资源描述：
《the r book analysis of variance》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、11AnalysisofVarianceInsteadoffittingcontinuous,measuredvariablestodata(asinregression),manyexperimentsinvolveexposingexperimentalmaterialtoarangeofdiscretelevelsofoneormorecategoricalvariablesknownasfactors.Thus,afactormightbedrugtreatmentforaparticularcancer,withfivelevels
2、correspondingtoaplaceboplusfournewpharmaceuticals.Alternatively,afactormightbemineralfertilizer,wherethefourlevelsrepresentfourdifferentmixturesofnitrogen,phosphorusandpotassium.Factorsareoftenusedinexperimentaldesignstorepresentstatisticalblocks;theseareinternallyhomogen
3、eousunitsinwhicheachoftheexperimentaltreatmentsisrepeated.Blocksmaybedifferentfieldsinanagriculturaltrial,differentgenotypesinaplantphysiologyexperiment,ordifferentgrowthchambersinastudyofinsectphotoperiodism.Itisimportanttounderstandthatregressionandanalysisofvariance(ANO
4、VA)areidenticalapproachesexceptforthenatureoftheexplanatoryvariables.Forexample,itisasmallstepfromhavingthreelevelsofashadefactor(saylight,mediumandheavyshadecloths)thencarryingoutaone-wayANOVA,tomeasuringthelightintensityinthethreetreatmentsandcarryingoutaregressionwithl
5、ightintensityastheexplanatoryvariable.Asweshallseelateron,someexperimentscombineregressionandANOVAbyfittingaseriesofregressionlines,oneineachofseverallevelsofagivenfactor(thisiscalledanalysisofcovariance;seeChapter12).TheemphasisinANOVAwastraditionallyonhypothesistesting.N
6、owadays,theaimofananalysisofvarianceinRistoestimatemeansandstandarderrorsofdifferencesbetweenmeans.Comparingtwomeansbyattestinvolvedcalculatingthedifferencebetweenthetwomeans,dividingbythestandarderrorofthedifference,andthencomparingtheresultingstatisticwiththevalueofStud
7、ent’stfromtables(orbetterstill,usingqttocalculatethecriticalvalue;seep.287).Themeansaresaidtobesignificantlydifferentwhenthecalculatedvalueoftislargerthanthecriticalvalue.Forlargesamples(n>30)ausefulruleofthumbisthatatvaluegreaterthan2issignificant.InANOVA,weareconcernedwit
8、hcaseswherewewanttocomparethreeormoremeans.Forthetwo-samplecase,thettestandtheANOVAareidentical,
