分析化学英文课件CH02 Data Analysis 120913.ppt

Chapter2-DataAnalysisErrorsanddatatreatment1

OutlineErrors:classification,distributionStatisticdatatreatmentPropagationoferrorsSignificantfiguresStandardizationcalibration2

AccuracyandprecisionAccuracy:closenessofmeasuredvaluetotrue(oraccepted)valuePrecision:closeness(agreement)betweenvaluesinasetofdatameasured123Truevalue28.03Set128.0228.1828.20Set228.1228.1328.10Set328.0228.0428.023

Accuracyofmeasurements:errorErrors:differencebetweenmeasuredvalue(xi)andtruevalue(T)Absoluteerror:Ea(x-T)Relativeerror:Er(Ea/T,asinpercentage)Thesmallerthe(relative)error,thebettertheaccuracy4

Accuracyofameasurement:deviationDeviation:differencebetweenameasuredvalueandthemeanRelativedeviation(RD)Meandeviationrelativemeandeviation(RMD)di=xi-5

Systematicandrandomerrorssystematicordeterminateerrors,unidirectional,thesamedirectionandmagnitudeforallmeasurementsrandomorindeterminateerrors,comefromuncontrolledvariables6

Errors:SystematicerrorsSystematic(determinate):definitevalue,assignablecause,sameorderofmagnitudeMethodEquipmentmaterialsPersonaljudgments(personalbias)Mistakes:fromcarelessnessorignorance7

RandomerrorsCausedbyuncontrollablevariables,inevitableBearnosign,canneverbetotallydetermined;Fluctuaterandomlywithreplicatedmeasurements8

DistributionofrandomerrorsAnequalnumberandtypeofpositiveandnegativeerrorsoccur;Smallerrorsoccurmuchmorefrequentlythanlargeones;Thevalueoccurmostfrequentlyistheonewithnoerror,thetruevalue9

FrequencydistributionnormaldistributionHistogramDensityplot10

Gaussian(normal)distributionf(x)frequencydensityx datavaluesasthevariableμ populationmeanσ populationstandarddeviationN(μ,σ)11

PopulationstandarddeviationDescribestheprecisionofapopulationofdata12

Standardnormaldistribution13

Standardizednormaldistributioncurve14

Predicationtheprobabilit