Statistical methods standard addition

R. Sundberg, Interplay between chemistry and statistics, with special reference to calibration and the generalized standard addition method. Chemom. Intell. Lab. Syst., 4 (1988) 299-305. 

In addition to statistical peculiarities, special features may also result from certain properties of samples and standards which make it necessary to apply special calibration techniques. In cases when matrix effects appear and matrix-matched calibration standards are not available, the standard addition method (SAM, see Sect. 6.2.6) can be used. 

Phosphoric Acid. The 2nd-order rate method for analyzing the TGA data was statistically best (Table IV) for the cellulose/H PO samples. This suggests that the conclusions from a prior study which assumed a lst-order reaction (29) may need to be reexamined. While Wilkinson s approximation method gave high r values, the rate constant is determined by the intercept rather than the slope in this method. Thus, the standard deviation of the rates determined by Wilkinson s approximation method is still relatively high when compared to the other methods. In addition, the reaction order as determined by the Wilkinson approximation method was unrealistically high, ranging from 2.6 to 5.8. 

Table 4.2 Statistical parameters for H-point standard addition method apphed to commercial madder pigment using silica as a diluent and morin as a reference compound...

Even when Community MRLs have been established, similar products in various member states may differ greatly with respect to the withdrawal times established by national authorities. Most member states employ a simple method by which the withdrawal time is set at the time when residues in all tissues in all the animals have depleted to below the respective MRL values. In addition, some member states then add an additional safety period if, for example, there are large variations in the depletion data set or other shortcomings are found in the studies. On the other hand, some other member states use statistical methods to establish withdrawal times. A greater degree of harmonization would be possible if a standard approach for calculating the withdrawal time was adopted throughout the European Union. Moreover, this would aid both the centralized and the decentralized procedures. 

QPPR can be derived from thermodynamic principles or by statistical analysis of measured data. In the latter case, a set of compounds for which Fand Pi, P2, , Pm are known is required to develop the model (the training set). An additional evaluation set of compounds with known F, Pi, P2, , Pm is recommended to evaluate the reliability and predictive capability of the model proposed. For a detailed description of the statistical methods, the reader is referred to [25], standard statistical texts, and to articles listed in the Toolkit Bibliography. 

In order to correctly design analytical procedures used for the detection of food allergens, it is necessary to have basic knowledge of food product chemistry to know how to collect, prepare, and store food samples to be able to fragment, mix, disintegrate, and extract samples to know (or be able to find quickly) relevant food quality standards and admissible contents of particular food ingredients and finally to understand precision of determinations, their sensitivity, and detection threshold levels, reproducibility, and errors of determination methods. In addition, it is essential to be able to gather the results of assays, process them with the aid of a computer and statistical methods, and to present the analytically derived data. 

Standard addition is used to quantify the concentration in unknown samples when matrix interferences are present. The use of standard addition has been extensively discussed by Rodriguez et al., Cardone, and Honorato et al. [23-26]. Exact amounts of the analyte in increasing concentrations are added to the sample. The response (Y) is plotted vs. the added concentration (X). A straight line is regressed through the data points. The concentration of the analyte in the sample is given by the intercept on the X-axis (Xsample = a/b). Standard addition is probably the best way to correct for matrix effects. Rodriguez et al. have described the statistical techniques that can be used for the validation of analytical methods with standard addition [23],... 

In addition to the usual statistical methods based on univariate descriptors (mean, median, and standard deviation) and analysis of variance, multivariate techniques of statistics and chemometrics are increasingly being used in data evaluation. Whereas the former are more rigorous in theoretical background and assumptions, the latter are useful in the presentation of the data, pattern recognition, and multivariate calibrations. Several good monographs on chemometrics are available (see for example [58-61]). 

The number of tests to be carried out will be stated in any standard test method. When agreed non-standard tests are used, at least 5 specimens representative of the batch should be tested. If the measured behaviour of individual test specimens varies significantly from the mean value, additional specimens should be tested so that statistical methods may be used to determine a characteristic response. 

For a quantitative measurement, the sample is aspirated into the flame and the intensity of radiation is measured at the emission wavelength of the analyte element to be determined. The concentration of the element in the sample is calculated from comparison with an external calibration curve or by the standard addition method. Both of these methods have been discussed in Chapter 2. A typical external calibration cnrve for lithium is shown in Figure 7.4. The calibration curve was constructed by aspirating Li standard solntions of 5 and 10 ppm Li and the blank solution (0.0 ppm Li). Each intensity was measured and a plot of intensity versns concentration made. Modem systems nse a statistical cnrve-fitting program to construct the calibration curve and to calculate the concentrations of unknowns. Note that an emission signal was detected in the standard that contained no... 

However, the method of standard addition is not only useful to quantify an analyte present in a matrix, it can also be employed to check if the matrix introduces any proportional error. Similar additions of analyte are made to a blank matrix (the dotted line in Fig. 1) and if there is no proportional error, then the slopes of both regression lines are equal. Therefore, the slope equality has to be tested through a convenient statistical test. To conclude, the method of standard additions is a powerful method that enables to quantify an analyte present in a matrix susceptible to modify its behavior. Nevertheless, this method is somewhat tedious, because it requires many preparations and injections to obtain enough points for a sufficient reliabihty. 

Figure 8.13 Idealized plots according to the Method of Standard Additions. Each point plotted is assumed to be the mean of several replicate determinations. The traditional method (left panel) simply plots the observed analytical signal Y vs the amount of calibration standard added x (the black square corresponds to the nonspiked sample, Y = Yq), and estimates the value of X by extrapolation of a least-squares regression line to Y = 0 (see text) however, this procedure implies that the confidence interval at this point (not shown, compare Figure 8.12) has widened considerably. By using a simple transformation from Y to (Y-Yq) the extrapolation procedure is replaced by one of interpolation, thus improving the precision (more narrow confidence interval). Reproduced from Meier and Ziind, Statistical Methods in Analytical Chemistry, 2nd Edition (2000), with permission of John Wiley Sons Inc.

An important practical concern that is easily overlooked is the amount (size) of the analytical sample that is available. If this is too small given the expected concentrations of analyte(s) and the minimum size of the aliquots required per analysis in order to avoid statistical limitations on precision (see discussion of Equations [8.95-8.97, Section 8.6) it will limit the strategic options available to the analyst, e.g., number of replicate analyses, applicability of the Method of Standard Additions etc. 

Although it is an elegant approach to the common problem of matrix interference effects, the method of standard additions has a number of disadvantages. The principal one is that each test sample requires its own calibration graph, in contrast to conventional calibration experiments, where one graph can provide concentration values for many test samples. The standard-additions method may also use larger quantities of sample than other methods. In statistical terms it is an extrapolation method, and in principle less precise than interpolation techniques. In practice, the loss of precision is not very serious. 

There are many other statistical techniques in addition to those presented in the preceding sections of this paper which can be used to advantage by the food research worker. Many of these are concerned with enumeration data (i.e., data which arise by counting), and others are recently developed methods for dealing with measurement data. Examples of the latter are control chart techniques, sequential analysis, procedures involving the sample range in place of the sample standard deviation, and nonparametric and distribution-free techniques. Since these methods have as yet received little attention by food research workers, published examples are difficult if not impossible to find. However, we have mentioned these methods so that interested persons may consult appropriate references (Ostle, 1954 Snedecor, 1948 Goulden, 1939 and Dixon and Massey, 1951) for the details of operation of particular techniques. 

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