Analytical chemistry uncertainties

International Union of Pure and Applied Chemistry, Guidelines for Calibration in Analytical Chemistry. Uncertainty Estimation and Figures of Merit for Multivariate Calibration, 2006. 

There are a few basic numerical and experimental tools with which you must be familiar. Fundamental measurements in analytical chemistry, such as mass and volume, use base SI units, such as the kilogram (kg) and the liter (L). Other units, such as power, are defined in terms of these base units. When reporting measurements, we must be careful to include only those digits that are significant and to maintain the uncertainty implied by these significant figures when transforming measurements into results. 

Many other mathematical operations are commonly used in analytical chemistry, including powers, roots, and logarithms. Equations for the propagation of uncertainty for some of these functions are shown in Table 4.9. 

Evaluation of reactivity ratios from the copolymer composition equation requires only composition data—that is, analytical chemistry-and has been the method most widely used to evaluate rj and t2. As noted in the last section, this method assumes terminal control and seeks the best fit of the data to that model. It offers no means for testing the model and, as we shall see, is subject to enough uncertainty to make even self-consistency difficult to achieve. 

Ellison, S., Wegscheider, W, and Williams, A., Measurement Uncertainty, Analytical Chemistry News Features, October 1, 1997, 607A-613A. 

Traceability of measurement results is essential in the establishment of a certified reference material. As stipulated in ISO Guides 30 and 35, a certified reference material can only be certified if there is an uncertainty statement with a traceability statement. Basically, traceability means anchoring. In classical analytical chemistry, that SI system is often the best choice as a reference (= anchoring poinf). However, there is a wide range of parameters either defined by a method or defined by the... 

To assess homogeneity, the distribution of chemical constituents in a matrix is at the core of the investigation. This distribution can range from a random temporal and spatial occurrence at atomic or molecular levels over well defined patterns in crystalline structures to clusters of a chemical of microscopic to macroscopic scale. Although many physical and optical methods as well as analytical chemistry methods are used to visualize and quantify such spatial distributions, the determination of chemical homogeneity in a CRM must be treated as part of the uncertainty budget affecting analytical chemistry measurements. 

If users are to benefit from the implementation and/or verification of traceability in analytical chemistry the unbroken pathway of references must be kept short. The uncertainty of the references (CRMs) used may significantly widen the uncertainty a user must attach to the result of his measiuement when addressing accuracy and traceability through comparison with a CRM. These comparisons should be only considered in a first or second level step as to keep the uncertainties of the results within limits fit for the purpose. The producers of CRMs must keep their uncertainties sufficiently small to allow introduction of the CRM at different points in the analytical pathway, without limiting the usefiilness of results through unduly expanded uncertainties. 

LGC - VAM Publications (i) The Fitness for Purpose of Analytical Methods, A Laboratory Guide to Method Validation and Related Topics, (2) Practical Statistics for the Analytical Scientist A Bench Guide By TJ Farrant, (3) Trace Analysis A structured Approach to Obtaining Reliable Results By E Pritchard, (4) Quantifying Uncertainty in Analytical Measurement, and (5) Quality in the Analytical Chemistry Laboratory. LGC/RSC Publications, London, England. 

The significance of the uncertainty concept in analytical chemistry has increased in the last century, notwithstanding that at first some conformity was missed. But inconsistencies have been dispelled (see Thompson [1995] AMC [1995]) and operational approaches have been presented by Hund et al. [2001]. Numerous examples of application have been given in EURACHEM [1995]. 

The principles of quality assurance are commonly related to product and process control in manufacturing. Today the field of application greatly expanded to include environmental protection and quality control within analytical chemistry itself, i.e., the quality assurance of analytical measurements. In any field, features of quality cannot be reproduced with any absolute degree of precision but only within certain limits of tolerance. These depend on the uncertainties of both the process under control and the test procedure and additionally from the expense of testing and controlling that may be economically justifiable. 

As a measuring science, analytical chemistry has to guarantee the quality of its results. Each kind of measurement is objectively affected by uncertainties which can be composed of random scattering and systematic deviations. Therefore, the measured results have to be characterized with regard to their quality, namely both the precision and accuracy and - if relevant - their information content (see Sect. 9.1). Also analytical procedures need characteristics that express their potential power regarding precision, accuracy, sensitivity, selectivity, specificity, robustness, and detection limit. 

In analytical chemistry, we do not have a standard mole. Therefore, solutions made up to a well-defined concentration using very pure chemicals are used as a basis from which we can compare other solutions or an instrument scale. This process is calibration . For some analyses, the chemical used may be a Certified Reference Material which has a well documented specification, e.g. in terms of the concentration of a particular species and the uncertainty of the specified value. However, it is not sufficient just to calibrate the apparatus/equipment used, it is important that the complete method of analysis is validated from extraction of the analyte from the sample to the final measurement. 

In contrast, a systematic error remains constant or varies in a predictable way over a series of measurements. This type of error differs from random error in that it cannot be reduced by making multiple measurements. Systematic error can be corrected for if it is detected, but the correction would not be exact since there would inevitably be some uncertainty about the exact value of the systematic error. As an example, in analytical chemistry we very often run a blank determination to assess the contribution of the reagents to the measured response, in the known absence of the analyte. The value of this blank measurement is subtracted from the values of the sample and standard measurements before the final result is calculated. If we did not subtract the blank reading (assuming it to be non-zero) from our measurements, then this would introduce a systematic error into our final result. 

Eurachem/CITAC, Quantifying Uncertainty in Analytical Measurement, Eurachem/CITAC Guide, 2nd Edition, ISBN 0-948926-15-5, (Eurachem), Co-operation on International Traceability in Analytical Chemistry (CITAC), 2000. [http //www.eurachem.org] (accessed 11 December, 2006). 

Eurachem. (1995). A focus for Analytical Chemistry in Europe, Quantifying Uncertainty in Analytical Measurement, 1st Edition, Berlin. 

Measurement uncertainty is one of the key issues in quality assurance. It became increasingly important for analytical chemistry laboratories with the accreditation to ISO/IEC 17025. 

The Guide to the Expression of Uncertainty in Measurement (GUM) to some extent is the Bible of uncertainty estimation. Since it was originally made for physical measurements in metrology laboratories, it is quite difficult to translate it into analytical chemistry problems, especially for routine measurements. 

In most cases a confidence level of 68% is not enough to take reliable decisions. To increase this confidence the combined standard uncertainty is multiplied with a factor to get an expanded uncertainty. If we choose a factor of 2 we get a level of confidence of approx. 95%. This is the most widely used expanded uncertainty in analytical chemistry. 

As already mentioned the modelling approach described in the GUM is difficult to translate into analytical chemistry because the testing procedures are very complex and it is a huge effort to identify and quantify all uncertainty sources. For routine laboratories often handling dozens or even hundreds of different test methods it is nearly impossible to cope that with the modelling approach. 

This requirement of being able to attach a quality label to our analytical results, made that statistics and the statistical treatment of our data have become of a tremendous importance to us. This is reflected by the fact that in 1972 ANALYTICAL CHEMISTRY started with the publication of a section on Statistical and Mathematical Methods in Analytical Chemistry in its bi-annual reviews. Although we feel us quite confident on how to express our uncertainty (or certainty) in the produced numbers, we are less sure on how to quantify our uncertainty in produced compound names or qualitative results. 

Analytical chemistry has been helped in recent years by the ubiquity of DNA evidence. Here the measurement uncertainty is not the issue, but simply the probability that a particular electrophoretic pattern could come from someone other than the defendant. Statements such as It is 1,000,000 times more likely that the DNA found at the crime scene came from Mr. X, than came from an unrelated, white male are put to juries, and it has been shown that mostly, with good direction from the judge, the message has been understood. In the next section I explore the consequences of treating the quoted measurement result with its uncertainty as an interval containing the value of the measurand with a certain probability. 

Limit of detection (LOD) sounds like a term that is easily defined and measured. It presumably is the smallest concentration of analyte that can be determined to be actually present, even if the quantification has large uncertainty. The problem is the need to balance false positives (concluding the analyte is present, when it is not) and false negatives (concluding the analyte is absent, when it is really present). The International Union of Pure and Applied Chemistry (IUPAC) and ISO both shy away from the words limit of detection, arguing that this term implies a clearly defined cutoff above which the analyte is measured and below which it is not. The IUPAC and ISO prefer minimum detectable (true) value and minimum detectable value of the net state variable, which in analytical chemistry would become minimum detectable net concentration. Note that the LOD will depend on the matrix and therefore must be validated for any matrices likely to be encountered in the use of the method. These will, of course, be described in the method validation document. 

Measurement uncertainty is the key to understanding modern approaches to quality assurance in analytical chemistry. A proper measurement uncertainty gives a range in which the value of the measurand is considered to... 

Analytical Chemistry is a scientific discipline which develops and applies methods, instruments and strategies to obtain information on the composition and nature of matter in space and time, as well as on the value of these measurements, i.e. their uncertainty, validation and/or traceability to fundamental standards... 

In most cases in analytical chemistry one faces the situation that the contribution of uncertainties of the references to measurement uncertainty is small relative to those contributions that come from the measurement process itself. Under such... 

For most purposes in analytical chemistry an expanded uncertainty (U) should be used when reporting a result, i.e. x U. U is calculated using the following equation ... 

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