1. Data Analysis: Quantitative Statements about Instrument and Method Performance

2. Quantitative Description of Instrument Performance: Why is it required To (quantitatively) describe instrument performance so that analytical measurements of unknowns can result in a quantitative result. For example: Calibration of a spectrofluorometer with quinine, followed by the analysis of unknown concentrations of quinine in tonic water.

3. Analytical Method Considerations COST SPEEDNEEDS COST: Training, equipment... SPEED: When is it required... NEEDS: E.g., required detection limit... Overall: An equal balance among the three.

4. Basic Terms Chapter 1 Page 11, Table 1-3 (Skoog Holler Nieman) Precision (Reproducibility): Absolute or relative standard deviation, coefficient of variation, variance Bias: Absolute or relative systematic error Sensitivity: Calibration or analytical... Response Factor: Response as a function of analyte concentration Limit of Quantitation (LOQ): A numerical value usually directly related to LOD (>) Detection Limit (LOD or MDL): Different methods (statistical) to establish LOD Not Detected: Signal not discernible from noise using the given analytical system Concentration Range: From LOQ to LOL Selectivity: Coefficient of selectivity (%)

5. Standard Deviation (s) for a small set of data. Rel. Standard Deviation (using arithmetic mean) %RSD or CV (Coefficient of variation) Standard Deviation of the Mean Variance Overall standard deviation Precision Small set of data Population

6. F-Test - Comparison of Variances Variance (s 1 ) 2 of TEST METHOD #1 (sample) Variance (s 2 ) 2 of TEST METHOD #2 (sample) The ratio of variances (where s 2 2 >s 1 2 ) Gaussian (Normal) Distributions

7. t-Test - Comparison of Means Mean of TEST METHOD #1 (sample) Mean of TEST METHOD #2 (sample) Are the means equal? The t-test we use is dependent on whether the variances of the two test methods are the same or different. Again, assume Gaussian Distributions. One-tailed t-test for equal variances, and two-tailed for unequal variances. The two-tailed presents more relaxed constraints on establishing equivalence.

8. A Look At Calibration Curves: A Primer Do I use R² to indicate linearity, the appearance of the curve...what then?

9. Linear Least Square Regression, Unweighted Ideal Calibration Curve Y-Int=0 Curve 1

10. Curve 2 Linear Least Square Regression, Unweighted With an extreme example, Points 1, 2, and 3 are each increased by 100%

11. Curve 3 Point 6 is increased by only 10%

12. Summary of Curve Comparisons Interpolation of concentrations using the estimated slopes and Y-intercepts

13. Use of Response Factors to Understand Curve Linearity Consider the following calibration curve. We have a value of 5 Units of “Bias” for all measurements. There is also detector saturation at the highest target analyte concentration, resulting in ~10% loss of expected response. Is this curve linear, and usable for quantitation at the low concentration range?

14. Analysis of Data Using Response Factor U.S.EPA indicates that a RF <15% CV is acceptable, with up to 25% CV on RF as acceptable for some methods.

15. What strategies can be employed to establish a clear understanding of the calibration curve? What about the Dixon Test to check the RF’s. Remember, a larger Confidence is actually a less reliable result. The RF data provide strong clues with respect to the detection limit (see later). Calibration Curve Example

16. Six Approaches to Quantification 1. External Standard: A calibration curve is first developed. No consideration for matrix here. The samples are run, as close to the same conditions as the standards. Sample responses are interpolated from the calibration curve. 2. Bracketing standards: Here, two standards around a sample response are used to quantify the target analyte concentration. Is just as accurate as external standard calibration. Not usually accepted by regulatory bodies, but works well particularly for research applications, surveys. 3. Average Response Factors: Simple, but powerful. Here, provided the y-int is small, the Ave. RF can be quite effectively used, and is as accurate as external standard calibration. 4. Internal Standard: A more elegant technique involving introducing a compound into the sample extract just prior to analysis. The ratio of responses of the internal standard to the known concentrations of target analyte is used to develop a calibration curve. Then, in the sample, the ratio of IS response to target analyte response of unknown concentration is interpolated from the curve. Good correction for instrumental factors affecting quanitification.

17. Six Approaches to Quantification 5. Standard Addition: Here, the actual background matrix is spiked with various (known) concentrations of the target analyte. 6. Isotope Dilution: The most elegant of all quanitification procedures. It involves adding an isotope of the target analyte to the sample prior to extraction. It therefore acts as a surrogate compound and internal standard, but most importantly, will elute at almost exactly the same retention volume as the unlabelled analyte. There are various versions of isotope dilution, such as radio immunoassay and neutron activation. The ultimate isotope dilution would be to present the radioactive isotope of the target analyte to the test system prior to incorporation into plant and animal tissue. This would therefore quite thoroughly mimic the actual physical-chemical environment of the target analyte. This strategy is actually used with new pesticide registrations. Here, radioactive isotopes of the pesticides are presented to plants. The fate of the pesticide can be easily tracked.