External standard calibration errors

FIGURE 6.30 External standard calibration curve for clozapine obtained with a /tPLC system. Error bars represent + one standard deviation. 

External standard calibration is used if the changes in the analytical system that may occur from the time the instrument has been calibrated to the time the sample analysis is completed are negligible. These changes are assumed to produce an insignificant error that is built into the daily calibration verification acceptance criteria. The response (calibration) factor of the external standard calibration is calculated according to Equation 1, Appendix 22, and it is measured in concentration or mass units (or their inverse). 

The calibration curve is used to correct 20-values of a sample that was measured under the same conditions as the standard (external standard). Some errors, especially the sample position and the transparency error, differ from... 

Errors in External-Standard Calibration When external standards are used, it is assumed that the same responses will be obtained when the same analyte concentration is present in the sample and in the standard. Thus, the calibration functional relationship between the response and the analyte concentration must apply to the. sample as well. Usually, in a determination, the raw response from the instrument is not used. Instead. the raw analytical response is corrected by measuring a blank. An ideal blank is identical to the sample but without the analyte. In practice, with complex samples, it is too time-consuming or impossible to prepare an ideal blank and a compromise must be made. Most often a real blank is either a solvent blank, containing the same solvent in which the sample is dissolved, or a reagent blank, containing the solvent plus all the reagents used in sample preparation. 

The method of standard additions can be used to check the validity of an external standardization when matrix matching is not feasible. To do this, a normal calibration curve of Sjtand versus Cs is constructed, and the value of k is determined from its slope. A standard additions calibration curve is then constructed using equation 5.6, plotting the data as shown in Figure 5.7(b). The slope of this standard additions calibration curve gives an independent determination of k. If the two values of k are identical, then any difference between the sample s matrix and that of the external standards can be ignored. When the values of k are different, a proportional determinate error is introduced if the normal calibration curve is used. 

Although internal standard calibration compensates for some errors in external standard quantitation, there are several difficulties in method development. First, choosing an appropriate internal standard can often be difficult, as this compound must be available in extremely pure form and it must never appear in the samples of interest. Second, it cannot interfere in either the extraction or the chromatography of the analytes. Finally, it must be structurally similar to the analytes, so that it undergoes similar extraction and chromatography, otherwise, the compensation will be lost. 

As has already been pointed out, two different methods of calibration have been used in the work so far reported. One can measure in terms of H/3, and in this way determine the ground state Lamb shift. If instead one uses a frequency standard, one can determine the IS Lamb shift by allowing for the other contributions to the measured IS - 2S interval this requires a value of the Rydberg constant from another source. Alternatively, if one assumes the IS Lamb shift known from theory at the level of accuracy of the experiment, one can regard the measurement as a determination of the Rydberg constant. All the most recent work has been in terms of the external standards provided by the tellurium transitions, but these introduce an uncertainty which in the case of the cw experiments dominates the final error. This situation must be... 

External Standard. This method is usually performed graphically. Known amounts of the analyte of interest are chromatographed, the areas are measured, and a calibration curve like Figure 7.6 is plotted. If the standard solutions of analyte vary in concentration, a constant volume must be introduced to the column for each. This requires a reproducible method of sample introduction a valve is adequate, but syringe injection in GC is usually inadequate, particularly for syringes that contain sample in the needle. Errors around 10% are common. 

It is therefore necessary to know how K varies with d in order to determine the size distribution. If this correction is not applied, the method is only valid for comparison purposes. Theoretical values of K may be used but this will also introduce errors, since the effective K values depend upon the optical geometry of the system. Calibration may also be against some external standard. The cumulative distribution undersize by weight is given by ... 

Fig. 22. Systematic error caused by nonlinear calibration in using the external standard method 47)...

The standard addition method is commonly used in quantitative analysis with ion-sensitive electrodes and in atomic absorption spectroscopy. In TLC this method was used by Klaus 92). Linear calibration with R(m=o)=o must also apply for this method. However, there is no advantage compared with the external standard method even worse there is a loss in precision by error propagation. The attainable precision is not satisfactory and only in the order of 3-5 %, compared to 0.3-0.5 % using the internal standard method 93). 

Even with blank corrections, several factors can cause the basic assumption of the external standard method to break down. Matrix effects due to extraneous species in the sample that are not present in the standards or blank can cause the same analyte concentrations in the sample and standards to give different responses. Differences in experimental variables at the times at which blank, sample, and standard are measured can also invalidate the established calibration function. Even when the basic assumption is valid, errors can still occur owing to contamination during the sampling or sample preparation steps. 

Similar to what is done for the external standard, for the construction of the calibration curve the A20-values are plotted versus 20obs and then approximated by a smooth curve. For polynomials a + bv + cx +... one can calculate all approximations from 0th order (zero point error only) up to 4th order (if at least six calibration points are available) and compare the corresponding sums of the squared differences (x ). As an optimal polynomial one can take that one... 

Some of the factors mentioned earlier which introduce error when calibrating with external standards only, can be compensated for by introducing a constant amount of an internal standard in both the unknown and the standard calibration samples. This should be a compound with similar chemical nature to the analytes, so that it will pass through the sample extraction and preparation procedure similarly. In general it should elute in the chromatographic system close to the other peaks in the system, but separated from all of them, so it can be identified and measured accurately. One calculates the ratio of the peaks responses to their concentrations. Then the ratio for each analyte. A, peak is compared to ratio of the internal standard, IS peak, to give the relative response factor (RRF), for the analyte to... 

Quantitative determination of the monoisotopic element cesium can only be performed by using a radioactive isotope or a different alkali element as an internal standard or by establishing a calibration curve as an external standard. A plot of such a curve is given in Fig. 13 for [Cs]" . For measurements, a number of standard solutions of CsCl in CCI4 are prepared and analyzed. The resultant values are displayed with an error of 22% corresponding to 2a (a = standard deviation). 

PCs. Proceed to calculate the means, standard deviations, relative standard deviations, and confidence intervals at a given probability. Calculate the relative error between the mean result for the ICV and the expected result for both types of calibration modes (i.e., external standard and standard addition). Comment on the effect of the external versus standard addition mode of GFAA calibration on the precision and accuracy in the ultratrace determination of Pb in drinking water. 

When at least three samples (preferably more) with known concentrations (standards) are analyzed at each concentration, standard deviations can be calculated from the peak areas (external standard and standard addition methods) or peak area ratios (internal standard method), thereby determining the confidence of data for unknown concentrations. The standard deviations are usually plotted as error bars at each point on the calibration graphs. 

The standard reference is internal water (H2O) but mostly, external water is used. Along with small but significant temperature and concentration dependences deviations may imply an error of +5 ppm for chemical shifts. Therefore, it is common place to give 5 values as integers only. The chemical shift of D2O, an external standard often used for calibrating and shimming, is 5 = -3. 

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