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1、9.NonparametricStatisticsStatisticalanalysesthatdonotdependupontheknowledgeofthedistributionandparametersofthepopulationarecallednonparametricordistribution-freemethods.不依赖于总体的分布及其参数的统计方法称为非参数方法或非分布方法。9.1SignTest符号检验1Thesimplestofallnonparametricmethodsisthesigntest,which
2、isusuallyusedtotestthesignificanceofthedifferencebetweentwomeansinapairedexperiment.最简单的非参数检验是符号检验检验两个总体均值差的显著程度Itisparticularlysuitablewhenthevariouspairsareobservedunderdifferentconditions,acaseinwhichtheassumptionofnormalitymaynothold.However,becauseofitssimplicity,the
3、signtestisoftenusedeventhoughthepopulationsarenormallydistributed.Asisimpliedbyitsnameinthistestonlythesignofthedifference191betweenthepairedvariatesisused.若两个总体的均值相等，那么符号‘＋’、‘－’的概率一样。D=signof(X1－X2)IfpdenotestheprobabilityofadifferenceDbeingpositiveandqtheprobabilityofit
4、sbeingnegative,wehaveashypothesisp=1/2.appropriateteststatisticisX,X~B(n,p)，X---N(‘+”)Totestthehypothesiswewillrejectinfavorofonlyiftheproportionofplussignsissufficientlylessthan1/2,thatis,whenthevaluexofourrandomvariableissmall.Hence,ifthecomputedP-valueislessthanorequal
5、tothesignificancelevel,werejectinfavorof.Totestthehypothesis191werejectinfavorwhentheproportionofplussignsissignificantlylessthanorsignificantlygreaterthan1/2.This,ofcourse,isequivalenttoxbeingsufficientlysmallorsufficientlylarge,respectively.Therefore,ifandthecomputedP-v
6、alueislessthanorequalto,orifandthecomputedP-valueislessthanorequalto,werejectinfavor.Example9.1.1Ataxicompanyistryingtodecidewhethertheuseofradialtiresinsteadofregularbeltedtiresimprovesfueleconomy.Sixteencarsareequippedwithradialtiresanddrivenoveraprescribedtestcourse.Wi
7、thoutchangingdrivers,thesamecarsarethenequippedwiththeregularbeltedtiresanddrivenonceagainoverthetestcourse.Thegasolineconsumption,inkilometersperliter,wasrecordedasfollows:CarRadialtiresBeltedtiresD14.24.1＋24.74.9－36.66.2＋47.06.9＋19156.76.8－64.54.4＋75.75.786.05.8＋97.46.9
8、＋104.94.9116.16.0＋125.24.9＋135.75.3＋146.96.5＋156.87.1－164.94.8＋Canweconcludeusingthe5%levelofsig
