内容简介

PrinciplesandTechniques、Design:BasicPrinciplesandTechniques、TheArtofExperimentation、Replication、Blocking、Randomization、Analysis:BasicPrinciplesandTechniques、PlanningExperiments、AChecklistforPlanningExperiments、RealExperiment——Cotton-SpinningExperiment等等。

目录

Preface
1.PrinciplesandTechniques
1.1.Design:BasicPrinciplesandTechniques
1.1.1.TheArtofExperimentation
1.1.2.Replication
1.1.3.Blocking
1.1.4.Randomization
1.2.Analysis:BasicPrinciplesandTechniques

2.PlanningExperiments
2.1.Introduction
2.2.AChecklistforPlanningExperiments
2.3.ARealExperiment——Cotton-SpinningExperiment
2.4.SomeStandardExperimentalDesigns
2.4.1.CompletelyRandomizedDesigns
2.4.2.BlockDesigns
2.4.3.DesignswithTwoorMoreBlockingFactors
2.4.4.Split-PlotDesigns
2.5.MoreRealExperiments
2.5.1.SoapExperiment
2.5.2.BatteryExperiment
2.5.3.Cake-BakingExperiment
Exercises

3.DesignswithOneSourceofVariation
3.1.Introduction
3.2.Randomization
3.3.ModelforaCompletelyRandomizedDesign
3.4.EstimationofParameters
3.4.1.EstimableFunctionsofParameters
3.4.2.Notation
3.4.3.ObtainingLeastSquaresEstimates
3.4.4.PropertiesofLeastSquaresEstimators
3.4.5.Estimationofo2
3.4.6.ConfidenceBoundfor~r2
3.5.One-WayAnalysisofVariance
3.5.1.TestingEqualityofTreatmentEffects
3.5.2.Useofp-Values
3.6.SampleSizes
3.6.1.ExpectedMeanSquaresforTreatments
3.6.2.SampleSizesUsingPowerofaTest
3.7.ARealExperiment——-SoapExperiment,Continued
3.7.1.Checklist,Continued
3.7.2.DataCollectionandAnalysis
3.7.3.DiscussionbytheExperimenter
3.7.4.FurtherObservationsbytheExperimenter
3.8.UsingSASSoftware
3.8.1.Randomization
3.8.2.AnalysisofVariance
Exercises

4.InferencesforContrastsandTreatmentMeans
4.1.Introduction
4.2.Contrasts
4.2.1.PairwiseComparisons
4.2.2.TreatmentVersusControl
4.2.3.DifferenceofAverages
4.2.4.Trends
4.3.IndividualContrastsandTreatmentMeans
4.3.1.ConfidenceIntervalforaSingleContrast
4.3.2.ConfidenceIntervalforaSingleTreatmentMean
4.3.3.HypothesisTestforaSingleContrastorTreatmentMean
4.4.MethodsofMultipleComparisons
4.4.1.MultipleConfidenceIntervals
4.4.2.BonferroniMethodforPreplannedComparisons
4.4.3.Scheff6MethodofMultipleComparisons
4.4.4.TukeyMethodforAllPairwiseComparisons
4.4.5.DunnettMethodforTreatment-Versus-ControlComparisons
4.4.6.HsuMethodforMultipleComparisonswiththeBest
reatment
4.4.7.CombinationofMethods
4.4.8.MethodsNotControllingExperimentwiseErrorRate
4.5.SampleSizes
4.6.UsingSASSoftware
4.6.1.InferencesonIndividualContrasts
4.6.2.MultipleComparisons
Exercises

5.CheckingModelAssumptions
5.1.Introduction
5.2.StrategyforCheckingModelAssumptions
5.2.1.Residuals
5.2.2.ResidualPlots
5.3.CheckingtheFitoftheModel
5.4.CheckingforOutliers
5.5.CheckingIndependenceoftheErrorTerms
5.6.CheckingtheEqualVarianceAssumption
5.6.1.DetectionofUnequalVariances
5.6.2.DataTransformationstoEqualizeVariances
5.6.3.AnalysiswithUnequalErrorVariances
5.7.CheckingtheNormalityAssumption
5.8.UsingSASSoftware
5.8.1.UsingSAStoGenerateResidualPlots
5.8.2.TransformingtheData
Exercises

6.ExperimentswithTwoCrossedTreatmentFactors
6.1.Introduction
6.2.ModelsandFactorialEffects
6.2.1.TheMeaningofInteraction
6.2.2.ModelsforTwoTreatmentFactors
6.2.3.CheckingtheAssumptionsontheModel
6.3.Contrasts
6.3.1.ContrastsforMainEffectsandInteractions
6.3.2.WritingContrastsasCoefficientLists
6.4.AnalysisoftheTwo-WayCompleteModel
6.4.1.LeastSquaresEstimatorsfortheTwo-WayCompleteModel
6.4.2.Estimationofo~fortheTwo-WayCompleteModel
6.4.3.MultipleComparisonsfortheCompleteModel
6.4.4.AnalysisofVariancefortheCompleteModel
6.5.AnalysisoftheTwo-WayMain-EffectsModel
6.5.1.LeastSquaresEstimatorsfortheMain-EffectsModel
6.5.2.Estimationofa2intheMain-EffectsModel
6.5.3.MultipleComparisonsfortheMain-EffectsModel
6.5.4.UnequalVariances
6.5.5.AnalysisofVarianceforEqualSampleSizes
6.5.6.ModelBuilding
6.6.CalculatingSampleSizes
6.7.SmallExperiments
6.7.1.OneObservationperCell
6.7.2.AnalysisBasedonOrthogonalContrasts
6.7.3.TukeysTestforAdditivity
6.7.4.ARealExperiment——AirVelocityExperiment
6.8.UsingSASSoftware
6.8.1.ContrastsandMultipleComparisons
6.8.2.Plots
6.8.3.OneObservationperCell
Exercises

7.SeveralCrossedTreatmentFactors
7.1.Introduction
7.2.ModelsandFactorialEffects
7.2.1.Models
7.2.2.TheMeaningofInteraction
7.2.3.SeparabilityofFactorialEffects
7.2.4.EstimationofFactorialContrasts
7.3.Analysis——EqualSampleSizes
7.4.ARealExperiment——Popcorn-MicrowaveExperiment
7.5.OneObservationperCell
7.5.1.AnalysisAssumingThatCertainInteractionEffectsAreegligible
7.5.2.AnalysisUsingNormalProbabilityPlotofEffectEstimates
7.5.3.AnalysisUsingConfidenceIntervals
7.6.DesignfortheControlofNoiseVariability
7.6.1.AnalysisofDesign-by-NoiseInteractions
7.6.2.AnalyzingtheEffectsofDesignFactorsonVariability.
7.7.UsingSASSoftware
7.7.1.NormalProbabilityPlotsofContrastEstimates
7.7.2.Voss-WangConfidenceIntervalMethod
7.7.3.IdentificationofRobustFactorSettings
7.7.4.ExperimentswithEmptyCells
Exercises

8.PolynomialRegression
8.1.Introduction
8.2.Models
8.3.LeastSquaresEstimation(Optional)
8.3.1.NormalEquations
……
9.AnalysisofCovariance
10.CompleteBlockDesigns
11.IncompleteBlockDesigns
12.DesignswithTwoBlockingFactors
13.ConfoundedTwo-LevelFactorialExperiments
14.ConfoundinginGeneralFactorialExperiments
15.FractionalFactorialExperiments
16.esponseSurfaceMethodology
17.andomEffectsandVarianceComponents
18.estdeModels
19.plit-PlotDesigns
A.ables
Bibliography
IndexofAuthors
IndexofExperiments
IndexofSubjects

精彩书摘

Intheanalysisofdata,itisdesirabletoprovidebothgraphicalandstatisticalanalyses.Plotsthatillustratetherelativeresponsesofthefactorsettingsunderstudyallowtheexperimentertogainafeelforthepracticalimplicationsofthestatisticalresultsandtocommunicateeffectivelytheresultsoftheexperimenttoothers.Inaddition,dataplotsallowtheproposedmodeltobecheckedandaidintheidentificationofunusualobservations,asdiscussedinChapter5.Statisticalanalysisquantifiestherelativeresponsesofthefactors,thusclarifyingconclusionsthatmightbemisleadingornotatallapparentinplotsofthedata.
Thepurposeofanexperimentcanrangefromexploratory(discoveringnewimportantsourcesofvariability)toconfirmatory(confirmingthatpreviouslydiscoveredsourcesofvariabilityaresufficientlymajortowarrantfurtherstudy),andthephilosophyoftheanalysisdependsonthepurposeoftheexperiment.Intheearlystagesofexperimentationtheanalysismaybeexploratory,andonewouldplotandanalyzethedatainanywaythatassistsintheidentificationofimportantsourcesofvariation.Inlaterstagesofexperimentation,analysisisusuallyconfirmatoryinnature.Amathematicalmodeloftheresponseispostulatedandhypothesesaretestedandconfidenceintervalsarecalculated.Inthisbook,weuselinearmodelstomodelourresponseandthemethodofleastsquaresforobtainingestimatesoftheparametersinthemodel.ThesearedescribedinChapter3.Ourmodelsincluderandom"errorvariables"thatencompassallthesourcesofvariabilitynotexplicitypresentinthemodel.Weoperateundertheassumptionthattheerrortermsarenormallydistributed.However,mostoftheproceduresinthisbookaregenerallyfairlyrobusttononnormality,providedthattherearenoextremeobservationsamongthedata.Itisrarenowadaysforexperimentaldatatobeanalyzedbyhand.Mostexperimentersandstatisticianshaveaccesstoacomputerpackagethatiscapableofproducing,attheveryleast,abasicanalysisofdataforthesimplestexperiments.Totheextentpossible,foreachdesigndiscussed,weshallpresentusefulplotsandmethodsofanalysisthatcanbeobtainedfrommoststatisticalsoftwarepackages.Wewillalsodevelopmanyofthemathematicalformulasthatliebehindthecomputeranalysis.Thiswillenablethereadermoreeasilytoappreciateandinterpretstatisticalcomputerpackageoutputandtheassociatedmanuals.Computerpackagesvaryinsophistication,flexibility,andthestatisticalknowledgerequiredoftheuser.TheSASsoftwareisoneofthebetterpackagesforanalyzingexperimentaldata.Itcanhandleeverymodeldiscussedinthisbook,andalthoughitrequiressomeknowledgeofexperimentaldesignonthepartoftheuser,itiseasytolearn.WeprovidesomebasicSASstatementsandoutputattheendofmostchapterstoillustratedataanalysis.

前言/序言

  Ourinitialmotivationforwritingthisbookwastheobservationfromvariousstudentsthatthesubjectofdesignandanalysisofexperimentscanseemlike"abunchofmiscellaneoustopics."Webelievethattheidentificationoftheobjectivesoftheexperimentandthepracticalconsiderationsgoverningthedesignformtheheartofthesubjectmatterandserveasthelinkbetweenthevariousanalyticaltechniques.Wealsobelievethatlearningaboutdesignandanalysisofexperimentsisbestachievedbytheplanning,running,andanalyzingofasimpleexperiment.
  Withtheseconsiderationsinmind,wehaveincludedthroughoutthebookthedetailsoftheplanningstageofseveralexperimentsthatwereruninthecourseofteachingourclasses.Theexperimentswererunbystudentsinstatisticsandtheappliedsciencesandaresufficientlysimplethatitispossibletodiscusstheplanningoftheentireexperimentinafewpages,andtheprocedurescanbereproducedbyreadersofthebook.Ineachoftheseexperiments,wehadaccesstotheinvestigatorsactualreport,includingthedifficultiestheycameacrossandhowtheydecidedonthetreatmentfactors,theneedednumberofobservations,andthelayoutofthedesign.Inthelaterchapters,wehaveincludeddetailsofanumberofpublishedexperiments.Theoutlinesofmanyotherstudentandpublishedexperimentsappearasexercisesattheendsofthechapters.omplementingthepracticalaspectsofthedesignarethestatisticalaspectsoftheanal-ysis.Wehavedevelopedthetheoryofestimablefunctionsandanalysisofvariancewithsomecare,butatalowmathematicallevel.Formulaeareprovidedforalmostallanalysessothatthestatisticalmethodscanbewellunderstood,relateddesignissuescanbediscussed,andcomputationscanbedonebyhandinordertocheckcomputeroutput.
  Werecommendtheuseofasophisticatedstatisticalpackageinconjunctionwiththebook.Useofsoftwarehelpstofocusattentiononthestatisticalissuesratherthanonthecalculation.OurparticularpreferenceisfortheSASsof~vare,andwehaveincludedtheelementaryuseofthispackageattheendofmostchapters.ManyoftheSASprogramfilesanddatasetsusedinthebookcanbefoundatwww.springer-ny.com.However,thebookcanequallywellbeusedwithanyotherstatisticalpackage.AvailabilityofstatisticalsoRwarehasalsohelpedshapethebookinthatwecandiscussmorecomplicatedanalyses——theanalysisofunbalanceddesigns,forexample.

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