ForewordIntroductionRecommendation INC-1 (1980) ScopeDefinitionsGeneral metrological termsThe term “uncertainty”Terms specific to this Basic conceptsMeasurementErrors, effects, and correctionsUncertaintyPractical considerationsEvaluating standard uncertaintyModelling the measurementType A evaluation of standard uncertaintyType B evaluation of standard uncertaintyGraphical illustration of evaluating standard uncertaintyDetermining combined standard uncertaintyUncorrelated input quantitiesCorrelated input quantitiesDetermining expanded uncertaintyIntroductionExpanded uncertaintyChoosing a coverage factorReporting uncertaintyGeneral guidanceSpecific guidanceSummary of procedure for evaluating and expressing uncertaintyRecommendations of Working Group and CIPMRecommendation INC-1 (1980)Recommendation 1 (CI-1981)Recommendation 1 (CI-1986)General metrological termsSource of definitionsDefinitionsBasic statistical terms and conceptsSource of definitionsDefinitionsElaboration of terms and conceptsExpectationVarianceStandard deviationCovarianceCovariance matrixCorrelation coefficientIndependenceThe -distribution; Student's distribution“True” value, error, and uncertaintyThe measurandThe realized quantityThe “true” value and the corrected valueErrorUncertaintyGraphical representationMotivation and basis for Recommendation INC-1 (1980)“Safe”, “random”, and “systematic”Justification for realistic uncertainty evaluationsJustification for treating all uncertainty components identicallyStandard deviations as measures of uncertaintyA comparison of two views of uncertaintyPractical guidance on evaluating uncertainty componentsComponents evaluated from repeated observations: Type A evaluation of standard uncertaintyRandomness and repeated observationsCorrelationsComponents evaluated by other means: Type B evaluation of standard uncertaintyThe need for Type B evaluationsMathematically determinate distributionsThe resolution of a digital indicationHysteresisFinite-precision arithmeticImported input valuesMeasured input valuesSingle observation, calibrated instrumentsSingle observation, verified instrumentsControlled quantitiesAsymmetric distributions of possible valuesUncertainty when corrections from a calibration curve are not appliedUncertainty of the method of measurementUncertainty of the sampleDegrees of freedom and levels of confidenceIntroductionCentral Limit TheoremThe -distribution and degrees of freedomEffective degrees of freedomOther considerationsSummary and conclusionsExamplesEnd-gauge calibrationThe measurement problemMathematical modelContributory variancesUncertainty of the calibration of the standard, Uncertainty of the measured difference in lengths, Uncertainty of the thermal expansion coefficient, ()Uncertainty of the deviation of the temperature of the end gauge, Uncertainty of the difference in expansion coefficients, Uncertainty of the difference in temperature of the gauges, Combined standard uncertaintyFinal resultExpanded uncertaintySecond-order termsSimultaneous resistance and reactance measurementThe measurement problemMathematical model and dataResults: approach 1Results: approach 2Calibration of a thermometerThe measurement problemLeast-squares fittingCalculation of resultsUncertainty of a predicted valueElimination of the correlation between the slope and interceptOther considerationsMeasurement of activityThe measurement problemAnalysis of dataCalculation of final resultsResults: approach 1Results: approach 2Analysis of varianceThe measurement problemA numerical exampleThe role of ANOVA in measurementMeasurements on a reference scale: hardnessThe measurement problemMathematical modelContributory variancesUncertainty of the average depth of indentation of the sample block, Uncertainty of the correction for the difference between the two machines, Uncertainty of the correction due to variations in the hardness of the transfer-standard block, Uncertainty of the national standard machine and the definition of hardness, The combined standard uncertainty, Numerical exampleGlossary of principal symbols