linearity, linear range, sensivity - ut · working range, calibra.on range *loq 0 20000000 40000000...
TRANSCRIPT
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Linearity,linearrange,sensi.vity
Linearity
Methodsabilitytoobtainsignals
whicharedirectlypropor.onaltotheconcentra1onofanalyteinthesample.
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Linearrange
Rangeofconcentra.onswherethesignalsaredirectlypropor1onaltothe
concentra1onoftheanalyteinthesample.
Sensi.vity
Thechangeininstrumentresponsewhichcorrespondstoachangein
themeasuredquan1ty.
Thegradientoftheresponsecurve.
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Experimentplanningforevalua.onoflinearity
• Typeofcalibra1onsamples• Concentra1onrange• Numberofconcentra1onlevels• Measurementprotocol
Typeofcalibra.onsamples• Standardsolu1ons– matrix-free
• Matrix-containingsamples– Matrix-matchedcalibra1on– Blankmatrixextract(preferablythesametypeasthesample)
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Concentra.onrange• Appropriateforthemethod• Expectedworkingrange±10%…20%• 70%…130%ofexpectedanalyteconcentra1on• Blanksample
Numberofconcentra.onlevels• Minimum6concentra1onlevelsareacceptable– Suggested10– Evenlyplaced– Preparedfromindependentdilu1ons
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Measurementprotocol• Assimilaraspossibletothereallifesitua1on– Randomorder– Betweenthesamples
• Analysedatleasttwice
Evalua.onoflinearity
• Visualevalua.on
• Residuals
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Visualevalua.on
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Signal(a
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Signal(a
u)
c(mg/kg)
LINEAR NOTLINEAR
Residual
εi = yi − yi
• Differencebetweenexperimentalsignalandcalculatedsignal
yi
yi
yi = slope ⋅ xi +
yi
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Signal(a
u)
c(mg/kg)
intercept
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Visualevalua.on
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Signal(a
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Signal
c(mg/kg)
LINEAR NOTLINEAR
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Signal(a
u)
c(mg/kg)
LINEAR?
Plotofresiduals
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Linear,homoscedas.c
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Residu
al(a
u)
c(mg/kg)
Linear,heteroscedas.c
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Residu
al(a
u)
c(mg/kg)
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Notlinear,heteroscedas.c
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Residu
al(a
u)
c(mg/kg)
Rela.veresiduals
• ±20%isacceptable
Yi =yi − yiyi
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Correla.oncoefficientrCoefficientofdetermina.onr2
• Totalvariabilityintheresponsethatisaccountedforbythemodel
• Notameasureoflinearity!
Linearrange
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“range”
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Signal(a
u)
c(mg/kg)
Dynamicrange,Analy.calrange
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Signal(a
u)
c(mg/kg)
Dynamicrange,Analy1calrange
Workingrange,Calibra.onrange
*LOQ
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Signal(a
u)
c(mg/kg)
Dynamicrange,Analy1calrange
Workingrange,Calibra1onrange
Linearrange,Lineardynamicrange
*LOQ
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Sensi.vity
• gradientofthecalibra1ongraph
Sensi.vity
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Signal(a
u)
c(mg/kg)
Slope = ΔSignalΔc
ΔSignal
Δc
Signal = 7610033⋅c+32270418