Calibration methods

1. Calibration methods Chemistry 243

2. Figures of merit: Performance characteristics of instruments • Precision • Accuracy • Selectivity • Sensitivity • Limit of Detection • Limit of Quantitation • Dynamic Range

3. 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!

4. 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!

5. Precision - Metrics Most important Often seen as % Handy, common

6. 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

7. Calibration Curve, Limit of Detection, Sensitivity Sensitivity* = Slope Signal Calibration Curve* *Same as Working Curve **Not improved by amplification alone S/N = 3 0 0 LOD Analyte Mass or Concentration

8. 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:

9. Calibration Curves:Sensitivity and LOD • For a given sample standard deviation, s, steeper calibration curve means better sensitivity • Insensitive to amplification More Sensitive Signal Less Sensitive S/N = 3 0 0 LOD LOD Analyte Mass or Concentration

10. 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

11. Calibration Curves:Dynamic Range and Noise Regions Calibration Curve becomes poor above this amount of analyte Signal Calibration Curve Poor Quant Noise Region Dynamic Range S/N = 3 0 0 LOD LOQ LOL Analyte Mass or Concentration

12. 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

13. 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

14. 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

15. 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

16. External standard calibration(ideal) Sample Unknown External Calibration Standards including a blank Signal Sample Unknown Amount S/N = 3 0 0 LOD Analyte Mass or Concentration

17. In class example of external standard calibration Sample Unknown External Calibration Standards including a blank Signal Skoog, Fig. 13-13 Sample Unknown Amount S/N = 3 0 0 LOD Analyte Mass or Concentration

18. 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

19. 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

20. 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

21. 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 Vs1 Vs2 Vs3 Vs4 Volume top-off step: Vx diluted to Vt Vs diluted to Vt Vt Vt Vt Vt

22. 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. Combined Signal S1 S4 0 S2 S3 0 Concentration

23. How to use standard additions k = slope or sensitivity Combined Signal 0 0 Concentration

24. How to use standard additions Signal from standard Signal from unknown

25. How to use standard additions Remember, Vstdis the variable. Knowns: cstd Vtotal Vx

26. How to use standard additions S, Combined Signal Get m (slope) and b (intercept) from linear least squares 0 0 Vs How do I handle k ?

27. Determine cx via standard curve extrapolation … At the x-intercept, S = 0 Skoog, Fig. 1-10 known known Seeking [analyte] Vstdwhen S = 0

28. … or determine cxby 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