Uncertainties concentration

The summary statistics for accuracy described in the previous section are just average statistics for the whole set of samples. They are important, because they allow monitoring of changes when the calibration model is optimised i.e. a dilferent data pretreatment or optimal number of factors is used). However, they do not provide an indication of the uncertainty for individual predicted concentrations. Uncertainty is defined as aparameter, associated with the result of a measurement, which characterises the dispersion of the values that could reasonably be attributed to the measurancT [60]. Therefore, uncertainty gives an idea of the quality of the result since it provides the range of values in which the analyst believes that the true concentration of the analyte is situated. Its estimation is a requirement for analytical laboratories [61] and is especially important when analytical results have to be compared with an established legal threshold. 

CRM No. or RM No. Matrix Myco toxin Certified value mass fraction or mass concentration Uncertainty mass fraction or mass concentration... 

The WRMs concentrations uncertainty, based on the certificate of the gas supplier and on the comparison with the PRMs... 

Concentration uncertainty on a dry sample basis from NBS certificates [146]. The certificates also contain informational data on other elements. 

Derivation of AEGL-1 (key study, critical effect, dose-exposure concentration, uncertainty factor application and justification, temporal extrapolation, assumptions, confidence, consistency with human data if... 

The accuracy and precision of spectrophotometric analyses are often limited by the indeterminate error, or noise, associated with the instrument. As pointed out in Chapter 25, a spectrophotometric absorbance measurement entails three steps a 0% T adjustment, a 100% T adjustment, and a measurement of % 7i The random errors associated with each of these steps combine to give a net random error for the final value obtained for T. The relationship between the noise encountered in the measurement of T and the resulting concentration uncertainty can be derived by writing Beer s law in the form... 

Figure 26-11 Experimental curves relating relative concentration uncertainties to absorbance for two spectrophotometers. Data obtained with (a) a Spectronic 20, a low-cost instrument (Figure 25-19), and (b) a Cary 118, a research-quality instrument. (From W. E. Harris and B. Kratochvil, An Introduction to Chemical Analysis, p. 384.

Figure 26-11b shows an analogous plot of experimental data obtained with a high-quality research-type ultraviolet/visible spectrophotometer. Note that, in contrast to the less expensive instrument, absorbances of 2.0 or greater can be measured here without serious deterioration in the concentration uncertainty. 

The measurement of ions or electrons at any point in the negative glow could be reproduced to better than 5% on successive experiments. However, the day to day fluctuations in the discharge increased the concentration uncertainties to something like 10 to 15%. The reproducibility in the residual electron current discussed in the next section was somewhat better than this, and the slope of the line gave cross sections that differed by less than 5% over a period of several weeks. 

FIGURE 13-7 Relative concentration uncertainties arising from various categories ol instrumontai noise. A, case ... 

The following questions concern the relative concentration uncertainty in spectrophotometry. 

It is important to appreciate that an error in measured voltage, such as lhat shown in Example 23-1 ( -0.13.3 V), would have an enormous effect on the accuracy of a concentration measurement based on that polenltal. Thus, as shown in Section 2.3H-2. a 0.001 V uncertainly in poicniial leads to a relative error of about 4% in the dcicrininatum of the hydrogen ion concentration of u solution by potential measurement with a gla.ss electrode. An error of the si/c found in Example 23-1 would result in a concentration uncertainty of two orders of magnitude or more. 

Reported radionuclide concentration, uncertainty, impurities, or chemical form Applied values of half-life, decay fractions, or energy Calculation of radionuclide dilution or decay... 

If the relative concentration uncertainty is given by Equation 13-13, use calculus to show that the minimum uncertainty occurs at 36.8% T. What is the absorbance that minimizes the concentration uncertainty Assume that is independent of concentration. 

Under shot-noise-limited conditions, the relative concentration uncertainty is given by Equation 13-14. Another form of the equation for the shot-noise-limited case is -... 

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