Uncertainty estimation in measurement of pKa values in nonaqueous media: A case study on basicity scale in acetonitrile medium

The difficulties in estimating uncertainty of pK_a values determined in nonaqueous media are reviewed and two different uncertainty estimation approaches are presented and applied to the pK_a values of the compounds on a previously established self-consistent spectrophotometric basicity scale in acetonitrile. One approach is based on the ISO GUM methodology (the “ISO GUM” approach) and involves careful analysis of the uncertainty sources and quantifying the respective uncertainty components. The second approach is based on the standard-deviation-like statistical parameter that has been used for characterization of the consistency of the scale (the “statistical” approach). It is demonstrated that the ISO GUM approach somewhat overestimates the uncertainty. The statistical approach is based on long-term within-laboratory statistical data and it is demonstrated that it underestimates the uncertainty. In particular it neglects the laboratory bias effects that are taken into account at least to some extent by the ISO GUM approach. Thus, together these two approaches allow to “bracket” the uncertainties of the pK_a values on the scale. The uncertainties of the pK_a values are defined in two different ways. Definition (a) includes the uncertainty of the pK_a of the reference base (anchor base of the scale) pyridine. Definition (b) excludes it. It is demonstrated that both definitions have their virtues. Definition (a) leads to the uncertainty ranges of 0.12-0.22 and 0.12-0.14 pK_a units at standard uncertainty level for different bases using the ISO GUM and statistical approach, respectively. Definition (b) leads to the uncertainty ranges of 0.04-0.19 and 0.02-0.08 pK_a units, respectively. The uncertainty of the pK_a of a given base is dependent on the quality of the measurements involved and on the distance from the reference base on the scale. The importance of the correlation between the pK_a values of bases belonging to the same scale is stressed.     

From a single analyzer to multiple instruments—The GUM approach

Assessment and expression of analytical quality have become novel spotlights in medical laboratories since accreditation began in the early 1990s, in Europe. Evaluation of uncertainty of measurement by definition was launched in Finland when the Finnish Accreditation Service (FINAS) accredited the first medical laboratories in the mid 1990s. In spite of all the analytical and statistical knowledge which has been available in medical laboratories for years, evaluation of total uncertainty of measurement has not yet caught on. The concept is still unfamiliar to experts and, indeed, little guidance has been available. National and international activities, with good results, can be shown when the educational aspect is considered. The Guide to the Expression of Uncertainty in Measurement (GUM) remains the main document for uncertainty evaluation. Uncertainty of measurement together with target value of uncertainty can be used as a good measure for analytical quality in large or smaller laboratories over time, because it is a quantitative indication and the evaluation is easy to repeat as running practical tools are available.Presented at the 8th Conference on Quality in the Spotlight, 17–18 March 2003, Antwerp, Belgium     

The influence of measurement errors on the determination of the degrees of freedom of dynamic systems

We consider the influence of measurement errors on the experimental calculation of dimensions of possible turbulent flow attractors. For this purpose we considered a Gaussian noise and we carried out some tests showing the existence of a lower limit below which the operational definition of dimension is not reliable.

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Sommario In questo lavoro viene presentata una valutazione della influenza degli errori di misura sulla determinazione sperimentale delle dimensioni di eventuali attrattori di deflussi turbolenti. A tale scopo si considera un rumore Gaussiano. I test effettuati permettono di definire l'esistenza di un minimo al di sotto del quale la definizione operativa di dimensione formisce valori non attendibili.

     

问题导向式教学在基础化学实验课堂中的应用——以“探讨二草酸合铜酸钾中铜离子测定条件”为例

Due to the facts that textbook-obedience and termwise experimenting dominate in the general chemistry laboratory classrooms, we have designed and carried out the problem-oriented teaching in order to improve the motivation of learning among the students, where the student-centered exploratory studying and practicing mode is highly desired. Problem-oriented teaching does not lead to exclusive resolutions to specific problems or experiments. Instead, it is supposed to induce multiple choices among student groups to complete experiments or resolve problems, where in-group/between-group discussions and practices would greatly activate the experimenting processes. Therefore, the sense of personal acquisition and self-progression during learning in laboratory classrooms can be easily achieved, while the good laboratory teaching will be realized as well. In this paper, we set up a problem-oriented teaching in optimizing the titration condition during measuring the copper content of K₂[Cu(C₂O₄)₂] using PAN (1-(2-pyridylazo)-2-naphthol) as the indicator. Grouping practices and experiments finally produced complementary results, as well as the satisfactory teaching and learning impacts.     

ISO uncertainty and collaborative trial data

 The possibility of using interlaboratory study repeatability and reproducibility estimates as the basis for measurement uncertainty estimates is discussed. It is argued that collaborative trial reproducibility is an appropriate basis for estimating uncertainty in routine testing provided certain conditions are met by the laboratory. The primary shortcomings relate to establishment of traceability and consequent estimation of bias associated with the method, and quantitatively establishing the relevance to the single laboratory. Approaches to resolving both difficulties are proposed, the former via full implementation of trueness determination suggested in ISO 5725 : 1994 or by independent checks on individual accuracy and precision, the latter via a reconciliation procedure. The paper also discusses other factors including sampling and sample pre-treatment, change in sample matrix, and the influence of level of analyte. Received: 28 October 1997 · Accepted: 17 November 1997     

Approaching the direct exponential curve resolution algorithm from a maximum likelihood perspective

The implementation of maximum likelihood parallel factor analysis (MLPARAFAC) in conjunction with the direct exponential curve resolution algorithm (DECRA) is described. DECRA takes advantage of the intrinsic exponential structure of some bilinear data sets to produce trilinear data by a simple shifting scheme, but this manipulation generates an error structure that is not optimally handled by traditional three-way chemometrics methods such as TLD and PARAFAC. In this work, the effects of these violations are studied using simulated and experimental data used in conjunction with the well-established TLD and PARAFAC. The results obtained by both methods are compared with the results obtained by MLPARAFAC, which is a method designed to optimally accomodate a variety of measurement error structures. The impact on the estimates of different parameters linked to the data sets and the DECRA method is investigated using simulated data. The results indicate that PARAFAC produces estimates of much poorer quality than TLD and MLPARAFAC. Also, it was found that the quality TLD estimates was comparable or only marginally poorer than the MLPARAFAC estimates. A number of commonly used algorithms were also compared to MLPARAFAC using two sets of published experimental data from kinetic studies. The MLPARAFAC estimates of rate constants were more precise than the other methods examined.     

A case study in the practical estimation of measurement uncertainty

This case study is written for analytical laboratories, in order to give support to the implementation of the concept of measurement uncertainty for routine measurements. The aim is to provide a practical, understandable and common way of performing measurement uncertainty calculations, based mainly on pre-existing quality control and validation data. Practical examples taken directly from environmental laboratory monitoring are presented and explained. However, the approach is very general and should be applicable to most testing laboratories in the chemical field. Following the protocol of evaluation illustrated in the case study, it is possible to ensure that most relevant uncertainty components associated with the method are covered. Contributions associated with sampling, homogenisation, sub-sampling, and so on, are, however, excluded.     

Measurement uncertainty for total ash and acid-insoluble ash determination of Chinese materia medica

The total ash and acid-insoluble ash contents of Chinese materia medica (CMM) have been widely used as one of the indices to illustrate the quality as well as purity of herbal medicines. Such an approach has also been adopted by many official organizations in writing monographs for pharmacopoeia worldwide. In the present study, a full validation on the methodology was conducted with the inclusion of various commonly encountered matrices in herbs, namely, leaf, flower, fruit, stem and root. The practice ensures method suitability for a wider scope of matrix variation in CMM. Moreover, in order to comply with the technical requirement of International Organization of Standardization 17025 quality assurance system, the concept of measurement uncertainty has also been incorporated in the present study. Measurement uncertainties for total ash and acid-insoluble ash contents have been estimated.     

Uncertainty of measurement for the determination of fluoride in water and wastewater by direct selective electrode potentiometry

A procedure to estimate the uncertainty of measurement applied to the fluoride determination of waters and wastewaters matrices by selective electrode potentiometry was implemented based on Eurachem Guide. The major sources of uncertainty were identified as the calibration standard solutions, fluoride concentration obtained by potential interpolation of the regression line and the precision. However the relative uncertainties depend on the anion concentration levels. The methodology proposed was presented to two fluoride concentration levels that are in the range of surface water samples (C _sample=1.12 mgF l⁻¹) and of wastewater matrices (C _sample=101.4 mgF l⁻¹). The expanded uncertainties calculated were 0.40 and 9.1 mg l⁻¹ for low and high concentration levels, respectively, using the reproducibility uncertainty as precision evaluation. The relative expanded uncertainty was around ±10% for the highest concentration, which can be considered acceptable for the ion selective electrode potenciometric methods and ±36% for the lowest concentrations. In this case the sample fluoride content is very close to the limit of quantification which has a relative uncertainty of about ±30%. If the repeatability was used in spite of duplicate analysis the same conclusions were obtained (C _sample=1.12 ± 0.39 mgF l⁻¹ and C _sample=101.4 ± 7.0 mgF l⁻¹). Although the calculated expanded uncertainties and consequently the combined uncertainty, do not vary significantly in the cases where it was used the repeatability or reproducibility for evaluating the precision, each relative variances uncertainty contributions do. When the repeatability is used to determine the combined uncertainty, the CSS and uncertainties contributions are the most dominant ones. However, if reproducibility is used, relative uncertainty variance contributions are distributed among CSS, C _F, and precision. In both cases, the contribution increases and r _CSS contribution decreases with the increasing of the concentration level. The precision variance contribution is only significant in the case where the reproducibility is used, and increases with the increasing of the concentration level. The uncertainty in the result calculated using the proposed methodology (C _sample ± U _sample = 2.17 ± 0.42 mgF l⁻¹) is in satisfactory agreement with the estimated expanded uncertainty obtained using the relative reproducibility standard deviation obtained in interlaboratory studies ().     

Estimation of measurement uncertainty by the budget approach for heavy metal content in soils under different land use

A reference database was used for the estimation of the standard uncertainties resulting from sampling, sample preparation, and analysis of soil samples from a target area in Switzerland. This evaluation was based on an extended reference sampling of the Comparative Evaluation of European Methods for Sampling and Sample Preparation of Soils Project. Samples were taken according to the national sampling protocols of 15 European countries and were analyzed for zinc, cadmium, copper, and lead. The combined uncertainty for all laboratories was estimated according to the ISO Guide to the Expression of Uncertainty in Measurement. It was found that the sampling uncertainty was not larger than the analytical uncertainty if more than ten sample increments were taken. The uncertainty due to variation in sampling depth and sample size reduction was only significant under unfavorable conditions. On the basis of an uncertainty budget the sampling protocols can be optimized and a ranking is possible, aimed at conditions that are fit for the specific purpose.Electronic Supplementary Material Supplementary Material is available in the online version of this article at