試題英文數(shù)理統(tǒng)計(jì)

填空（一）各章節(jié)的introductionContinuousvariablesorintervaldatacanassumeanyvalueinsomeintervalofrealnumbers.連續(xù)變量或間隔數(shù)據(jù)可以假設(shè)在某個(gè)實(shí)數(shù)間隔中的任意值。（measurement）Discretevariablesassumeonlyisolatedvalues.離散變量只假定孤立的值。(counting)Thelowerorfirstquartileisthe25thpercentileandtheupperorthirdquartileisthe75thpercentile.ThefistqurtileQ1isthemedianoftheobservationsfallingbelowthemedianoftheentiresampleandthethirdquartileQ3isthemedianoftheobservationsfallingabovethemedianoftheentiresample.TheinterquartilerangeisdefinedasIQR=Q3-Q1.第一個(gè)四分位數(shù)Q1是低于整個(gè)樣本中位數(shù)的觀測(cè)值的中位數(shù)，第三個(gè)四分位數(shù)Q3是高于整個(gè)樣本中位數(shù)的觀測(cè)值的中位數(shù)。四分位數(shù)范圍定義為IQR=Q3-Q1。Statisticsappliedtothelifesciencesinoftencalledbiostatisticsorbiometry.統(tǒng)計(jì)學(xué)應(yīng)用于生命科學(xué)，通常稱為生物統(tǒng)計(jì)學(xué)或生物計(jì)量學(xué)。Adescriptivemeasureassociatedwitharandomvariablewhenitisconsideredovertheentirepopulationiscalledaparameter.當(dāng)在整個(gè)總體中考慮一個(gè)隨機(jī)變量時(shí)，與它相關(guān)的描述性度量稱為參數(shù)Oneisforcedtoexamineasubsetorsampleofthepopulationandmakeinferencesabouttheentirevariableofasampleiscalledastatistic.人們被迫檢查總體中的一個(gè)子集或樣本，并對(duì)樣本中的整個(gè)變量做出推斷，這被稱為統(tǒng)計(jì)量。Thesummarydescriptivecharacteristicsofapopulationofobjectsarecalledpopulationparametersorjustparameters.對(duì)一個(gè)物體總體的概括描述特征稱為總體參數(shù)或簡(jiǎn)稱參數(shù)。These（population）parametersareusuallydenotedbyGreeklettersanddonotvarywithinapopulation.這些(人口)參數(shù)通常用希臘字母表示，在人口中不發(fā)生變化。thesummarydescriptivecharacteristicsofasampleofobjects,isasubsetofthepopulationarecalledstatistics.6.概括描述一個(gè)樣本對(duì)象的特征，是總體的一個(gè)子集，稱為統(tǒng)計(jì)量。Measuresofcentraltendency:meanmedianandmode.Thepopulationmeanisthesumofthevaluesofthevariableunderstudydividedbythetotalnumberofobjectsinthepopulation.8.總體平均值是被研究變量的值除以總體對(duì)象總數(shù)的總和。Themostwidelyutilizedmeasureofcentraltendencyisthearithmeticmeanoraverage.9.使用最廣泛的集中趨勢(shì)度量是算術(shù)平均值或平均。10、Thedepthofavalueisitspositionrelativetothenearestextremewhenthedataarelistedinorderfromsmallesttolargest.值的深度是當(dāng)數(shù)據(jù)按從小到大的順序排列時(shí)，它相對(duì)于最近的極值的位置。Themodeisdefinedasthemostfrequentlyoccurringvalueinadataset.模態(tài)定義為數(shù)據(jù)集中出現(xiàn)頻率最高的值。Thereareseveralcommonlyusedmeasurestodescribethelocationorcenterofapopulationorsample，theseincludemean、medianandmode，themeasuresofdispersionandvariability:variance，standarddeviationandrange.Thequantityisthesumofthesesquareddeviatesandisreferredtoasthecorrectedsumsquares,denotedbyCSS.Ifafixedamount（c）isaddedorsubtractedfromeachobservationinadataset,thesamplemeanwillbeincreasedordecreasedbythatamount（c），butthevariancewillbeunchanged（equal）.Multiplicativecodinginvovlesmultiplyingordividingeachobservationinadatasetbyaconstant.乘法編碼是將數(shù)據(jù)集中的每個(gè)觀測(cè)值乘以或除以一個(gè)常數(shù)acompactwaytoreportthedescritiveinformationinvovlingthequartilesandtherangiswithafive-summaryofthedata.Itconsistsofthemedian,thetwoquartilesandtwoextremes.Thevisualcounterparttoafive-summaryisaboxplot.五摘要的視覺(jué)對(duì)應(yīng)物是盒狀圖。Theprobabilityoftheeventisanumericalmeasureofthelikeihoodordegreeofpredictabilitythattheeventwilloccur.TheempiricalprobabilityofaneventAisdefinedasH0:nullhypothesis；Ha:alternativeorresearchhypothesisWehavegeneratedtwomutuallyexclusiveandall-inclusivepossibilities.21H0:nullhypothesis;Ha:alternativeorresearchhypothesis我們已經(jīng)產(chǎn)生了兩種相互排斥又包羅萬(wàn)象的可能性。thevaluestodeterminesignificantdifferencesfromexpectationwehavecutoffvalues,usuallycalledcriticalvalues.22.我們用截?cái)嘀祦?lái)確定與期望有顯著差異的值，通常稱為臨界值。Thepowerofthetestdependsonboththelevelofsignificance(α)andthevalueofμ0-μ1,thetruedifferencebetweenmeans.檢驗(yàn)的威力取決于顯著性水平(α)和平均值之間的真實(shí)差值μ0-μ1Thespreadofthedistributionisdeterminedbythestandarderror,sandn.Quantiativevariablesfallintotwomajorcategoriescontinuousvariables（orintervaldata）？anddiscretevariables.EventA1andA2areindependentifandonlyifP（A1∩A2）=P（A1）·P（A2）Arandomvariableandisavariablewhoseactualvalueisdeterminedbychanceoperations一個(gè)隨機(jī)變量，它的實(shí)際值由隨機(jī)操作決定LetXbeanormalrandomvariableZwithmeanμ，andstandarddeviationσ，thrtransformationZ=（x-μ）/σ，expressXasthestandardnormalrandomvariablewithμ=0andσ=128設(shè)X為平均μ的正態(tài)隨機(jī)變量Z，標(biāo)準(zhǔn)差σ，變換Z=(X-μ)/σ，將X表示為μ=0，σ=1的標(biāo)準(zhǔn)正態(tài)隨機(jī)變量LetXbebinomialrandomvariablewithparametersnandp.Theμ=E（X）=npandσx2=VarX=np（1-p）.LetXbeaPoissonrandomvariablewithparameterμ.TheE（X）=μandσx2=VarX=μ.（z不要）is（ida）anormaldistributionwithμ=0andσ=1，while（不要t）is（ida）atdistributionwithμ=0andσdependingonthesamplesize，Therandomvariable（n-1）s2/σ2isachi-square/（X2）distribution.withμ=E（X2）=v（自由度）/n-1，andVarX2=2v/2（n-1）Forlargevalueofn，thebinomialrandomvariable（X）isappromatelynormalwithmeanμ=npandσ=√np（1-p）.Asimpleruleofthumbisthatthisapproximationisacceptableforvaluesnandpsuchthatnp（1-p）＞3Inhypithesistest，H0isusuallycallednullhypothesis，Haiscalledthealternativeorresearchhypothesis.TherelationshipbetweenH0andHaismutuallyexclusiveandall-inclusivepossibilities.IfwerejectH0，wemightmakeaTypeIerror（rejectingatrueHo），andtheprobabilityisα，IfrejectHawemightmakeTypeIIerror（acceptingafalseHo），andtheprobabilityisdenotedbyβ，1-βiscalledthepowerofthetest如果我們拒絕H0，我們可能犯I型錯(cuò)誤(拒絕一個(gè)真Ho)，概率是α，如果我們拒絕Ha，我們可能犯II型錯(cuò)誤(接受一個(gè)假Ho)，概率用β表示，1-β稱為測(cè)試的冪Thequantity∑（Xi-X拔）2isthesumofthesquareddeviatesandisreferredtoasthecorrectedsumsquaresdenotedbyCSS.數(shù)量(Xi-X拔)偏離平方的總和,稱為糾正平方和用CSS。Thepatternofbehaviorofadiscreterandomvariableisdescribedbyamathematicalfunctioncalledadensityfunctionorprobabilitydistribution離散隨機(jī)變量的行為模式是由稱為密度函數(shù)或概率分布的數(shù)學(xué)函數(shù)來(lái)描述的Themodernstudyofthelifesciencesincludesexperimentationdategatheringandinterpretation.生命科學(xué)的現(xiàn)代研究包括實(shí)驗(yàn)、數(shù)據(jù)收集和解釋。Bonferronitalower（smaller）αlevel37Bonferroni是較低(較小)的α能級(jí)Regressionanalysisxcanmeasurewithouterror.Correlationanalysisbothvariablesmeasuredwitheroor.回歸分析可以無(wú)誤差地測(cè)量。相關(guān)分析兩個(gè)變量測(cè)量的誤差。Linearregression：SSTotal=SSR+SSE（=SSTreat+SSError）？RandomizedcompleteblockdesignANOVA.SSTotal：SSTreat（k-1）SSBlock（b-1）、SSError（k-1）（b-1）.meanseparationtechniquesormultiplecomparisons.approaches：Bonferronittest.Dubcan'smultiperangetest（DMRT）Afivenumbersummary：thetwoquartiles、twoextremes、median.Arandomvariableisavariablewhoseactualvaluesisdeterminedbychanceoperations.TheemiricalprobabilityofaneventAisdefinedasP（A）=nA/n=numberoftimesAoccurred？/numberoftrialsrun.Thenumbernfactoralisdenotedbyn！，ThenumberofwaysofchoosingKobjectsfromnwithoutregardtoorderis（nk）=nCk（括號(hào)里n在上k在下）n的階乘用n表示!，從n個(gè)對(duì)象中任意順序選擇K個(gè)對(duì)象的方法個(gè)數(shù)為ANOVA：AnalysisofVarianceModelIANOVA：analyzeasafixeseffectsModelIIANOVA：analyzeasarandom-effectsParameter參數(shù)characteristics特征Population總體：Nμσ2；Sample樣本：n、x拔、s2；statistics統(tǒng)計(jì)數(shù)；variable變量；mean（x拔、μ）平均數(shù)；Median中位數(shù)；Mode中數(shù)；range極差；variance方差（σ2、s2）；StandardDevration標(biāo)準(zhǔn)差（σ、s）；biostatistics/biometry生物統(tǒng)計(jì)學(xué)；Quartiles四分位數(shù)IQR=Q3-Q1；a平方和與自由度的拆分RandomizedcopleteblockdesignANOVATheanalysisofvariancetableforarandomizedcompleteblockdesignSourceofvarianceSSdfMSFc.v.TreatmentsSSTreatk-1SeeTableC.6BlocksSSBlocksb-1ErrorSSError(k-1)(b-1)TotalSSTotalkb-1FactorialDesignTwo-wayANOVASourceofvarianceSSdfCellsSSCellsab-1AfactorsSSAa-1BfactorsSSBb-1A×BinteractionSSA×B(a-1)(b-1)ErrorSSErrorab(n-1)TotalSSTotalabn-1各種分布的特征:概率分布泊松分布標(biāo)準(zhǔn)正態(tài)分布t分布分布F分布半期考試填空問(wèn)答題考試內(nèi)容：第五章ExplainwhymostresearchersaremorecomfortablerejectingH0thanacceptingit.Useaprobabilityargumentinyourexplanation.DiscusstherelationshipbetweentheCentralLimitTheoremandthesamplingdistributionfor.TheCentralLimitTheoremdescribesthesamplingdistributionofasnormalorapproximatelynormalwithastandarddeviationequaltothestandarderrorofthemean.theCentralLimitTheoremOutlinethefactorsaffectingTypeⅡerrorandthepowerofatestofthehypothesis.Explainwhyitisinappropriatetousetheterm“proof”whenperformingtestsofhypothesis.InstandardEnglish,toprovesomethingmeanstoestablishconclusivelyitstruthorvalidity.Withtestsofhypothesiswealwayshavesomeprobabilityorpossibilityofbeingincorrect.AcceptinganH0TypeⅠerror(acceptingafalseH0)andhasaprobabilityofα.RejectingWhyareH0andHaalwayswrittenasmutuallyexclusiveandall-inclusivepredictions?計(jì)算置信區(qū)間均值之間的比較（獨(dú)立樣本t檢驗(yàn)不考）提出假設(shè)H0：Ha：確定檢驗(yàn)統(tǒng)計(jì)量若總體方差已知，使用Z分布若總體方差已知，使用t分布做出統(tǒng)計(jì)判斷P125P151方差分析（答題模式同半期一樣，11.3中2×2列聯(lián)表）One-wayANOVAThehypothesesareH0:Ha:atleastonepairofμ’sarenotequal.TheanalysisofvariancetableSourceofvariationSunofsquaresdfMsFc.v.TreatmentsSSTreatk-1SeeTableC.6ErrorSSErrorN-kTotalSSTotalN-12×2ContingencyTablesn11n12n1.n21n22n2.n.1n.2n..ThehypothesesareH0:twotitlesareindependent.Ha:twotitlesaredependent.Thescientificmethod:ObservationofaParticularEventStatementoftheProblemFormulationofaHypothesisMakingaPredictionDesignoftheExperimentExplainwhymostresearchersaremorecomfortablerejectingH0thanacceptingit.Useaprobabilityargumentinyourexplanation.Solution:BecauseifwerejectH0,wemightmakeaTypeⅠerrorandtheprobabilityisα.IfweacceptHα,wemightmakeaTypeⅡerrorandtheprobabilityisβ.Butascertainingtheprobabilityofthiskindoferrorisimpossibleinmostexperimentalsituations.SomostresearchersaremorecomfortablerejectingH0thanacceptingit.DiscusstherelationshipbetweentheCentralLimitTheoremandthesamplingdistributionfor.Solution:TheCentralLimitTheoremdescribesthesamplingdistributionofX-barasnormalorapproximatelynormalwithastandarddeviationequaltothestandarderrorofthemean.OutlinethefactorsaffectingTypeⅡerrorandthepowerofatestofthehypothesis.Solution:TheprobabilityofaTypeⅡerrorisdecreasedandthepowerofatestsubsequentlyincreasedwhenthesamplingdistributionsunderH0andHαoverlapless.Thespreadofthesedistributionsisdecreasedbydecreasingσorincreasingn.Explainwhyitisinappropriatetousetheterm“proof”whenperformingtestsofhypothesis.Solution:InstandardEnglish,toprovesomethingmeanstoestablishconclusivelyitstruthorvalidity.Withtestsofhypothesiswealwayshavesomeprobabilityorpossibilityofbeingincorrect.AcceptinganH0couldleadtoaTypeⅠerror(acceptingafalseH0)andhasaprobabilityofα.RejectinganH0couldleadtoaTypeⅡerror(rejectingatrueH0)andhasaprobabilityofβ.Whileαorβissometimesquitesmalleachisneverzero.WesayH0issupportedornotsupportedbythestatisticaltest,neverthatthetestprovesH0tobetrueorfalse.WhyareH0andHαalwayswrittenasmutuallyexclusiveandallinclusivepredictions?Solution:Accordingtothephilosophyofscienceonlyoneofthehypothesescanbetrue.IfH0istrue,thenHαmustbefalseandviceversa.ThisrequiresthatH0andHαbewrittenasmutuallyexclusiveandall-inclusivepredictions.Exactlyoneofthesepredictionswillbesupportedbythestatisticaltest.Todothistheymustbeinclusiveofallpossibleoutcomes.Canyouthinkofbiologicalexampleswherethiskindoflogicmightleadyoutochooseverysmallalphalevels?Solution:Supposeanewtreatmentforaparticularcanceristhoughttoprolonglifebysixmonths.Ifthistreatmentisverycostlyorpainful,youwouldchooseasmallalphaleveltobeveryconfidentthatitactuallyworksbeforeitismarketedasaneffectivetreatment.Itwouldbetragictosubmitpatientstopainfulorcostlytreatmentthatarenoteffective.ExplaintheCentralLimitTheorem.Solution:WhensamplingfromanonnormallydistributedpopulationwithmeanμXandvarianceσ2x,thedistributionofthesamplemean(samplingdistribution)willhavethisproperty:ThedistributionofX-barswillbeapproximatelynormalitybecomingbetterasthesamplesizeincreases.Generally,thesamplesizerequiredforthesamplingdistributionofX-bartoapproachnormalitydependsontheshapeoftheoriginaldistribution.Samplesof30ormoregiveverygoodnormalapproximationsforthissamplingdistributionofX-barinnearlyallsituations.Listthe9typicalstepsinastatisticaltestofhypothesis.Solution:(1)Statetheproblem.Formulatethenullandalternativehypotheses:H0:μ=10ozHα:μ≠10ozChoosethelevelofsignificance.Determinetheappropriateteststatistic.Calculatetheappropriateteststatistic.(a)Determinethecriticalvaluesforthesamplingdistributionandappropriatelevelofsignificance.(b)DeterminethePvalueoftheteststatistic(7)(a)Comparetheteststatistictothecriticalvalues(b)ComparethePvaluetoyourchosenlevelofsignificance(8)Basedonthecomparisoninstep7,acceptorrejectH0(9)Stateyourconclusionandanswerthequestionposedinstep1.Whenregressionanalysisisappropriate,wedothefollowing:GraphdatatoascertainthatalinearrelationshipisapparentCalculatetheregressionequationusingtheleastsquaresmethodTestthesignificanceofthisequationwithanalysisofvarianceIftheH0isrejected,plottheequationwithanalysisofvarianceFinally,calculateanyrequiredconfidenceintervalsinsupportoflinearrelationshipBoxPlotsDrawahorizontalorverticalreferencescalebasedontherangeofthedatasetCalculatethemedian,Q1,Q3,andtheIQRDeterminethefencesf1andf3usingtheformulasbelow.Anypointslyingoutsidethesefenceswillbeconsideredoutliersandmaywarrantfurtherinvestigation.f1=Q1-1.5(IQR)f3=Q3+1.5(IQR)Locatethetwo“adjacentvalues”,therearethesmallestandlargestdatavaluesinsidethefencesLightlymarkthemedian,quartilesandadjacentvaluesonthescale.Chooseascaletospreadthesepointsoutsufficiently.Besidethescale,constructaboxwithendsatthequartilesandwithadashedinteriorlinedrawnatthemedian.Generallythiswillnotbeatthemiddleofthebox.Drawa“whisker”(linesegment)fromthequartilestotheadjacentvaluesthataremarkedwithcrosses“X”.Markanyoutliersbeyondthefences(equivalently,beyondtheadjacentvalues)withopencircles”○”.Five-numbersummary:Median:XmedianQuartiles:Q1Q3Extremes：LargestnumberSmallestnumberModelANOVASolution:（1）ThehypothesesareH0:μ1=μ2=μ3=…,μkHa:Atleastofoneoftheμi’sarenotequalAccordingtotheformulationtocomputetheSSTotal=SSTreat+SSErrorThesummarydatatotestH0appearinthetablebelowSourceofvariationSumofsquaresdfMSFc.vTreatmentSSTreatk-1SSTreat/k-1MSTreat/MSEseeTableC.6ErrorSSErrorN-kSSError/N-kTotalSSTotalN-1ThecriticalvaluefromTableC.6witha=0.05andv1=k-1andv2=b-1,isC.V.SincewhenC.V.＜F,werejectH0,acceptHa.Itindicatesthatthetreatmentmeansaresignificantlydifferent.AndthenifC.V.＞F,weacceptH0,rejectHa.Itindicatesthatthemeansquaresdietsisnotsignificantlydifferent.If.C.V.＜F,wefindatleasttwoofthesemeansaresignificantlydifferent.weusetheDMRTtofindwhichmeanhavethesignificantlydifferent.firstthemeansarealreadyrank-ordered.WecalculatetheSSRp,ifcalculatedvalue＞SSRp,itissignificantlydifferent.①rpisatablevalueofTableC.7(2)MSEistheerrormeansquarefromtheANOVAtable(3)nisthecommonsamplesizeWeusedifferentsuperscriptletterstosaytheyaresignificantdifferences.Ifcalculatedvalue＜SSRp,itisnotsignificantlydifferent.Weusesamesuperscriptletterstosaytheyarenotsignificantdifferences.Forexample`X1a,`X2a,`X3bWecangettheconclusionthatthemeanfortheX1andX2isnotsignificantlydifferent,themeanfortheX2andX3issignificantlydifferent,themeanfortheX1andX3issignificantlydifferent.RandomizedCompleteBlockDesignANOVASolution:ThehypothesesareH0:μ1=μ2=μ3=…,μkHa:Atleastofoneoftheμi’sarenotequalAccordingtotheformulationtocomputetheSSTotal=SSTreat+SSErrorThesummarydatatotestH0appearinthetablebelowSourceofvariationSumofsquaresdfMSFc.v.TreatmentSSTreatk-1SSTreat/k-1MSTreat/MSEseeTableC.6BlocksSSBlocksb-1SSBlocks/b-1ErrorSSError(k-1)(b-1)SSError/(k-1)(b-1)TotalSSTotalkb-1ThecriticalvaluefromTableC.6witha=0.05andv1=k-1andv2=(k-1)(b-1),isC.V.SincewhenC.V.＜F,werejectH0,acceptHa.Itindicatesthatthetreatmentmeansaresignificantlydifferent.AndthenifC.V.＞F,weacceptH0,rejectHa.Itindicatesthatthemeansquaresdietsisnotsignificantlydifferent.If.C.V.＜F,wefindatleasttwoofthesemeansaresignificantlydifferent.WeusetheDMRTtofindwhichmeanhavethesignificantlydifferent.firstthemeansarealreadyrank-ordered.WecalculatetheSSRp,ifcalculatedvalue＞SSRp,itissignificantlydifferent.rpisatablevalueofTableC.7MSEistheerrormeansquarefromtheANOVAtablenisthecommonsamplesizeWeusedifferentsuperscriptletterstosaytheyaresignificantdifferences.Ifcalculatedvalue＜SSRp,itisnotsignificantlydifferent.Weusesamesuperscriptletterstosaytheyarenotsignificantdifferences.Forexample`X1a,`X2a,`X3bWecangettheconclusionthatthemeanfortheX1andX2isnotsignificantlydifferent,themeanfortheX2andX3issignificantlydifferent,themeanfortheX1andX3issignificantlydifferent.FactorialDesignTwo-WayANOVASolution:HeanalysisofvariancetableSourceofvariationSSdfMSE(MS)CellsSScellsab-1MScellsAfactorsSSBa-1MSABfactorsSSAb-1MSBA*BinteractionSSA*B(a-1)(b-1)MSA*BErrorSSErrorab(n-1)MSETotalSSTotalabn-1(1)TestforinteractionbetweenfactorsFirsttestforinteractionbetweenthetwotypeoffacterbeinginvestigated.ThehypothesesareH0：(αβ）ij=0foralli,jHa：(αβ）ij≠0forsomei,j.TheappropriatetestforthisnullhypothesisisFA*B=MSA*B/MSE,withdegreesoffreedom,ν1=(a-1)(b-1),ν2=ab(n-1)fromTableC.6witha=0.05andv1=(a-1)(b-1)andv2=ab(n-1),isC.V.WhenFA*B＜C.V.,weacceptH0.Therearenointeractions.Sotheanalysisiscontinuedcarryingouttwotests.(2)Iftherearenointeractions(a)TestwhethertherearedifferencesinmeansforA-factortreatmentSThehypothesesareH0：μi..，sallequal(αi=0foralli)Ha：atleastonepairofμi..，snotequalUsingtheteststatisticFA=MSA/MSE,Withdegreesoffreedomν1=a-1,ν2=ab(n-1)whenC.V.＜FA,werejectH0,acceptHa.Itindicatesthatatleastonepairofμi..，snotequal.AndthenifC.V.＞FA,weacceptH0,rejectHa.ItindicatesthatthemeanforfactorAlevelareallequal.If.C.V.＜FAwefindatleastsomeofthesemeansaresignificantlydifferent.weusetheDMRTtofindwhichmeanshavethesignificantlydifferent.WecalculatetheSSRp,ifcalculatedvalue＞SSRp,itissignificantlydifferent.Weusedifferentsuperscriptletterstosaytheyaresignificantdifferences.Ifcalculatedvalue＜SSRp,itisnotsignificantlydifferent.Weusesamesuperscriptletterstosaytheyarenotsignificantdifferences.Forexample`X1a,`X2a,`X3bWecangettheconclusionthatthemeanfortheX1andX2isnotsignificantlydifferent,themeanfortheX2andX3issignificantlydifferent,themeanfortheX1andX3issignificantlydifferent.(b)Similary,testwhethertherearedifferencesinmeansforB-factortreatmentsThehypothesesareH0：μi..，sallequal(αi=0foralli)Ha：atleastonepairofμi..，snotequalUsingtheteststatisticFB=MSB/MSE,Withdegreesoffreedomν1=b-1,ν2=ab(n-1)whenC.V.＜FBwerejectH0,acceptHa.Itindicatesthatatleastonepairofμi..，snotequal.AndthenifC.V.＞FB,weacceptH0,rejectHa.ItindicatesthatthemeanforfactorAlevelareallequal.If.C.V.＜FBwefindatleastsomeofthesemeansaresignificantlydifferent.weusetheDMRTtofindwhichmeanshavethesignificantlydifferent.WecalculatetheSSRp,ifcalculatedvalue＞SSRp,itissignificantlydifferent.Weusedifferentsuperscriptletterstosaytheyaresignificantdifferences.Ifcalculatedvalue＜SSRp,itisnotsignificantlydifferent.Weusesamesuperscriptletterstosaytheyare