相关系数种类(Types of correlation coefficients)

相关系数种类(Typesofcorrelationcoefficients)Typesofcorrelationcoefficients(I)Pearsonproductdifferencecorrelation(K.Pearsonproduct-momentcorrelation;R)Xvariables:isometry,ratiovariables(continuousvariables)Yvariables:isometry,ratiovariables(continuousvariables)formula:characteristics:numericalstability,standarderror.cases:therelationshipbetweenworkinghoursandincome(two)Spearmanrankcorrelation(Spearmanrankcorrelation;RS)Xvariables:ordinalvariablesYvariables:ordinalvariablesformula:withoutthesamerank:(Distherankdifferenceoftwovariablesymmetry)peoplewiththesamegrade:T:thenumberofpeoplewhoreceivethesamegrade.features:suitablefortworaterstoevaluateNpieces,orthesamerater,twotimestoevaluateNpieces.cases:evaluationofNstudents'worksbytworeviewers.(three)Kendallrankcorrelation(Kendall'scoefficientofrankcorrelation;(tau))Xvariables:humanordervariablesYvariables:humanordervariablesformula:S:rankordinalquantity;N:thenumberofpersonsevaluatedorthenumberofworksfeatures:quitesimplecases:evaluationofNstudents'worksbytworeviewers.(four)Kendallconcordancecoefficient(theKendall'scoefficientofconcordance;W)Xvariables:ordinalvariablesYvariables:ordinalvariablesformula:(1)withoutthesamegrade:;(2)peoplewiththesamegrade:;;K:thenumberofraters;N:thenumberofpersonsbeingevaluatedorthenumberofentriesfeatures:especiallyfortheinterraterreliability(interjudgereliability);testtheconsistencyoftheevaluationofNworksbymanyreviewers.cases:evaluationofNstudents'worksbymultisiteevaluation.(five)Kappaconsistencycoefficient(Kcoefficientofagreement;K)Xvariables:categoricalvariablesYvariables:categoricalvariablesThe3.formula:theKappaconsistencycoefficientistheratioofthepercentageoftheactualevaluationoftheraterstothepercentageofthemaximumpossiblenumberofratersevaluatedbytheraters(LinWei,1992).Formulafor:P(A):thepercentageofKraterratings;N:totalnumber;K:raternumber;m:ratingcategory;N:finegriddataP(E):Kscoreraterscantheoreticallyassessthepercentageofconsistency;whentherater'sratingisexactlythesame,thenK=1,whentherater'sratingiscompletelyinconsistent,thenK=0.4.characteristics:theKendeerharmonycoefficient,thescoreislimitedintheevaluationobjectcanbeevaluated.Thatis,canlisttheorder.However,insomecasescannotbeassessedobjectlistrankorder,andcanonlybeclassifiedinacategory,atthistime,youmustuseKappatoindicatetheconsistencycoefficient,theconsistencyoftherelationshipbetweenthescore.5.cases:Kpsychiatrists,Npatientswereclassifiedintomcategoriesofmentalillnessafterdiagnosis.(six)twoseriescorrelation(biserialcorrelation;RBIs)Xvariables:anthropogenictwovariables(nominalvariables)Yvariables:continuousvariables(isometric,ratiovariables)formula:features:useinprojectanalysis;standarderrorislarge;RBIsmaybegreaterthan1.cases:therelationshipbetweenIQandacademicachievementornot.(seven)pointtwoseriescorrelation(point-biserialcorrelation;rpq)Xvariables:realtwovariables(nominalvariables)Yvariables:continuousvariablesformula:Table1:theaverageofthefirstclass;themeanofthefirstclass;St:thestandarddeviationofthetotalfraction;P:Table1percentageofthenumberofpeople;Q:percentageofpeopleintablesecond.characteristic:standarderrorissmallerthanrbis.cases:therelationshipbetweengender(male,female)andincome.(eight)correlation(phicoefficient;)Xvariables:realtwovariables(nominalvariables)Yvariables:realtwovariables(nominalvariables)CDformula:characteristics:closelyrelatedtoChisquaretest.cases:parentalparentingstyle(authoritative,democratic).(nine)contingencycorrelation(contingencycoefficient;C)Xvariables:realtwoormorenominalvariablesYvariables:realtwoormorenominalvariablesformula:themaximumvalueofCisN,andthetotalnumberischaracteristics:closelyrelatedtoChisquaretest.cases:theattitudeofthepeople(teachersandstudents)towardstheimplementationofthepolicy(agreement,noopinion,noagreement).(ten)fourpointcorrelation(tetrachoriccorrelation;TET)Xvariables:humantwonominalvariables(rawdataareequidistantvariables)Yvariables:humantwonominalvariables(rawdataareequidistantvariables)ABCDformula:cases:academicachievement(pass,fail)andIQ(high,low)relationship.(eleven)netcorrelation(Partialcorrelation;r12.3)Xvariables:continuousvariablesYvariables:continuousvariablesformula:(significanttestt=)The4.characteristic:removingtheimportantinfluencefactorsrelatedtothetwovariables,therelationshipbetweenthetwovariablescanbeobtained.:getridoftheinfluenceofintelligence,formathematicsandChineseachievementrelated.(twelve)curvecorrelationorcorrelationratio(correlationratio;)1.Xvariables:continuousvariables2.Yvariables:continuousvariablesformula:The4.characteristic:withtheincreaseofXvariables,theYvariableincreasesfirst,andthenbeginstodeclineafterbeingaddedtoacertainstage.Therelationshipbetweenthetwovariablesiscalledcurvecorrelationorcorrelationratio.5.cases:therelationshipbetweenworkefficiencyandanxiety.Thecorrelationcoefficientofthevariabletype,weresummarizedasshownintable14-1:Tablefordetailsofallrelevantvariables14-1finishingXYNominalvariableOrdervariableVariablesaboveequidistantNominalvariableContingencycorrelationRelatedKappaconsistencycoefficientFourpointscorrelationPointtwoseriescorrelationTwoseriescorrelationMultipleseriescorrelationOrdervariableSpearmanrankcorrelationKendallrankcorrelationKendallconcordancecoefficientVariablesaboveequidistantPointtwoseriescorrelationTwoseriescorrelationMultipleseriescorrelationPearsonproductmomentcorrelationNetcorrelationCorrelationratioThecharacteristicsofproductdifferencecorrelationcoefficient(I).(two)thevalueofcorrelationcoefficientiscloselyrelatedtothenumberofN(number).1.itisknownfromtheformulathatNisoneoftheimportantfactorsdeterminingtheRvalueofcorrelationcoefficient.2.themagnitudeoftheRvaluedoesnotmeanthatthereisahighcorrelationorlowcorrelationbetweenthetwovariables(becauseitislikelytobecausedbytheprobability),andthesizeofthesample(N)andthesignificantlevelshouldbeconsideredagain.(1)ingeneral,thesmallertheN,thecorrelationcoefficientrvaluemustbelarger,cansaytherelationshipbetweenthetwovariables;onthecontrary,thegreatertheN,thecorrelationcoefficientcannotbetoolarge,wehavetwovariablesrelatedtoexistence.(2)thesmallerthevalue,thegreaterthevalueofthephaserelationship,andtherelativeexistence.Asshownintable14-2:Tables14-2,NandRNDF=.05=.01ThreeOne.997.999FiveThreeTenEight.632.765ThirtyTwenty-eight.361.463OnehundredandtwoOnehundred.195.254(three)thedegreeofcorrelationisnotproportionaltoR.Thecorrelationcoefficientisonlyanindexindicatingwhetherthetwovariablesarecloselyrelated,sothecorrelationcoefficientcannotberegardedasaratiooranisometryvariable.Suchas:r1=.80,r2=.20,cannotbesaidthatthevalueofR1isfourtimesofr2.(four)thereisarelationship,butdoesnotmeanthatthereisacausalrelationship.Twoeventsoccuratthesametime,orhappenbeforeandafter,wecanonlysaythatthetwoeventsarerelated,butnotnecessarilythereisacausalrelationshipexists.One