动态可爱卡通作品

ExperimentalDesignObjective: Planningexperimentstoallowcollectionofvaliddata&powerfulstatisticalanalysisofthedataProfessorZeweiLuo,Office:S224,Tel:45404E-mail:z.luo@bham.ac.ukExperimentalDesignObjective: 1ExampleI.Doesgastricfreezingrelievegastriculcers?

PatientswithgastriculcersswallowdeflatedballoonintowhicharefrigeratedliquidwasintroducedDatapublishedinJournalofAmericanMedicalAssociationshowedthatpatientssotreatedhadlessstomachacidandpainthanuntreatedpatientsThedesignI:ThedesignII:

Patientswithgastriculcersaredividedintotwogroups.PatientsingroupIaregivenballoonscontainingrefrigeratedliquidandthoseingroupIIaregivenballoonscontainingnothing(placebo).Noneofthepatientsaretoldwhichballoonaregiven!Databasedonthisexperimentshowed34%improvedwithcoldtreatmentbut34%improvementwasalsoobservedwithplacebo!Anappropriatecontrolisneededtomakeasensiblecomparison!ExampleI.Doesgastricfreezi2ExampleII.DocatspreferMousey(M)toDoggy(D)?Data:

twocatfoods:Mousey(M)&Doggy(D)tomeasureamountoffoodeateningramswhenofferedtoacat.

togiveMandDtoncatseach.Soweneed2ncats(n2).wehavetogroupthe2ncatsrandomlyintothetwofeedinggroupsThedesign:Mgroup:x1,x2,….,xn Dgroup:y1,y2,….,ynExampleII.DocatspreferMou3动态可爱卡通作品4动态可爱卡通作品5However,ifthecatsarerandomlygroupedWheredi=1ifcatiisfatand0otherwise;li=1ifcatiisslimand0otherwiseandPr{di=1}=Pr{di=0}=Pr{li=1}=Pr{li=0}=1/2,i.e.fatorslimcatsareequallylikelygiven“Mousey”or“Doggy”,thentheexpectedvalueofthetstatisticisnowwheneverm=d

Thus,withrandomization,backgroundofexperimentaltreatmentscanbehomogenizedandthussystematicerrorscanbeeffectivelyremoved!However,ifthecatsarerando6(ii).influencesofreplicationinanexperimentaldesign(explainedbythecatfoodexample)

increasingreplicatenumberincreasesaccuracyofmeanestimatebecause

increasingreplicationincreasesd.f.oftteststatistic(2n-2)andinturndecreasesthethresholdtodisproveHo,forexampledfP

0.05P

0.01112.70663.65724.3039.92542.7764.60462.4473.70782.3063.355102.2283.169202.0862.845302.0422.750

1.9602.576Amodestnumberofreplicateslowersthe“hurdle”fortheteststatistictojumpovertoreachsignificance

(ii).influencesofreplicatio7

Howmanyreplicatesareneededtodetectagenuinedifferenceinpreferencebetweenthetwocatfoodswithagivenconfidenceof1-a?Youshouldknow(a).mx=E(x),my=E(y)and(b).s2=Var(ei)Theycanbeobtainedfrompublisheddataorestimatedfromatrial.Forexample,oneplanstotest10%differencebetweenthetwocatfoodwith=25andTheaboveinequalityequationcanbesolvedforanygivena.Forexample,whena=0.05,n

16Howmanyreplicatesareneede8Restraintsonscaleofexperiments?Whyexperimentalscalematters?

balancebetweencostsofalargescaleandgainsinexperimentalefficiencylargescalemaycauseun-controlofexperimentalerrors,forexampleGradientinfertilityofsoilLowHighAfieldtrialtotestyieldperformanceofasetofvarietiesSmallareahasahomogeneousenvironmentsosmalls2

Largeareahasaheterogeneousenvironmentsos2largeRestraintsonscaleofexperim9Solution:divideexperimentintoseveralsub-experiments“blocks”anddissectvariationofblockcomponentfromtotalvariationGradient

infertilityofsoilLowHighSolution:divideexperimentin10Randomizedblocks

BlockatrightanglestogradientifknownGradientinfertilityofsoilLowHighYesNoRandomizedblocks Blockatrig11DesignofrandomisedblocksEachblockwouldcontainthesamenumberofsubjects(plants).Eachblockwouldcontainallthetreatments.Theplantsandtreatmentsineachblockwouldbeseparatelyrandomised.So,eachblockisacompletebutsmallversionoftheexperiment.Theenvironmentaleffectofthegradientisthereforeremovedands2minimised.DesignofrandomisedblocksEac12TheexampleGradientCompletelyrandomised5randomisedblocksTheexampleGradientCompletely13OneWayANOVA4.670.05-0.01174.0537.2511819174.05670.50844.55ItemdfSSMSFProb.BetweenvarietiesWithinvarietiesTotalOneWayANOVA4.670.05-0.01174.14ANOVAtableItemdfSSMSFPVarieties(V)1174.05174.0510.2<0.01Blocks(B)4429.50107.386.28<0.01VxB470.017.501.02nsReplicates10171.017.10Total19844.5ANOVAtableItemdfSSMSFPVarieti15EffectofblockingThereplicateerrorwithinvarietiesisverymuchreducedandsothe‘Variety’effectsmaybedetectedwithlargerchance(experimentalpower)IncreasesPoweroftestCalledaRandomisedCompleteBlockExpt.(RCB).EffectofblockingThereplicat16Typesof‘block’ShelvesinincubatorDifferentoccasionsorsitesDifferentoperatorsTypesof‘block’Shelvesininc17The“1C+3Rs”principlesofexperimentaldesigns

needof“positive”and/or“negative”controltocontrastgenuineeffectsofexperimentaltreatments(C)needofrandomizationtohomogenizebackgroundofexperimentaltreatment(s)andtoremovesystemat