Error standard-addition method

Nimura, Y. Carr, M. R. Reduction of the Relative Error in the Standard Additions Method, Analyst 1990, 115, 1589-1595. The following paper discusses the importance of weighting experimental data when using linear regression Karolczak, M. To Weight or Not to Weight An Analyst s Dilemma, Curr. Separations 1995, 13, 98-104. 

More efficient estimation methods exist than the simple method described here [17]. The generalized standard addition method (GSAM) shares the strong points (e.g correction for interferences) and weak points (e.g. error amplification because of the extrapolation involved) of the simple standard addition method [18]. 

The standard addition method of calibration (see Chapter 1) is often used to combat the uncertainties of varying interference effects in electrothermal atomization. However, care should be taken with this approach, as errors from spurious blanks and background may go undetected. It must also be emphasized that the technique of standard additions does not correct for all types of interference. 

The technique may be subject to a number of positive and/or negative systematic errors, depending on the element to be determined, the instrumental technique used, the matrix composition, and still other factors. However, as shown in Table 2.2, there is a tendency towards the use of the standard additions method and CRMs to minimize some possible matrix effects and to ensure validity of results. Nevertheless, it appears from the survey of the literature that the solubilization sampling introduction technique compares favorably with other atomic spectrometric methods for the determination of trace elements in a variety of matrices. 

Fig. 3.5 Systematic errors in the standard addition method Cx analyte concentration expected when the calibration dependence is nonlinear in the extrapolation region, c i concentration found when the calibration dependence is reconstructed by a linear calibration graph, c 2 concentration found when analyte in a sample is of different chemical form to that of analyte added to the sample...

Chemical interference is practically non existent as a result of the high temperature of the plasma. On the other hand, physical interference may be observed. This stems from variations in the sample atomisation speed which is usually due to changes in nebulisation efficiency caused by differences in the physical properties of the solutions. Such effects may be caused by differences in viscosity or vapour tension between the sample solutions and the standards due, for example, to differences in acidity or total salt content. The technique most commonly used to correct this physical interference is the use of internal standards. In this technique a reference element is added at an identical concentration level to all the solutions under analysis, standards, blank and samples. For each element, the ratio of simultaneous measurements of the lines of the element and the internal standard is then determined in order to compensate for any deviation in the response of the plasma. If the internal standard behaves in the same way as the element to be determined, this method can be used to improve the reliability of the result by a factor of 2 to 5. It can also, however, introduce significant errors because not all elements behave in the same way. It is thus necessary to take care when using it. Alternatives to the internal standard method include incorporating the matrix into the standards and the blank, sample dilution, and the standard addition method. 

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). 

The standard addition method represents a combination of the calibration with the aid of both an external and an internal standard. It is used in ion chromatography predominantly in matrix problems. After analysis of the analyte sample under suitable chromatographic conditions, a known amount of the compoment of interest is added and the sample is again chromatographed. In the calculation of the concentration, the volume change has to be taken into account. A peak that is not of interest serves as internal standard to compensate for the dosing error. Calculation is performed according to Eq. (202) ... 

Sometimes, the matrix of the standards is quite different from the one of the samples to be analyzed. This may give big determination errors (due, for example, to the formation of binary or ternary complexes with other ligands present into the matrix). In this case, it is better to use the standard addition method, where the standards are not independently measured from the samples. In this method, n identical aliquots are taken for each sample, and increasing known quantities of the standard are introduced in them and diluted to the same final volume. Once the graph of absorbance values vs. added concentration is represented, the extrapolation to zero absorbance will give the desired unknown concentration of the analyte. 

When the analytical signal is affected by the sample matrix, serious errors in the analytical results can arise due to improper calibration, especially for sample lots with highly variable matrix composition. The standard addition method is a powerful tool for compensating matrix effects, but its implementation in flow analysis usually involves a complex manifold and can impair the sampling rate (see 8.6.3). Matrix matching, i.e. matching the bulk compositions of the standard and sample solutions, is another way to achieve accurate results, but requires information about the sample matrix, which is not always available. To address this issue, expert systems have been exploited. 

From sx the 95% confidence interval on the estimate may be determined by multiplication by the appropriate /-value (/o.o5",n-2)-Standard addition is used when there are potential interferents that would lead to a systematic error that is proportional to concentration. Calculation of the concentration by the standard addition method causes these errors in the measurements to cancel. It is also useful if the analyte cannot be extracted from its matrix, and there is not a matrix matched calibrant available. This may be the case in environmental analysis. Note, however, that standard addition does not compensate for a constant additive interferent. 

An investigation of two GF-AAS methods has been carried out in the authors laboratory (Brown et al., 1984). The first was a conventional approach using direct analysis of serum using a stabilized temperature platform in the graphite tube. The study demonstrated the necessity of using the method of standard additions as a means of standardization, since there were profound differences in the slopes of standard curves constructed from aqueous standards, sera from normal Individuals, and sera from uremic patients. Thus, considerable analytical errors would result from using aqueous standards or standards made up in normal sera as a means of standardizing assays for uremic patients. The standard additions method allows each serum sample matrix to serve as its own standard and, therefore, provide more accurate analyses. 

ETAAS. In ETAAS atomization takes place in an electrothermal atomizer which is heated to the appropriate temperature programme. The detection limits of the method are about two or three orders of magnitude better than FAAS. It is applicable to about 40 elements but generally for about 20 elements detection limits at the ng and pg level can be reached. Commensurable or better sensitivities have only INAA, ICP-MS and stripping voltammetry. Therefore ETAAS is widely used for environmental analysis. However the method suffers from serious interferences leading to systematic errors due to thermochemical processes in the atomizer. Background absorption is also a potential source for systematic errors. Spectral interferences are additive and cannot be corrected by the popular standard addition method. ETAAS is also not free of memory effects for refractory elements. 

Quantitation by the standard addition technique Matrix interferences result from the bulk physical properties of the sample, e.g viscosity, surface tension, and density. As these factors commonly affect nebulisation efficiency, they will lead to a different response of standards and the sample, particularly with flame atomisation. The most common way to overcome such matrix interferences is to employ the method of standard additions. This method in fact creates a calibration curve in the matrix by adding incremental sample amounts of a concentrated standard solution to the sample. As only small volumes of standard solutions are to be added, the additions do not alter the bulk properties of the sample significantly, and the matrix remains essentially the same. Since the technique is based on linear extrapolation, particular care has to be taken to ensure that one operates in the linear range of the calibration curve, otherwise significant errors may result. Also, proper background correction is essential. It should be emphasised that the standard addition method is only able to compensate for proportional systematic errors. Constant systematic errors can neither be uncovered nor corrected with this technique. 

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. 

For quantitative investigations, standard lines are necessary, or the standard addition method must be used. The evaluation of the derivative peaks is made by measuring the peak height according to the PP, PZ, or PT method or by estimation of the peak area. After this test, the technique which gives the smallest error deviation should be chosen. If the derivative spectra have more than one maximum, not all peaks are suited for evaluation it may be that the one of them is superposed by satellites which can lead to deviations in the linearity of the standard curves. 

Perhaps the greatest problem in trace analysis is assurance of the accuracy of the results (i.e., the avoidance of systematic errors). Systematic sources of error are possible in every step of an analytical process. The most reliable method for detecting systematic errors is continuous and comprehensive quality assurance, particularly by occasional analysis of (certified) standard reference materials. Strictly speaking, an analytical method cannot be calibrated if suitable (i.e., representative) standard reference materials adequately representing the matrix of the expected test samples are not available. However, internal laboratoiy reference materials can then usually be prepared, whose matrix largely resembles the matrix of the test portions expected. If problems occur in the preparation of such reference samples, the standard addition method (SAM) can be applied, in which internal laboratory standards are added stepwise to the test sample (analyte and matrix)... 

Four techniques are commonly used in quantitative analysis the normalization method, the external standard method, the internal standard method, and the standard addition method. Whatever method is used, the accuracy often depends on the sample preparation and on the injection technique. Nowadays these are two main sources of error in quantitative analysis. The quantitative results produced by PCGC and CGC are comparable. 

The precision obtainable in standard addition methods is optimum when the added amounts of analyte are of the same order of magnitude as the analyte concentrations present in the sample. An estimate of the analytical error can be made from the propagation of the errors of the measured intensities [64]. If X is a function of n measured values, each resulting from N replicate measurements, the standard deviation of the estimate s (X) can be calculated from their estimates xn (k=],2, 3.n) and standard deviations si ... 

The concentrations of the alkali metals Cs, Li, and Rb were detected by LEI in different types of reference rock samples. Rock samples were dissolved by standard methods and analyses performed without preconcentration, with pure aqueous standards for calibration. Concentrations were determined by both calibration curve and standard additions methods. The results obtained by the two techniques coincided within experimental errors. Concentrations varied in the range... 

The standard addition method [35] represents a combination of calibration with the aid of both external and internal standards. In ion chromatography, it is used predominantly for the analysis of samples with difficult matrices. Matrix problems may lead to an increase in nonprecision and/or express themselves as constant or proportional systematic deviations of the analytical results. Matrix influence can be identified via calculation of the recovery function. In constant systematic deviation, the error is independent of the analyte component. Such a deviation will cause a parallel shift of the calibration line. A possible origin for this deviation might be a codetection of a matrix component. In proportional systematic deviations, the error depends on the concentration of the analyte component. This type of deviation results in a change of the slope of the calibration line. Deviations of this kind can be caused by individual sample preparation steps such as sample digestion and sample extraction, and also by matrix effects. Systematic deviations can be identified by standard addition and/or calculation of the recovery function. 

Notes. (1) The evaluation is preferably carried out by the standard addition method, i.e. in a parallel run 100 /itg of morphine are added either at the start of the chromatogram or into the sample of blood. Errors can be minimized in this way, as all factors which influence the results, such as adsorption during the course (wandering) of the spot or incomplete elution, similarly affect the substance to be analysed and the standard. 

The standard addition method avoids this kind of error. In this case, all the measurements take place in the original sample solution. The latter is spiked by one or some consecutive additions of a standard, i.e. known amounts of the substance to be analysed. If possible, these additions are done such that the concentration of all the other constituents is kept constant. Commonly, a large volume of the sample (conditioned by TISAB addition etc.) is spiked with a small volume of standard solution. For calculation of the result Cx, the... 

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