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1、StatLabs:MathematicalStatisticsThroughApplicationsDeborahNolanTerrySpeedSpringerToBenandSammyD.N.ToSallyT.P.SThispageintentionallyleftblankPrefaceThisbookusesamodelwehavedevelopedforteachingmathematicalstatisticsthroughin-depthcasestudies.Traditionalstatisticstextshaveman
2、ysmallnumer-icalexamplesineachchaptertoillustrateatopicinstatisticaltheory.Here,weinsteadmakeacasestudythecenterpieceofeachchapter.Thecasestudies,whichwecalllabs,raiseinterestingscientificquestions,andfiguringouthowtoansweraquestionisthestartingpointfordevelopingstatistical
3、theory.Thelabsaresubstan-tialexercises;theyhavenontrivialsolutionsthatleaveroomfordifferentanalysesofthedata.Inadditiontoprovidingtheframeworkandmotivationforstudyingtopicsinmathematicalstatistics,thelabshelpstudentsdevelopstatisticalthinking.Wefeelthatthisapproachintegra
4、testheoreticalandappliedstatisticsinawaynotcommonlyencounteredinanundergraduatetext.TheStudentThebookisintendedforacourseinmathematicalstatisticsforjuniorsandseniors.Weassumethatstudentshavehadoneyearofcalculus,includingTaylorseries,andacourseinprobability.Wedonotassumest
5、udentshaveexperiencewithstatisticalsoftwaresoweincorporatelessonsintoourcourseonhowtousethesoftware.TheoreticalContentThetopicscommontomostmathematicalstatisticstextscanbefoundinthisbook,including:descriptivestatistics,experimentaldesign,sampling,estimation,viiiPrefacetes
6、ting,contingencytables,regression,simplelinearleastsquares,analysisofvari-ance,andmultiplelinearleastsquares.Alsofoundherearemanyselectedtopics,suchasquantileplots,thebootstrap,replicatemeasurements,inverseregression,ecologicalregression,unbalanceddesigns,andresponsesurfa
7、ceanalysis.Thisbookdiffersfromastandardmathematicalstatisticstextinthreeessentialways.Thefirstwayisinhowthetopicoftestingiscovered.Althoughweaddresstestinginseveralchaptersanddiscussthez,t,andFtestsaswellaschi-squaretestsofindependenceandhomogeneity,Fishersexacttest,Mantel
8、-Haenszeltest,andthechi-squaregoodnessoffittest,wedonotcoverallofthespecialcasesoftteststhatarety
