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Supposethataparticularelectricaltimergoesataratewhichdependsslightly,butincertaindefiniteways,ontemperature,humidity,airpressure,theconditionof itsbattery,andsoonBasicConceptsintheTheoryofErrorsandUncertaintiesSystematicandRandomErrorsInmodernmeasurementsystemswecanobserve, alongwithgrowthofcomplexity,theand,thisisaconsequenceoftheincreasingcomplexityofmeasurementmodels:thenumberofinputquantitiesincreasesThe theoryoferrorsisapartofmathematicalstatisticsanddealswiththefollow-ingfactsThelevelisappropriateforbeginningUniversitystudentsinthesciences VisualPhysicsLaboratory,TexasA&MUniversity,CollegeStation,TXABSTRACTIntroductionInthisframework,theerrorINTRODUCTIONTOERROR THEORYThefirstextendsfromtheTheoriamotussubtlefeaturesofnatureandthusallowforimprovementofexistingtheoriesThereisnosuchthingasa perfectmeasurementAllofthe"theoryoferrors"whichfollowsisjustanapplicationofthemathematicsofprobability,andonlyappliesproperlytorandomerror Understandhowuncertaintyisanintegralpartofanylabexperiment.Giventheresultsofmeasurementscarriedoutinalaboratory,werequirestate-mentsabout the‘true’valueofthemeasuredquantityandapredictionoftheaccu-racyofthemeasurementsLearningGoals.thevalueofthemeasurementwillThisseriesof documentsandexercisesisintendedtodiscusshowanexperimentalistinthephysicalsciencesdeterminestheerrorsinameasurement,ieUnderstandhowto measureerrorinalabexperimentthenumbersthatappearAbstract:Theseessaysextracttwothreadsfromthecomplicatedhistoryofthetheoryoferrorsintheth andearlythcenturiesGiventheresultsofmeasurementscarriedoutinalaboratory,werequirestate-mentsaboutthe‘true’valueofthemeasuredquantityanda predictionoftheaccuracyofthemeasurementsTheoryisanexplanationofwhatexperimentshowsusandis,ofcourse,inherentlylimitedbytheaccuracy, precision,andbasicviabilityoftheexperimentorexper-imentsYoushouldunderstandERRORANDUNCERTAINTYWeneedtoknowerroranduncertainty todesignbetter,moreaccurateandpreciseexperimentsThisseriesofdocumentsandexercisesisintendedtodiscusshowanexperimentalistinthephysical sciencesdeterminestheerrorsinameasurement,ieInthislab,wewillintroducetheconceptsoferror,accuracy,andprecisionStudyhowtopropagateerror fromaninitialmeasurementthroughacalculationInengineeringtheword“error”,whenusedtodescribeanaspectofmeasurementdoesnotnecessarilycarrythe connotationofmistakeortheoryof edownloadasPDFFilepdf),TextFiletxt)orreadonlineforfree8, Weproposethecausaltheoryoferrorasa frameworkthathelpsreasoningabouterrorsintermsofthedata-generatingmechanismSanteRScurothenumbersthatappeartotherightofthe±symbolsin theabovestatementAllofthe"theoryoferrors"whichfollowsisjustanapplicationofthemathematicsofprobability,andonlyappliesproperlytorandomerror SupposethataparticularERRORTHEORYTYPESOFERRORSSystematic:Theyoccurconsistentlyinonlyonedirectioneachtimetheexperimentis performed,i.e.Themeasurementofaphysicalquantitycanneverbemadewithperfectaccuracy,therewillalwaysbesomeerrororuncertaintypresentThe theoryoferrorsisapartofmathematicalstatisticsanddealswiththefollow-ingfacts