calibration methods chemistry 243. figures of merit: performance characteristics of instruments...

Calibration methods

Chemistry 243

Figures of merit: Performance characteristics of instruments

Precision Accuracy Selectivity Sensitivity Limit of Detection Limit of Quantitation Dynamic Range

Precision vs. Accuracy in the common verbiage (Webster’s)

Precision: The quality or state of being precise; exactness;

accuracy; strict conformity to a rule or a standard; definiteness.

Accuracy: The state of being accurate; exact conformity to

truth, or to a rule or model; precision.

These are not synonymous when describing instrumental measurements!

Precision and accuracy in this course

Precision: Degree of mutual agreement among data obtained in the same way. Absolute and relative standard deviation, standard error of

the mean, coefficient of variation, variance. Accuracy: Measure of closeness to accepted value

Extends in between various methods of measuring the same value

Absolute or relative error Not known for unknown samples

Can be precise without being accurate!!! Precisely wrong!

Precision - Metrics

Most important

Often seen as %

Handy, common

Sensitivity vs.Limit of Detection NOT THE SAME THING!!!!! Sensitivity: Ability to discriminate between small

differences in analyte concentration at a particular concentration. calibration sensitivity—the slope of the calibration

curve at the concentration of interest Limit of detection: Minimum concentration that

can be detected at a known confidence limit Typically three times the standard deviation of the

noise from the blank measurement (3s or 3s is equivalent to 99.7% confidence limit)

Such a signal is very probably not merely noise

Calibration Curve, Limit of Detection, Sensitivity

Sig

nal

00

Analyte Mass or Concentration

S/N = 3

Calibratio

n Curve*

LOD

Sensitivity* = Slope

*Same as Working Curve**Not improved by amplification alone

Selectivity

Degree to which a method is free from interference from other contaminating signals in matrix

No measurement is completely free of interferences Selectivity coefficient:

A A B B C CS m c m c m c

,B

B AA

mk

m

Calibration Curves:Sensitivity and LOD

Sig

nal

0


S/N = 3

LOD

Mor

e S

ensi

tive

Less Sensitive

LOD0

For a given sample standard deviation, s, steeper calibration curve means better sensitivity

Insensitive to amplification

Dynamic range The maximum range over which an accurate

measurement can be made From limit of quantitation to limit of linearity

LOQ: 10 s of blank LOL: 5% deviation from linear

Ideally a few logs Absorbance: 1-2 MS, Fluorescence: 4-5 NMR: 6

Calibration Curves:Dynamic Range and Noise Regions

Sig

nal

00


S/N = 3

LOD

Dynamic Range

Calibratio

n Curve

CalibrationCurvebecomespoor abovethis amountof analyte

NoiseRegion

LOQ

PoorQuant

LOL

Types of Errors Random or indeterminate errors

Handled with statistical probability as already shown Systematic errors

Instrumental errors Personal errors Method errors

Gross errors Human error

Careless mistake, or mistake in understanding Often seen as an outlier in the statistical distribution “Exactly backwards” error quite common

Systematic errors Present in all measurements made in the same way

and introduce bias. Instrumental errors

Wacky instrument behavior, bad calibrations, poor conditions for use Electronic drift, temperature effects, 60Hz line noise,

batteries dying, problems with calibration equipment. Personal errors

Originate from judgment calls Reading a scale or graduated pipette, titration end points

Method errors Non-ideal chemical or physical behavior

Evaporation, adsorption to surfaces, reagent degradation, chemical interferences

Instrument calibration

Determine the relationship between response and concentration Calibration curve or working curve

Calibration methods typically involve standards Comparison techniques External standard* Standard addition* Internal standard*

* calibration curve is required

External standard calibration (ideal)

External Standard – standards are not in the sample and are run separately

Generate calibration curve (like PS1, #1) Run known standards and measure signals Plot vs. known standard amount (conc., mass, or mol) Linear regression via least squares analysis

Compare response of sample unknown and solve for unknown concentration All well and good if the standards are just like the

sample unknown

Sig

nal

00


S/N = 3

LOD

External standard calibration(ideal)

SampleUnknown

SampleUnknownAmount

ExternalCalibrationStandardsincludinga blank

In class example of external standard calibration

Skoog, Fig. 13-13

0log

molar absorptivity

pathlength

concentration

PA bc

P

b

c

Sig

na

l

00


S/N = 3

LOD

SampleUnknown

SampleUnknownAmount

ExternalCalibrationStandardsincludinga blank

Real-life calibration Subject to matrix interferences

Matrix = what the real sample is in pH, salts, contaminants, particulates Glucose in blood, oil in shrimp

Concomitant species in real sample lead to different detector or sensor responses for standards at same concentration or mass (or moles)

Several clever schemes are typically employed to solve real-world calibration problems: Internal Standard Standard Additions

Internal standard A substance different from the analyte added in a

constant amount to all samples, blanks, and standards or a major component of a sample at sufficiently high concentration so that it can be assumed to be constant.

Plotting the ratio of analyte to internal-standard as a function of analyte concentration gives the calibration curve.

Accounts for random and systematic errors. Difficult to apply because of challenges associated

with identifying and introducing an appropriate internal standard substance. Similar but not identical; can’t be present in sample

Lithium good for sodium and potassium in blood; not in blood

Standard additions Classic method for reducing (or simply

accommodating) matrix effects Especially for complex samples; biosamples Often the only way to do it right

You spike the sample by adding known amounts of standard solution to the sample Have to know your analyte in advance

Assumes that matrix is nearly identical after standard addition (you add a small amount of standard to the actual sample)

As with “Internal Standard” this approach accounts for random and systematic errors; more widely applicable

Must have a linear calibration curve

How to use standard additions To multiple sample volumes of an unknown,

different volumes of a standard are added and diluted to the same volume.

Fixed parameters: cs = Conc. of std. – fixed Vt = Total volume – fixed Vx = Volume of unk. – fixed cx = Conc. of unk. - seeking

Non-Fixed Parameter: Vs = Volume of std. – variable

Calibration Standard(Fixed cs)

Vx Vx Vx Vx

Vs3Vs2 Vs4Vs1

Vt VtVt Vt

Volume top-off step: Vx diluted to Vt

Vs diluted to Vt

How to use standard additions

To multiple sample volumes of an unknown, different volumes of a standard are added and diluted to the same volume.

Co

mb

ined

Sig

nal

Concentration00S1 S2 S4S3

𝑆𝑡𝑜𝑡𝑎𝑙=𝑆𝑠𝑡𝑑+𝑆𝑥


00

Concentration

Co

mb

ined

Sig

nal

k = slope or sensitivity


𝑆𝑠𝑡𝑑=𝑘 ∙ 𝑓 𝑑𝑖𝑙 ∙𝑐𝑠𝑡𝑑=𝑘𝑉 𝑠𝑡𝑑𝑐𝑠𝑡𝑑

𝑉 𝑡𝑜𝑡𝑎𝑙

𝑆𝑥=𝑘 ∙ 𝑓 𝑑𝑖𝑙′ ∙𝑐 𝑥=𝑘𝑉 𝑥𝑐𝑥



Signal from st

andard

Signal from unkn

own


𝑆𝑡𝑜𝑡𝑎𝑙=𝑘𝑉 𝑠𝑡𝑑𝑐𝑠𝑡𝑑


+𝑘𝑉 𝑥𝑐 𝑥



Remember,Vstd is thevariable.

Knowns:cstd Vtotal

Vx

𝑆𝑡𝑜𝑡𝑎𝑙=𝑚𝑉 𝑠𝑡𝑑+𝑏

𝑚=𝑘𝑐𝑠𝑡𝑑


𝑏=𝑘𝑉 𝑥𝑐𝑥







00

Vs

S, C

om

bin

ed

Sig

na

lGet m (slope) and b (intercept) from

linear least squares

How do I handle k ?

𝑆𝑡𝑜𝑡𝑎𝑙=𝑚𝑉 𝑠𝑡𝑑+𝑏

𝑚=𝑘𝑐𝑠𝑡𝑑


𝑏=𝑘𝑉 𝑥𝑐𝑥


Determine cx via standard curve extrapolation …

At the x-intercept, S = 0

Seeking[analyte]

known

knownSkoog, Fig. 1-10

Vstd when S = 0





𝑘𝑉 𝑠𝑡𝑑𝑐𝑠𝑡𝑑


=−𝑘𝑉 𝑥𝑐𝑥


𝑉 𝑠𝑡𝑑𝑐𝑠𝑡𝑑=−𝑉 𝑥𝑐𝑥

𝑐𝑥=−(𝑉 𝑠𝑡𝑑 )0𝑐𝑠𝑡𝑑

𝑉 𝑥

… or determine cx by directly using fit parameters

Final calculation: All knowns

… in conclusion, an easy procedure to perform and interpret;you take values you know and do a linear least squares fit to get m and b

𝑐𝑥=−𝑉 𝑠𝑡𝑑𝑐𝑠𝑡𝑑

𝑉 𝑥

𝑆𝑡𝑜𝑡𝑎𝑙=𝑚𝑉 𝑠𝑡𝑑+𝑏=0

𝑚𝑉 𝑠𝑡𝑑=−𝑏 𝑉 𝑠𝑡𝑑=−𝑏𝑚

𝑐𝑥=−(− 𝑏

𝑚 )𝑐 𝑠𝑡𝑑

𝑉 𝑥

=𝑏𝑐𝑠𝑡𝑑

𝑚𝑉 𝑥

calibration methods chemistry 243. figures of merit: performance characteristics of instruments...

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