNested Factor 173
6.4.3 MixedModelandModelIIVariabilityAnalysis 174
6.4.4 DiagnosticChecking 175
6.5 OtherFeaturesAssociatedwithTwoFactorNestedDesigns 171
6.5.1 RelativeEfficiency 177
6.5.2 PowerAnalysis 177
6.5.3 UnequalReplicates 178
6.6 ThreeFactorNestedDesign 178
6.6.1 ModelfortheMeasuredResponse 178
6.6.2 ANaVATableandTest Statistics 179
6.7 RepeatedMeasuresDesign 179
6.7.1 DesignStructure 179
6.7.2 ModelfortheMeasuredResponse 180
6.7.3 ANaVATableandTest Statistics 182
6.7.4 Follow-upProcedures 186
6.7.5 DiagnosticChecking 188
6.7.6 UnbalancedDesigns 189
6.8 CrossOverDesign 190
6.8.1 DesignStructure 191
6.8.2 ModelfortheMeasuredResponse 192
6.8.3 ANaVATableandTest Statistics 193
6.9 Split-PlotDesigns 196
6.9.1 DesignStructure 196
6.9.2 ModelfortheMeasuredResponse 196
6.9.3 ANaVATableandTestStatistics 197
Problems 198
6A.l Appendix:SoftwareInformationforNestedDesigns 202
6A.2 Appendix:SoftwareInformationforRepeatedMeasuresDesigns 204
6A.3 Appendix:SoftwareInformationforCrossOverDesigns 205
Chapter7 Two-level FactorialDesigns
7.1 Introduction 207
7.2 Contrasts andEffectEstimation 209
7.2.1 Contrasts 209
7.2.2 EffectEstimation 212
7.2.3 MissingValues 214
7.3 InitialAnalysisComponents 214
7.3.1 ExploratoryAnalysis 214
TableofContents ix
7.3.2 EffectEstimatePlots 214
7.3.3 DataPlots andSummaries 218
7.4 StatisticalComponents ofAnalysis 220
7.4.1 StatisticalAssessmentofProposed ModeL 220
7.4.2 Prediction 221
7.4.3 DiagnosticChecking 222
7.5 GeneralUnreplicated2kDesigns 224
7.6 UseofReplication 226
7.7 Three-levelDesigns 227
Problems 227
7A Appendix:SoftwareInformationforTwo-levelFactorialDesigns 229
Chapter8 Two-level FractionalFactorialDesigns
8.1 Introduction 234
8.2 Confounding 234
8.3 BlockConstruction Procedures 236
8.3.1 Even/OddMethod 236
8.3.2 LinearCombinationMethod 238
8.4 FractionalFactorialDesigns 239
8.4.1 AliasStructure 242
8.4.2 DesignResolution 245
8.5 AnalysisComponentsforFractionalFactorialDesigns 248
8.5.1 ExploratoryAnalysis 249
8.5.2 EffectEstimatesAnalysis 249
8.5.3 DataPlotsandSummaries 250
8.5.4 StatisticalComponents 251
8.6 Three-levelFractionalFactorialDesigns 258
Problems 259
8A Appendix:SoftwareInformationforTwo-levelFractionalFactorial
Designs 262
Chapter9 Two-level OrthogonalArrays
9.1 Introduction 267
9.2 ArrayStructures 267
9.3 ExperimentalPlans 270
9.3.1 PlansBasedonthe OA8(27) Structure 270
9.3.2 PlansBasedontheOA16(215) Structure 272
9.3.3 AliasingandResolutioninOrthogonalArrays 274
9.3.4 SaturatedDesigns 276
9.4 AnalysisComponentsforTwo-LevelOrthogonalArrays 277
9.5 Three-levelOrthogonalArrays 281
9.6 Plackett-BurmanDesigns 282
Problems 283
9A Appendix:SoftwareInformationforTwo-LevelOrthogonalArray
Designs 286
Chapter10 TaguchiMethods
10.1 Introduction 289
10.2 DesignStructures 291
10.3 Performance Statistics 297
10.4 DataAnalysisComponentsforTwo-levelTaguchiParameterDesigns 300