Standard additions: myth and reality

Standard additions is a calibration technique devised to eliminate rotational matrix effects in analytical measurement. Although the technique is presented in almost every textbook of analytical chemistry, its behaviour in practice is not well documented and is prone to attract misleading accounts. The most important limitation is that the method cannot deal with translational matrix effects, which need to be handled separately. In addition, because the method involves extrapolation from known data, the method is often regarded as less precise than external calibration (interpolation) techniques. Here, using a generalised model of an analytical system, we look at the behaviour of the method of standard additions under a range of conditions, and find that, if executed optimally, there is no noteworthy loss of precision.     

Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean

In validation of quantitative analysis methods, knowledge of the response function is essential as it describes, within the range of application, the existing relationship between the response (the measurement signal) and the concentration or quantity of the analyte in the sample. The most common response function used is obtained by simple linear regression, estimating the regression parameters slope and intercept by the least squares method as general fitting method. The assumption in this fitting is that the response variance is a constant, whatever the concentrations within the range examined.The straight calibration line may perform unacceptably due to the presence of outliers or unexpected curvature of the line. Checking the suitability of calibration lines might be performed by calculation of a well-defined quality coefficient based on a constant standard deviation.The concentration value for a test sample calculated by interpolation from the least squares line is of little value unless it is accompanied by an estimate of its random variation expressed by a confidence interval. This confidence interval results from the uncertainty in the measurement signal, combined with the confidence interval for the regression line at that measurement signal and is characterized by a standard deviation s_x0 calculated by an approximate equation. This approximate equation is only valid when the mathematical function, calculating a characteristic value g from specific regression line parameters as the slope, the standard error of the estimate and the spread of the abscissa values around their mean, is below a critical value as described in literature.It is mathematically demonstrated that with respect to this critical limit value for g, the proposed value for the quality coefficient applied as a suitability check for the linear regression line as calibration function, depends only on the number of calibration points and the spread of the abscissa values around their mean.     

Effect of the driving frequency on the emission characteristics of a radio-frequency glow discharge excitation source boosted by the introduction of a d. c. bias current.

In a radio-frequency-powered glow discharge lamp, a d.c. bias current which is driven by a self-bias voltage can lead to an enhancement of the emission intensities excited by the plasma. The driving frequency of the r.f. plasma is an important parameter to determine the self-bias voltage; lower r.f. frequencies induce greater self-bias voltages. The effects of the bias current introduction on the emission characteristics were compared between a 13.56-MHz plasma and a 6.78-MHz plasma. As a result, the 6.78-MHz plasma offered a better analytical performance, probably due to higher self-bias voltages, if the introduced Ar pressure was optimized. This method was applied to a Mo determination in Fe-matrix alloy samples. At bias currents of 40 - 50 mA, the emission intensities of the Mo I 379.82-nm line were about 10-times larger than those obtained with the conventional plasma when the 6.78-MHz plasma was produced at an r.f. power of 60 W. The detection limit obtained for this calibration was 2.0 x 10(-4) mass % Mo at an 80-W r.f. power and at a d.c. bias current of 68 mA.     

Determination of Allura Red and Tartrazine in Food Samples by Sequential Injection Analysis Combined with Voltammetric Detection at Antimony Film Electrode

An antimony film electrode prepared on‐line and installed as part of a sequential injection system, was used as an electrochemical detector to determine azo dyes in food samples. The influence of several flow variables were evaluated using a central composite design. In optimal conditions, the linear range of the calibration curve varied from 1–5 µM, with a limit of detection limit of 0.3 µM. The relative standard deviation of analytical repeatability was <5.0 %.The method was validated by comparing the results obtained with those provided by HPLC; no significant difference were seen.     

Determination of aluminium in the edible part of fish by GFAAS after sample pretreatment with microwave activated oxygen plasma

An analytical method for the determination of aluminium in the edible part of fish was developed using a new pre-treatment method in a microwave activated oxygen plasma and graphite furnace atomic absorption spectrometry. The linearity of the calibration line as well as of different standard addition lines were very good within the measurement area of 0–60 μg Al/L. The recovery with spiked ocean perch fillet was good. The unsatisfactory recovery of aluminium with the reference-material (mussel tissue) may be due to high quantities of insoluble aluminium-silicates. An installed quality-control-card indicated that the method showed no significant fluctuation as well as contamination over the complete analysis time. The limit of detection calculated as 3 times the standard deviation of the blank absorbance divided by the slope of the calibration line was 1 μg Al/L. Received: 7 December 1998 / Revised: 14 February 1999 / Accepted: 24 February 1999     

Calibration uncertainty

Methods recommended by the International Standardization Organisation and Eurachem are not satisfactory for the correct estimation of calibration uncertainty. A novel approach is introduced and tested on actual calibration data for the determination of Pb by ICP-AES. The improved calibration uncertainty was verified from independent measurements of the same sample by demonstrating statistical control of analytical results and the absence of bias. The proposed method takes into account uncertainties of the measurement, as well as of the amount of calibrant. It is applicable to all types of calibration data, including cases where linearity can be assumed only over a limited range. Received: 25 August 2001 Accepted: 21 December 2001     

Determination of aluminium in the edible part of fish by GFAAS after sample pretreatment with microwave activated oxygen plasma

An analytical method for the determination of aluminium in the edible part of fish was developed using a new pre-treatment method in a microwave activated oxygen plasma and graphite furnace atomic absorption spectrometry. The linearity of the calibration line as well as of different standard addition lines were very good within the measurement area of 0–60 μg Al/L. The recovery with spiked ocean perch fillet was good. The unsatisfactory recovery of aluminium with the reference-material (mussel tissue) may be due to high quantities of insoluble aluminium-silicates. An installed quality-control-card indicated that the method showed no significant fluctuation as well as contamination over the complete analysis time. The limit of detection calculated as 3 times the standard deviation of the blank absorbance divided by the slope of the calibration line was 1 μg Al/L. Received: 7 December 1998 / Revised: 14 February 1999 / Accepted: 24 February 1999     

From total allowable error via metrological traceability to uncertainty of measurement of the unbiased result

The concept of "total allowable error", investigated by Westgard and co-workers over a quarter of a century for use in laboratory medicine, comprises bias as well as random elements. Yet, to minimize diagnostic misclassifications, it is necessary to have spatio-temporal comparability of results. This requires trueness obtained through metrological traceability based on a calibration hierarchy. Hereby, the result is associated with a final uncertainty of measurement purged of known biases of procedure and laboratory. The sources of bias are discussed and the importance of commutability of calibrators and analytical specificity of the measurement procedure is stressed. The practicability of traceability to various levels and the advantages of the GUM approach for estimating uncertainty are shown.     

Extrapolation and interpolation of asymptotic series by self-similar approximants

The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical physics, when one is interested in finding the equation of state for a strongly interacting system. A special attention is payed to the study of the basic properties of fluctuating fluid membranes. It is shown that these properties can be well described by means of the method of self-similar approximants. For this purpose, the method has been generalized in order to give accurate predictions at infinity for a function, whose behavior is known only at the region of its variable close to zero. The obtained results for fluctuating fluid membranes are in good agreement with the known numerical data.     

Quality of calibration in inductively coupled plasma atomic emission spectrometry

Calibration is a crucial step during the whole analytical process. A procedure is suggested to assess the quality of linear regression used for the calibration graph, based on the use of confidence limits for the concentration, as the regression coefficient is not appropriate for this purpose. This procedure has been applied to inductively coupled plasma atomic emission spectrometry. It indicates that the use of only three standards should be discouraged because of unacceptably high confidence limits for the concentration. Moreover, use of weighted regression is more adequate in performing the least squares method and provides more constant confidence limits over the concentration range used to construct the calibration graph. This procedure could be easily added to any commercially available ICP system software.     

A new approach to the integrated calibration in flow injection analysis

A new proposal how to perform the analytical procedure according to the integrated calibration method is presented. An original flow injection system has been designed for this purpose. When using only a single standard solution, the measurement information gathered during a single analytical course permits construction of four calibration graphs and calculation of as many as four independent estimations of the analyte concentration in the sample examined. As the calibration method applied integrates the set of standards method and the standard addition method, the analytical estimations may be obtained in both the interpolative and the extrapolative manner and the final result can be effectively verified in terms of accuracy. The system developed was experimentally tested on the example of spectrophotometric determination of chromium. It has been proved to be capable of saving time and reagents as well as providing reliable analytical results. Owing to the instrumental simplicity and analytical efficiency the system is expected to be useful for routine analysis.     

Optimised determinations of water in ethanol by encoded photometric near-infrared spectroscopy: a special case of sequential standard addition calibration

A special limiting case of sequential standard addition calibration (S-SAC) has been applied to measurement of the water content of ethanol using encoded photometric near infrared spectroscopy. The method has shown good comparability with certified reference materials and to measurements made by Karl Fischer titration. The technique is quick and easy to use and should have application in high throughput and process measurement, for instance in biofuels analysis at port-of-entry or in bio-refineries. The characteristics of this limiting case of S-SAC have been fully described, and the corrections required to the value obtained by extrapolation to avoid bias have been calculated. The precision of the S-SAC procedure has been studied, and proposals have been made to optimise this with respect to the analytical precision. The technique should be applicable for the measurement of water in ethanol mass fractions of up to 0.1 g g⁻¹ with an expanded uncertainty of less than 2% (relative).     

Validation of accuracy by interlaboratory programme

A statistical design is proposed for assessing the accuracy of an analytical method by its application to a certified reference material in an interlaboratory programme. The validation of accuracy is based on the difference between the certified value and the overall mean of the test programme and is linked to the concept that below a certain limit this difference has no practical significance. It is shown that a certified reference material cannot be used to detect bias in a method if the bias is smaller than the confidence interval of the certified value.     

Interpolation and extrapolation problems of multivariate regression in analytical chemistry: benchmarking the robustness on near-infrared (NIR) spectroscopy data

Modern analytical chemistry of industrial products is in need of rapid, robust, and cheap analytical methods to continuously monitor product quality parameters. For this reason, spectroscopic methods are often used to control the quality of industrial products in an on-line/in-line regime. Vibrational spectroscopy, including mid-infrared (MIR), Raman, and near-infrared (NIR), is one of the best ways to obtain information about the chemical structures and the quality coefficients of multicomponent mixtures. Together with chemometric algorithms and multivariate data analysis (MDA) methods, which were especially created for the analysis of complicated, noisy, and overlapping signals, NIR spectroscopy shows great results in terms of its accuracy, including classical prediction error, RMSEP. However, it is unclear whether the combined NIR + MDA methods are capable of dealing with much more complex interpolation or extrapolation problems that are inevitably present in real-world applications. In the current study, we try to make a rather general comparison of linear, such as partial least squares or projection to latent structures (PLS); "quasi-nonlinear", such as the polynomial version of PLS (Poly-PLS); and intrinsically non-linear, such as artificial neural networks (ANNs), support vector regression (SVR), and least-squares support vector machines (LS-SVM/LSSVM), regression methods in terms of their robustness. As a measure of robustness, we will try to estimate their accuracy when solving interpolation and extrapolation problems. Petroleum and biofuel (biodiesel) systems were chosen as representative examples of real-world samples. Six very different chemical systems that differed in complexity, composition, structure, and properties were studied; these systems were gasoline, ethanol-gasoline biofuel, diesel fuel, aromatic solutions of petroleum macromolecules, petroleum resins in benzene, and biodiesel. Eighteen different sample sets were used in total. General conclusions are made about the applicability of ANN- and SVM-based regression tools in the modern analytical chemistry. The effectiveness of different multivariate algorithms is different when going from classical accuracy to robustness. Neural networks, which are capable of producing very accurate results with respect to classical RMSEP, are not able to solve interpolation problems or, especially, extrapolation problems. The chemometric methods that are based on the support vector machine (SVM) ideology are capable of solving both classical regression and interpolation/extrapolation tasks.     

Quantifying uncertainty in determination of polysaccharides in glycoconjugate vaccines based on in-house validation data

The measurement uncertainty in quantifying polysaccharides in glycoconjugate vaccines was estimated in order to ascertain compliance of these products in the batch release procedure of an Official Medicines Control Laboratory. A single-laboratory validation approach of an internal analytical procedure to quantify the total saccharide by the way of the sialic acid (N-Acetylneuraminic acid) concentration in a meningococcal glycoconjugate vaccine by High Performance Anion Exchange Chromatography coupled with Pulsed Amperometric Detection is reported. Uncertainty components from precision, bias and other sources were evaluated. It turned out that uncertainty is dominated by the precision contribution, while bias was mainly due to the non-recovery from hydrolysis. As a consequence, a correction factor was considered. At a confidence level of approximately 95%, the expanded uncertainty of the total polysaccharide concentration in a vaccine, when measured using the internal method, was found to be 11.5%.     

Calibration model of simultaneous multielement atomic-emission analysis using analytical line groups of each determined element

A calibration model of multielement methods for simultaneous determination of micro- and macro-concentrations of elements by computing the arc atomic-emission spectra has been developed. A calibration procedure for the analytical line group of the elements to be determined is offered. It allows the lower and upper limits of the concentration range for each line of the determined element to be calculated by means of the least-square method (LSM) and the Weibull distribution law is used to extend the concentration region. The calibration model was successfully tested for different arc optical emission spectroscopy (OES) methods. Received: 17 June 1997 / Revised: 3 November 1997 / Accepted: 7 November 1997     

Calibration model of simultaneous multielement atomic-emission analysis using analytical line groups of each determined element

A calibration model of multielement methods for simultaneous determination of micro- and macro-concentrations of elements by computing the arc atomic-emission spectra has been developed. A calibration procedure for the analytical line group of the elements to be determined is offered. It allows the lower and upper limits of the concentration range for each line of the determined element to be calculated by means of the least-square method (LSM) and the Weibull distribution law is used to extend the concentration region. The calibration model was successfully tested for different arc optical emission spectroscopy (OES) methods. Received: 17 June 1997 / Revised: 3 November 1997 / Accepted: 7 November 1997     

Statistical and probabilistic approaches to confidence intervals of linear calibration in liquid chromatography.

The aim of this paper is to compare the reliability of two approaches to estimate the 95% confidence intervals of linear calibration in real situations. One is the statistical approach, which is well known in statistics, and the other is the probabilistic approach, which is based on a theory to predict the precision of instrumental analyses mainly from signal and noise, called FUMI (Function of Mutual Information) theory. The high-performance liquid chromatographic determination of quisalofop and maltose is taken as an example. Calibration lines obtained under the same experimental conditions are superimposed on the 95% confidence intervals to investigate whether the resulting confidence intervals can include all the calibration lines reasonably. A pair of 95% confidence intervals (upper and lower limits) can be calculated from each calibration line, but varies from calibration line to calibration line, although obtained under the same experimental conditions. The variability and reliability of the 95% intervals are also examined.     

An expression of uncertainty in calibration using stepwise or separate dilution of a stock solution.

The traditional method for linear calibration can estimate the confidence intervals of calibration lines from a set of experimental data for a single calibration line. However, the following situations, often encountered in laboratories, are out of reach of the method, since the concentrations of the standard solutions are not independent of each other: (A) a standard solution is diluted from a more concentrated one in a stepwise way (stepwise dilution); (B) every standard solution for a calibration experiment is prepared from a stock solution, but the stock solution is newly prepared for each calibration (separate dilution with the variable concentration of the stock solution). This paper puts forward a theory to calculate the confidence intervals of calibration lines in the above situations. Analyses made up of sample weighing, dilution, HPLC measurement and calibration with the linear least-squares fitting are taken as examples. The proposed theory is numerically compared to the traditional method.     

Creatinine determination in urine samples by batchwise kinetic procedure and flow injection analysis using the Jaffé reaction: chemometric study

The classical Jaffé reaction for the determination of creatinine in urine samples is tested. A comparative study of the main analytical characteristics focussed to minimize the bias error and improve the precision, for the batchwise and flow injection (FI) methods is realized. Also, the effect of the albumin concentration in the determination of creatinine has been studied. Different analytical signals were studied. Absorbance increments at different times permit to estimate the creatinine concentration free from bias error in urine by the batchwise method using the calibration graph obtained with creatinine standards and no measurement of the blank solution is needed. The lineal interval was 0.92–50 mg l⁻¹ and seven samples can be processed per hour by an operator. No previous treatment of the urine sample is necessary. The FI method provides also good results. The lineal interval was 30–100 mg l⁻¹ and the sample rate was around 20 samples per hour. If increased albumin levels are detected in the urine, standard addition method or the calibration graphs with standards in presence of albumin are needed in order to obtain accurate results when FI method is employed. The obtained accuracy of the both methods allows its application as diagnostic tool to establish the urinary creatinine levels.