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1、8ClassicalTestsThereisabsolutelynopointincarryingoutananalysisthatismorecomplicatedthanitneedstobe.Occam’srazorappliestothechoiceofstatisticalmodeljustasstronglyastoanythingelse:simplestisbest.Theso-calledclassicaltestsdealwithsomeofthemostfrequentlyusedkindsofanalysisforsingle-sampleandt
2、wo-sampleproblems.8.1SinglesamplesSupposewehaveasinglesample.Thequestionswemightwanttoanswerarethese:Whatisthemeanvalue?Isthemeanvaluesigni?cantlydifferentfromcurrentexpectationortheory?Whatisthelevelofuncertaintyassociatedwithourestimateofthemeanvalue?Inordertobereasonablycon?dentthat
3、ourinferencesarecorrect,weneedtoestablishsomefactsaboutthedistributionofthedata:Arethevaluesnormallydistributedornot?Arethereoutliersinthedata?Ifdatawerecollectedoveraperiodoftime,isthereevidenceforserialcorrelation?Non-normality,outliersandserialcorrelationcanallinvalidateinferencesma
4、debystandardparametrictestslikeStudent’sttest.Itismuchbetterincaseswithnon-normalityand/oroutlierstouseanon-parametrictechniquesuchasWilcoxon’ssigned-ranktest.Ifthereisserialcorrelationinthedata,thenyouneedtousetimeseriesanalysisormixed-effectsmodels.TheRBook,SecondEdition.MichaelJ.Crawle
5、y.?2013JohnWiley&Sons,Ltd.Published2013byJohnWiley&Sons,Ltd.CLASSICALTESTS3458.1.1DatasummaryToseewhatisinvolvedinsummarizingasinglesample,readthedatacalledyfromthe?lecalledclassic.txt:data<-read.table("c:\temp\classic.txt",header=T)names(data)[1]"y"attach(data)Asusual,webeginwithasetof
6、singlesampleplots:anindexplot(scatterplotwithasingleargument,inwhichdataareplottedintheorderinwhichtheyappearinthedataframe),abox-and-whiskerplot(seep.212)andafrequencyplot(ahistogramwithbinwidthschosenbyR):par(mfrow=c(2,2))plot(y)boxplot(y)hist(y,main="")y2<-yy2[52]<-21.75plot(y2)y2.02.2
7、2.42.62.83.02.02.22.42.62.83.0020406080100Indexy2Frequency05201510510152.02.22.42.62.83.0020406080100yIndex346THERBOOKTheindexplot(bottomright)isparticularlyvaluablefordrawingattentiontomistakesinthedataframe.Supposethatthe52ndvaluehadbeenenteredas21.75insteadof2.17
