The F Test
3.2 Methodology, Terms and Definitions
3.2.6 Selectivity and Interference
On the other hand, analytical sensitivity is
γ⫽m/s, i.e. Equation(3.7) If m⫽∆signal/∆concentration, for unit concentration,
m⫽Sand γ⫽m/sor γ⫽S/N (3.10) It must also be remembered that DL3s⫽3s(1/m) or proportional to s/mor 1/γ.
Therefore, we can write the following relation:
S/N⫽1/RSD ∝ γ ∝1/DL (3.11)
The relation above emphasises the fact that the precision of a signal is very impor- tant. The requirements of high S/N, low RSD, high γ(sensitivity) and low DL all depend on a small standard deviation, the target of a high-quality signal and thus the result.
conditions are met, interference will occur, resulting in the formation of extraneous analytical signal not related to analyte concentration in sample. On the other hand, an interferant may be totally inert from chemical point of view, but will cause an ana- lytical signal, such as spectral that will cause interference. Most of these types of interferences do not depend on the presence of analyte and thus called additive inter- ferences. In some cases, the interferant may alter the amount of the analyte that is available to cause the analytical signal; this may be an enhancement or depression which will result in an apparent increase or decrease in calibration slope, respectively.
When the analyte is not present, this type of interference is absent; therefore, only the slope of the calibration is affected and the term multiplicative interference can be used. It is very often seen that an analytical signal may suffer both additive and mul- tiplicative interferences simultaneously. The effects of additive and multiplicative interferences on a calibration line are shown in Figure 3.6.
These definitions for interferences lead to the conclusion that the additive inter- ferences may be handled in the absence of analyte, but the multiplicative interfer- ences should be handled in the presence of analyte.
Additive interferences may be characterized and handled by preparing samples containing all the matrix components but analyte; this is called a matrix-matched blank. Such a blank may be conveniently prepared if the matrix is well characterized such as a metal, an alloy or a well-defined synthetic material. The problem here is handled by either the direct use of a similar material that contains the analyte at a non-detectable level. Alternatively, reconstitution of the matrix from its well-defined components is attempted. This approach is called matrix simulation. After a suc- cessful matrix simulation, the blank may conveniently be spiked with known con- centrations of analyte; a calibration line prepared by these samples can be used in correction of both the additive and multiplicative interferences. Unfortunately, this approach may often prove very difficult or impossible, since very high-purity com- ponents should be used in reconstitution and in some cases the matrix is too com- plex and cannot be simulated at all.
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Figure 3.6 Several kinds of errors on a linear calibration plot. (a) no interference, ideal plot;
(b) multiplicative interference only; (c) additive interference only; (d) multiplica- tive and additive interferences
In some cases, a blank is used to solve only a part of the additive interferences such as the analytical signals which may be caused by solvent, pH buffer and other reagents involved in analysis. In any case, blank measurement is made for correction purposes; the analyst must be aware of what is being corrected for. Some users would subtract the blank signal from the other readings; in this case, the calibration plot will tend to have a very small intercept. The better way is to use the blank sig- nal as an input to calibration line where analyte concentration is 0 and then to use the calibration line with an intercept. This approach will provide a better visibility and thus appreciation of blank and more realistic evaluation of data is possible.
Multiplicative interferences can be handled in several ways. One of them is as described above matrix simulation and spiking with analyte. Especially for biologi- cal, clinical or food samples, this approach cannot be used as the matrices are too complex to be simulated. In this case, another approach may be used in which the sample itself is employed as the matrix for determining by adding successive analytes to the parallel portions of sample solutions and preparing a calibration plot from these spiked solutions. This approach is named as method of standard additions; known additions or analyte additions are also used. A calibration line prepared by the method of standard additions is shown in Figure 3.7. The intercept on the x-axis is used to calculate the analyte concentration after correction for dilution. The terms endogenousand exogenousare used to denote the analyte that is originally present in sample and spiked, respectively. While a calibration is prepared by standard addi- tions, it would be very beneficial to construct another calibration plot at the same time by using standard solutions of analyte in solvent or in a simulated matrix. This is required because if the slopes are identical, the use of the standard additions is not needed, and the conventional calibration can safely be employed. It should be noted that for small number of samples, the use of standard additions would not make a large difference regarding the number of solutions to be prepared and measurements to be made; total analysis time is not affected much. However, as the number of sam- ples increase, the extra load of work is obvious when standard additions technique is to be used. If the need for standard additions is justified, there may be another
Figure 3.7 Method of standard additions: (a) calibration plot for aqueous standards; (b) cal- ibration plot for standard additions. Cxis the endogenous analyte concentration in spiked solution
approach to minimize the amount of labour. If the information on the nature of the samples is available such that all the samples have similar matrices, a single calibra- tion line by standard additions may be extrapolated to zero point and employed as a conventional calibration. In order to do this, a statistically sound number of randomly selected samples should be tested to see whether the slopes of the individual standard addition calibration lines have insignificant differences using statistical tests.
The observation of the following points is a minimum requirement in order to have a successful correction of multiplicative interferences by the method of stan- dard additions:
(i) The analytical signals obtained must be in a linear range, so that extrapolation of line to obtain the intercept on the x-axis would not cause any error.
(ii) The endogenous and exogenous analyte species should be in the same form regarding the oxidation state, chemical environment, etc. Another way of expressing this fact is that the sensitivity for endogenous and exogenous ana- lytes should be the same.
A large range of matrices are to be handled in food analysis. Therefore, the need for the use of standard additions should be frequently checked on new kinds of sam- ples even when it is known that an aqueous calibration line has been known to be sufficient.
One vital point to be remembered is that the method of standard additions pro- vides a correction for the multiplicative interferences at best only; the additive inter- ferences cannot be eliminated by this approach. A rather useful demonstration of this point has been made by Welz.4
Internal standard methodis mostly employed to improve the precision for a cali- bration and thus analytical determinations. Analytical signal may be affected in a random manner by analytical parameters such as weighing, diluting, flame or arc temperature. A second species, which is called as internal standard, is selected and added in a precisely known and constant amount or concentration to all the stan- dards, blanks and samples. During the calibration, instead of analyte signal, a ratio of analyte signal to internal standard signal is used. The improvement in precision should be verified by comparing the respective calibration lines regarding the corre- lation coefficients (R) of both linear regression lines. It is expected that the use of internal standard will improve the quality of a linear fit, since the analytical signal caused by its presence should be a constant, and the ratio used should serve as a kind of normalization against fluctuations in the analytical measurement system.
The following points are to be observed and fulfilled for a successful application of internal standard method:
(i) The species chosen as internal standard should be present in all the stan- dards, blanks and samples originally only at a level of concentration which is not detectable.
(ii) The analytical signals for the analyte and internal standard should be affected by the fluctuating analytical variables exactly in the same manner and pro- portions.
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(iii) If there are any multiplicative interferences, their effect for analyte and inter- nal standard should be identical. This condition may be more difficult to ful- fil as compared to the others, since most of the multiplicative interferences are chemical in nature and therefore may be selective for analyte.
(iv) Internal standard should not cause any interference.
Internal standard approach is used best in minimizing the multiplicative interfer- ences which function in a random manner.
In many cases, the absolute amount of the interferant is more effective to induce an observed interference than the interferant/analyte ratio. This behaviour allows one to dilute the sample to a point where the interference is not observed; naturally, at this point analyte concentration should be still higher than LOQ.
In some cases, the interference effect reaches to a saturation point; further increase in interferant concentration does not affect the analytical signal any more. If this is the case, it is possible to add more interferant to the sample until the analytical sig- nal remains constant. At this point, the method of standard additions may be useful.