Statistical Principles for the Design of Experiments: Applications to Real Experiments

584 Pages·2012·3.78 MB·English

by  R. Mead

Statistical Principles for the Design of Experiments
Thisbookisaboutthestatisticalprinciplesbehindthedesignofeffectiveexperiments
andfocusesonthepracticalneedsofappliedstatisticiansandexperimentersengaged
in design, implementation and analysis. Emphasising the logical principles of sta-
tistical design, rather than mathematical calculation, the authors demonstrate how
all available information can be used to extract the clearest answers to many ques-
tions.Theprinciplesareillustratedwithawiderangeofexamplesdrawnfromreal
experiments in medicine, industry, agriculture and many experimental disciplines.
Numerousexercisesaregiventohelpthereaderpractisetechniquesandtoappreciate
thedifferencethatgooddesigncanmaketoanexperimentalresearchproject.
Based on Roger Mead’s excellent Design of Experiments, this new edition is
thoroughlyrevisedandupdatedtoincludemodernmethodsrelevanttoapplications
inindustry,engineeringandmodernbiology.Italsocontainssevennewchapterson
contemporarytopics,includingrestrictedrandomisationandfractionalreplication.
r. mead isEmeritusProfessorofAppliedStatisticsattheUniversityofReading.
s. g. gilmour is Professor of Statistics in the Southampton Statistical Sciences
ResearchInstituteattheUniversityofSouthampton.
a. mead isSeniorTeachingFellowintheSchoolofLifeSciencesattheUniversity
ofWarwick.
CAMBRIDGE SERIES IN STATISTICAL AND
PROBABILISTIC MATHEMATICS
EditorialBoard
Z.Ghahramani(DepartmentofEngineering,UniversityofCambridge)
R.Gill(MathematicalInsitute,LeidenUniversity)
F.P.Kelly(DepartmentofPureMathematicsandMathematicalStatistics,
UniversityofCambridge)
B.D.Ripley(DepartmentofStatistics,UniversityofOxford)
S.Ross(DepartmentofIndustrialandSystemsEngineering,
UniversityofSouthernCalifornia)
M.Stein(DepartmentofStatistics,UniversityofChicago)
This series of high-quality upper-division textbooks and expository monographs covers all
aspectsofstochasticapplicablemathematics.Thetopicsrangefrompureandappliedstatistics
toprobabilitytheory,operationsresearch,optimisationandmathematicalprogramming.The
books contain clear presentations of new developments in the field and also of the state of
theartinclassicalmethods.Whileemphasisingrigoroustreatmentoftheoreticalmethods,the
booksalsocontainapplicationsanddiscussionsofnewtechniquesmadepossiblebyadvances
incomputationalpractice.
Acompletelistofbooksintheseriescanbefoundatwww.cambridge.org/statistics.
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Statistical Principles for the
Design of Experiments
R. Mead
UniversityofReading
S. G. Gilmour
UniversityofSouthampton
A. Mead
UniversityofWarwick
CAMBRIDGE UNIVERSITY PRESS
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Informationonthistitle:www.cambridge.org/9780521862141
(cid:2)C R.Mead,S.G.GilmourandA.Mead2012
BasedonTheDesignofExperimentsbyR.Mead.
(cid:2)C CambridgeUniversityPress1988
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2012
PrintedandboundintheUnitedKingdombytheMPGBooksGroup
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloguinginPublicationdata
Mead,R.(Roger)
Statisticalprinciplesforthedesignofexperiments:applicationstorealexperiments/R.Mead,Universityof
Reading,S.G.Gilmour,UniversityofSouthampton,A.Mead,UniversityofWarwick.
pagescm.–(Cambridgeseriesinstatisticalandprobabilisticmathematics)
Includesbibliographicalreferencesandindex.
ISBN978-0-521-86214-1(hardback)
1.Experimentaldesign. I.Gilmour,S.G. II.Mead,A.(Andrew) III.Title.
QA279.M38825 2012
001.4(cid:3)34–dc23 2012023181
ISBN978-0-521-86214-1Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceor
accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto
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Contents
Preface pagexi
PartI Overture
1 Introduction 3
1.1 Whyastatisticaltheoryofdesign? 3
1.2 History,computersandmathematics 4
1.3 Theinfluenceofanalysisondesign 5
1.4 Separateconsiderationofunitsandtreatments 6
1.5 Theresourceequation 7
2 Elementaryideasofblocking:therandomisedcomplete
blockdesign 9
2.1 Controllingvariationbetweenexperimentalunits 9
2.2 Theanalysisofvarianceidentity 12
2.3 Estimationofvarianceandthecomparisonoftreatmentmeans 18
2.4 Residualsandthemeaningoferror 22
2.5 Therandomallocationoftreatmentstounits 24
2.6 Practicalchoicesofblockingpatterns 26
3 Elementaryideasoftreatmentstructure 29
3.1 Choiceoftreatments 29
3.2 Factorialstructure 29
3.3 Modelsformaineffectsandinteractions 30
3.4 Theanalysisofvarianceidentity 33
3.5 Interpretationofmaineffectsandinteractions 36
3.6 Advantagesoffactorialstructure 38
3.7 Treatmenteffectsandtreatmentmodels 40
4 Generalprinciplesoflinearmodelsfortheanalysisof
experimentaldata 42
4.1 Introductionandsomeexamples 42
4.2 Theprincipleofleastsquaresandleastsquaresestimators 43
4.3 Propertiesofleastsquaresestimators 46
v
vi Contents
4.4 Overparameterisation,constraintsandpracticalsolutionofleast
squaresequations 49
4.5 Subdividingtheparameters;extraSS 55
4.6 Distributionalassumptionsandinferences 60
4.7 Contrasts,treatmentcomparisonsandcomponentSS 62
4.8 Covariance–extensionoflineardesignmodels 66
4.9 Computersforanalysingexperimentaldata 79
AppendixtoChapter4 87
4.A2 Leastsquaresestimatorsforlinearmodels 87
4.A3 Propertiesofleastsquaresestimators 88
4.A4 Overparameterisationandconstraints 90
4.A5 PartitioningtheparametervectorandtheextraSSprinciple 94
4.A6 Distributionalassumptionsandinferences 96
4.A7 TreatmentcomparisonsandcomponentSS 100
4.A8 Thegeneraltheoryofcovarianceanalysis 102
PartII Firstsubject
5 Experimentalunits 107
5.0 Preliminaryexamples 107
5.1 Differentformsofbasicexperimentalunits 109
5.2 Experimentalunitsascollections 113
5.3 Apartastheunitandsequencesoftreatments 115
5.4 Multiplelevelsofexperimentalunits 118
5.5 Timeasafactorandrepeatedmeasurements 120
5.6 Protectionofunits,randomisationrestrictions 121
6 Replication 124
6.0 Preliminaryexample 124
6.1 Theneedforreplication 124
6.2 Thecompletelyrandomiseddesign 125
6.3 Differentlevelsofvariation 128
6.4 Identifyingandallowingfordifferentlevelsofvariation 132
6.5 Howmuchreplication? 136
7 Blockingandcontrol 142
7.0 Preliminaryexamples 142
7.1 Designandanalysisforverysimpleblockedexperiments 143
7.2 Designprinciplesinblockedexperiments 146
7.3 Theanalysisofblock-treatmentdesigns 153
7.4 BIBdesignsandclassesoflessbalanceddesigns 159
7.5 Orthogonality,balanceandthepracticalchoiceofdesign 164
7.6 Experimentaldesignsforlarge-scalevarietytrials 173
Contents vii
8 Multipleblockingsystemsandcross-overdesigns 182
8.0 Preliminaryexamples 182
8.1 LatinsquaredesignsandLatinrectangles 182
8.2 Multipleorthogonalclassificationsandsequencesofexperiments 186
8.3 Row-and-columndesignswithmoretreatmentsthanreplicates 188
8.4 Three-dimensionaldesigns 199
8.5 Thepracticalchoiceofrow-and-columndesign 201
8.6 Cross-overdesigns–timeasablockingfactor 204
8.7 Cross-overdesignsforresidualorinteractioneffects 207
9 Multiplelevelsofinformation 218
9.0 Preliminaryexamples 218
9.1 Identifyingmultiplelevelsindata 218
9.2 Theuseofmultiplelevelsofinformation 220
9.3 Randomeffectsandmixedmodels 227
9.4 AnalysisofmultipleleveldatausingREML 229
9.5 Multipleblockingsystems 230
10 Randomisation 233
10.1 Whatisthepopulation? 233
10.2 Randomtreatmentallocation 234
10.3 Randomisationtests 236
10.4 Randomisationtheoryoftheanalysisofexperimentaldata 241
10.5 Practicalimplicationsofthetwotheoriesofanalysisof
experimentaldata 246
10.6 Practicalrandomisation 248
11 Restrictedrandomisation 256
11.0 Preliminaryexample 256
11.1 Time-trendresistantrunordersanddesigns 256
11.2 Modellingspatialvariation 257
11.3 Neighbourbalance 260
11.4 Advantagesanddisadvantagesofrestrictingrandomisation 261
11.5 Ignoringblockinginthedataanalysis 263
11.6 Covarianceorblocking 264
11.7 Sequentialallocationoftreatmentsinclinicaltrials 266
PartIII Secondsubject
12 Experimentalobjectives,treatmentsandtreatmentstructures 275
12.0 Preliminaryexamples 275
12.1 Differentquestionsandformsoftreatments 275
12.2 Comparisonsbetweentreatments 277
12.3 Presentationofresults 282
viii Contents
12.4 Qualitativeorquantitativefactors 283
12.5 Treatmentstructures 289
12.6 Incompletestructuresandvaryingreplication 294
12.7 Treatmentsasasample 298
12.8 Screeningandselectionexperiments 299
13 Factorialstructureandparticularformsofeffects 305
13.0 Preliminaryexample 305
13.1 Factorswithtwolevelsonly 305
13.2 Improvedyieldcomparisonsintermsofeffects 310
13.3 Analysisbyconsideringsumsanddifferences 315
13.4 Factorswiththreeormorelevels 319
13.5 Theuseofonlyasinglereplicate 324
13.6 Analysisofunreplicatedfactorials 327
14 Fractionalreplication 334
14.0 Preliminaryexamples 334
14.1 Theuseofafractionofacompletefactorialexperiment 335
14.2 Half-replicatesof2nfactorials 336
14.3 Simplefractionsforfactorswithmorethantwolevels 340
14.4 Smallerfractionsfor2nstructures 345
14.5 Irregularfractionsfor2nstructures 349
14.6 Otherfractionsforthree-levelfactorsandformixedlevels 353
14.7 Verysmallfractionsformaineffectestimation 359
15 Incompleteblocksizeforfactorialexperiments 363
15.0 Preliminaryexamples 363
15.1 Smallblocksandmanyfactorialcombinations 363
15.2 Factorswithacommonnumberoflevels 370
15.3 Incompletelyconfoundedeffects 375
15.4 Partialconfounding 378
15.5 Confoundingforgeneralblocksizeandfactorlevels 389
15.6 Thenegativeapproachtoconfoundingfortwo-levelfactors 396
15.7 Confoundingtheoryforotherfactorialstructures 402
15.8 Confoundinginfractionalreplicates 412
15.9 Confoundinginrow-and-columndesigns 417
16 Quantitativefactorsandresponsefunctions 425
16.0 Preliminaryexamples 425
16.1 Theuseofresponsefunctionsintheanalysisofdata 425
16.2 Designobjectives 429
16.3 Specificparameterestimation 430
16.4 Optimaldesigntheory 437
16.5 Discrimination 439