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1、Chapter2ProbabilityTheoryProbabilitiesarenumbersofthesamenatureasdistancesingeometryormassesinmechanics.Thetheoryassumestheyaregivenbutneedassumenothingabouttheirnumericalvaluesorhowtheyaremeasuredinpractice.WilliamFeller(1906-1970),Americanmathematician2.1OrientationAfteranalyzingthedistributionof
2、thedataviathemethodsofexploratorydataanalysisthenextstepisstatisticalinference,whichisascientificmethodformakinginferencesaboutapopulationbasedupondatacollectedfromasample.Thereliabilityoftheseinferences,andthisisapointwhoseimportancecannotbeexaggerated,dependscruciallyonhowonechoosesthesample.Theth
3、eoreticalideal,whichisoftenquitedifficulttoimplement,isthatweselectthesampleviarandomsampling;thatis,everysubsetofthepopulationofthesamesizehasanequalchance(probability)ofbeingselected.Ifthesampleisselectedbyamethodwhichdeviatessignificantlyfromtherandomsamplingideal,thentheinferenceswilltendtobebiase
4、dbecause,insomesense,thesamplegivesadistortedpictureofthepopulation.IntheirbookStatisticalMethods(7thed.,1980,IowaStateUniversityPress,Ames,Iowa,p.6),SnedecorandCochrandescribeaninterestingclassroomexperimentthatillustrateshowbiasedsamplingcanoccur.Inaclassexercise,apopulationofrocksofvaryingsizesw
5、asspreadoutonalargetablesothatalltherockscouldbeseen.Afterinspectingtherocksandliftinganythattheywished,studentswereaskedtoselectsamplesoffiverockssuchthattheiraverageweightwouldestimateasaccuratelyaspossibletheaverageweightofthewholepopulationofrocks.Theaverageweightsofthestudents’samplesconsistent
6、lyoverestimatedthepopulationmean.Thestudents’consistentoverestimationofthepopulationmeanisanexampleofbiasedsampling.SnedecorandCochranofferthefollowingreasonableexplanationfortheobservedbias:“Alargerandheavierrockismoreeasilynoticedthanasmallerone.”Sincedifferentstudentswill,ingeneral,selectdifferentr
7、ocksfortheirsample,itfollowsthatthevalueoftheaverageweightoftherocksinthesamplewillalsovary.Thisisanexampleofasamplingexperiment;itisalsoanexampleofanexperimentwhoseoutcomesaresubjecttochance.Inthischaptero
