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1、DescribingtheUncertaintiesinExperimentalResultsRobertJ.MoffatIIItisnolongeracceptable,inmostcircles,topresentexperimentalresultsProfessorofMechanicalEngineering,withoutdescribingtheuncertaintiesinvolved.Besidesitsobviousroleinpub-StanfordUniversity,Stanfor
2、d,Californialishing,uncertaintyanalysisprovidestheexperimenterarationalwayofeval-uatingthesignificanceofthescatteronrepeatedtrials.Thiscanbeapowerfultoolinlocatingthesourceoftroubleinamisbehavingexperiment.Totheuserofthedata,astatement(bytheexperimenter)of
3、therangewithinwhichtheresultsofthepresentexperimentmighthavefallenbychancealoneisofgreathelpindecidingwhetherthepresentdataagreewithpastresultsordif-ferfromthem.Thesebenefitscanberealizedonlyifboththeexperimenterandthereaderunderstandwhatanuncertaintyanaly
4、sisis,whatitcando(andcannotdo),andhowtointerpretitsresults.Thispaperbeginswithageneraldescriptionofthesourcesoferrorsinen-gineeringmeasurementsandtherelationshipbetweenerroranduncertainty.Thenthepathofanuncertaintyanalysisistracedfromitsfirststep,identify-
5、ingtheintendedtruevalueofameasurement,throughthequantitativeestima-tionoftheindividualerrors,totheendobjective--theinterpretationandre-portingoftheresults.Thebasicmathematicsofbothsingle-sampleandmultiple-sampleanalysisarepresented,aswellasatechniquefornum
6、ericallyexecutinguncertaintyanalyseswhencomputerizeddatainterpretationisin-volved.Thematerialpresentedinthispapercoversthemethodofdescribingtheuncertaintiesinanengineeringexperimentandthenecessarybackgroundma-terial.Keywords:experimentaluncertainty,erroran
7、alysis,single-sampleanalysis,multiple-sampleanalysis,systemerrorsINTRODUCTIONbarsonaplotofthedataorcalculatingtheroot-mean-squaredeviationofdatafromacurvefit,or(worseyet)calculatingtheTheerrorinameasurementisusuallydefinedasthedifferencemeanabsolutevalueof
8、thatdeviation.Thosearesimplytech-betweenitstruevalueandthemeasuredvalue.Thisdefinitionisniquesforprovidingsomemeasureofthescatterintheresultsandclearbutnotveryhelpful:theonlyrealsituationsinwhichweprovidenowa