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1、ReceiverOperatingCharacteristic(ROC)CurvePreparation-ATutorialMassachusettsWaterResourcesAuthorityEnvironmentalQualityDepartmentReportENQUAD2005-20CitationMorrison,AnnMichelle.2005.ReceiverOperatingCharacteristic(ROC)CurvePreparation-ATutorial.Boston:Massachus
2、ettsWaterResourcesAuthority.ReportENQUAD2005-20.5p.2005-20ROCCurvePreparationReceiverOperatingCharacteristic(ROC)CurvePreparation–AtutorialReceiverOperatingCharacteristic(ROC)curvesweredevelopedinthefieldofstatisticaldecisiontheory,andlaterusedinthefieldofsign
3、aldetectionforanalyzingradarimagesduringWorldWarII(1).ROCcurvesenabledradaroperatorstodistinguishbetweenanenemytarget,afriendlyship,ornoise.ROCcurvesassessthevalueofdiagnostictestsbyprovidingastandardmeasureoftheabilityofatesttocorrectlyclassifysubjects.Thebio
4、medicalfieldusesROCcurvesextensivelytoassesstheefficacyofdiagnostictestsindiscriminatingbetweenhealthyanddiseasedindividuals(2).ROCcurvescan(1)assesstheoveralldiscriminatoryabilityofdifferentpotentialindicatorvariablesbygeneratingacommonmetricforcomparisonand(
5、2)aidintheselectionofaspecificvalueofanindicatorvariabletouseasathreshold,orlimit,thatprovidesadesiredtrade-offinthetruepositiverateandfalsepositiverate.Withrespecttobeachwaterqualityindicatorvariables,ROCcurvescanquantifytheoveralleffectivenessofdifferentindi
6、catorvariablestocorrectlyandincorrectlyclassifyabeachassuitableforswimmingandgenerateasinglemetricbywhichthedifferentindicatorvariablescanbecompared.Statisticaltheorystatesthattherearetwopopulationsofwater:thatwhichissuitableforswimmingandthatwhichisunsuitable
7、forswimming.Thedistributionsofthesepopulationsoverlap.Whenyouchooseanindicator,suchasEnterococcusdensitytodefinethetransitionbetweenwaterthatissuitableforswimmingandwaterthatisunsuitableforswimming,tworegionsofinteresttoregulatorsareformed(Figure1).Thetrueposi
8、tiverate(TPR)correspondstotheproportionofwatersamplesunsuitableforswimmingthatarecorrectlyidentifiedbytheindicatorvariablethreshold,whichinFigure1isantecedentrainfall.Thefalseposit
