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Quoted values of measurement uncertainty (MU) are only ever estimates, being subject to their own uncertainties. This has implications for selecting a way to compare two values of MU.

The increasing trend for non-expert users to undertake analytical measurements using an expanding range of chromatographic approaches can lead to the use of unsuitable separation methods and the generation of poor-quality data. Technical Brief AMCTB No. 107 introduced liquid chromatography and guidance on selection of the appropriate separation modality. This publication aims to provide a quick and easy to use educational tool for optimizing the mode of liquid chromatographic separation. It will be of value to both expert and non-expert users across the natural, life and physical sciences.

Hand-held X-ray fluorescence spectroscopy has brought great advances in the study of cultural heritage materials, allowing fast, non-invasive and non-destructive analysis of artworks or works of art on-site, particularly in museums, conservation studios, and during archaeological excavations. This Technical Brief discusses the main advantages and limitations of the technique applied to archaeological artefacts, together with its potential to answer research questions for archaeologists and conservators.

Waxes, both natural and synthetic, are present throughout heritage collections - from archaeological and ethnographic, archival and historical, to traditional and contemporary art. Very often wax-containing objects show degradation issues: analytical chemistry, by allowing us to understand the original composition and the degradation mechanisms of these materials, provides the key to designing appropriate conservation strategies and materials for wax-containing objects in our heritage collections.

The past 30 years have seen increasing availability of methods and equipment using thermal desorption for the measurement of airborne substances. These methods offer excellent sensitivity and are well-suited to automation and, in particular, diffusive sampling, a sampling technique which is both easier to use and less obtrusive than pumped sampling. With advances in equipment, thermal desorption is being used in an increasingly wide variety of applications. The capabilities and limitations of thermal desorption equipment and measurement methods were the subject of AMC Technical Brief No. 97. This supplementary Technical Brief aims to illustrate the uses and applications of thermal desorption methods in analytical measurement.

A collaborative trial (an interlaboratory study) is reputed to be the most reliable way of validating an analytical procedure applied to a defined class of test material. The most important outcome of a trial is the collection of reproducibility standard deviations estimated at various mass fractions of the analyte. These standard deviations are good estimates of standard uncertainties to be expected when the procedure is used in proficient laboratories. However, collaborative trials are expensive to conduct, as much as ₤50k-100k per trial, depending on the number of test materials under study and the number of laboratories involved. As an outcome, the popularity of trials is declining while the need for information from them is escalating.

The accurate measurement of trace level substances in complex mixtures requires advanced instrumental techniques that generally use some form of separation prior to analysis, such as chromatography. There is an increasing trend for users that do not specialise in separation science to undertake this work. With the plethora of available liquid chromatographic techniques this can lead to the inappropriate selection of separation methods, resulting in data that is incoherent or misleading. Hence, despite the existence of comprehensive guidance for users, there remains a need to provide quick and easy to use educational tools that are applicable across the natural and physical sciences.

It has become accepted practice for laboratories to report the value of the uncertainty of each measured quantity value (i.e. measurement uncertainty, MU). Informally, the MU expresses the range of values within which the true value of the analyte concentration (i.e. the value of the measurand) is asserted to lie. It is much less widely appreciated that the estimate of MU is also not an exact or 'true' value. The quoted MU is actually only an estimate, and has its own uncertainty which also can be expressed using a confidence interval (CI) for a specified confidence level (e.g. 95%).

Many inferences from statistical methods use the assumption that experimental data form a random sample (using that word in the statistical, not the chemical or physical, sense) from a population with a normal (Gaussian) distribution of measurement errors or other variations. In most cases this assumption is not actually tested, so if it is not valid false deductions may be made from the data. This Technical Brief considers cases where the normal distribution is generally taken to be valid, discusses how likely that is to be true, and how it is possible to test whether a data sample might come from a normally distributed population.

There is now abundant evidence that we analytical chemists are tending to underestimate the uncertainty of our measurements. There are two main underlying reasons for this. One reason is technical: it is easy to overlook important contributions to uncertainty, so the models used to estimate uncertainty may be incomplete. The second reason may be psychological: there may be an unconscious selection bias in the information we use to assess uncertainty. What should we do about this missing, 'dark', uncertainty?

The determination of nitrogen as a quantitative marker for seafood fat-free protein, allowing the calculation of seafood content of seafood products, is well established, and is the official chemical enforcement method. It is also is widely used by food producers to check the specification and added water of their seafood raw materials. A "nitrogen factor" is the average nitrogen content of seafood tissues, on a fat free basis unless the fat content is low as in white fish. Most seafood is prepared by using wet processes as part of good hygienic practice (GHP). Therefore, in establishing nitrogen factors for seafood, keeping water uptake to a minimum and using good manufacturing practice (GMP) has to be taken into account.

Proficiency testing of analytical laboratories is now ubiquitous-laboratories need to participate regularly to receive accreditation. The outcome helps participants to detect unexpected sources of uncertainty. But sampling, as well as analysis per se, introduces its own uncertainty in most types of analysis. Sampling uncertainty arises partly from heterogeneity in the 'target' (the particular mass of material for which the sample is a surrogate), but also from variation in the manner in which the sample is extracted. Different samplers will do the job somewhat differently, even when following a single protocol. The potential value of proficiency tests for sampling is therefore obvious. And in recent years, feasibility studies and schemes have appeared in several application sectors. Different sectors have very different constraints on how sampling and proficiency testing can be carried out. Nevertheless, the need for general guidelines is obvious.

Surface-enhanced Raman spectroscopy (SERS) has been increasingly used in the last decade for the identification of organic colourants in works of art. 'Surface-enhancement' is the giant increase in Raman scattering intensity experienced by organic molecules adsorbed on atomically rough metallic surfaces. In the case of organic colourants, which are in general strongly luminescent under laser excitation and therefore cannot usually be identified by conventional Raman microscopy (see AMCTB no. 67), SERS yields a strong and clearly resolved spectrum, allowing for easy identification. Unlike ordinary Raman spectroscopy, SERS often requires sampling, yet the sample size is considerably smaller (from 20 to 100 micrometres) than that required for high-performance liquid chromatography (HPLC), the benchmark technique for organic colourants analysis. For this reason, SERS has seen substantial use in the analysis of works of art such as prints, drawings, paintings, and polychrome sculpture. This technical brief focuses on the practical aspects of SERS and its application to the analysis of cultural heritage material, as well as on its current limitations.

Quantitative real-time PCR (qPCR) is based on the assumption that the amplification of DNA target molecules is exponential. DNA targets may be quantified by comparing the number of amplification cycles required to achieve a predetermined signal threshold to that obtained for a calibrant. However, many factors complicate this calculation, creating uncertainties and inaccuracies. Digital PCR (dPCR) is a modification of the qPCR method that can be employed to quantify precisely defined nucleic acid targets. The technique is based on the concept of limiting dilutions, which involves the partitioning of a PCR reaction into multiple sub-reactions such that each sub-reaction either contains none or one or more DNA targets. Following thermal cycling, reactions are classified as either positive (target detected) or negative (no target detected), hence providing the basis for a digital output format. By determining the proportion of empty partitions, Poissonian statistics can be applied and the initial number of target molecules present can be estimated.

The phrase chemical metrology generates a wide variety of responses from analytical chemists and a degree of confusion. This technical brief aims to dispel the mythology of metrology, explain important aspects and demonstrate the value of metrology to chemical measurements. It is shown that the basic principles of metrology have been applied since ancient times and served well for thousands of years as the key to consistent measurements. Application of the principles to physical measurements was formalised towards the end of the 19th century to meets the needs of industrialisation and global trade. The most recent change in global adoption of metrology took place at the end of the 20th century with the decision to extend the system to analytical chemistry. The brief describes how this decision is being implemented and the progress which has been made towards an international infrastructure for chemical and more recently biological measurements.

The determination of nitrogen as a quantitative marker for meat fat-free protein and the calculation of meat content of compound foods began almost 100 years ago. It is the established official chemical method to enforce labelling declarations of meat content in food products, and also widely used by food producers to check the specification and added water of their meat raw materials. A "nitrogen factor" is the average nitrogen content of a specific cut or whole animal on a fat free basis. The AMC has been overseeing studies to determine nitrogen factors since the 1950's, and more recent government funded studies have been made to accommodate changing rearing regimes and the genetics of the animals.

Chemical analysis is undertaken to help us make decisions about particular masses of a test material. Does this shipment of peanuts fall within the permitted limit for the concentration of aflatoxins? What should I pay for this batch of tin ore? How much phosphate fertiliser should I apply to this field? Can we release today's effluent stream into the river? Is the iridium content of this geological layer higher than that of the adjacent beds? In instances like these we need information about a large amount of test material (the target), but we can only remove for analysis a much smaller amount, the sample.

Accreditation has proved effective in ensuring the quality of analytical measurements but is now increasingly being applied to primary sampling, as the first part of the measurement process. Several international standards relevant to accreditation of sampling are available, either for organisations undertaking the sampling (ISO/IEC 17025 or 17020), or for the certification of the sampler (i.e., the person who takes the samples) (ISO/IEC 17024). Achieving and demonstrating the fitness-for-purpose of chemical measurements requires a holistic approach to ensuring the quality of the sampling, sample preparation and analytical measurement. Accreditation provides the framework within which both samplers and analytical chemists can demonstrate appropriate quality.

The uncertainty factor is a new way to express measurement uncertainty. It is especially applicable when the uncertainty is large (e.g., expanded relative uncertainty20%), which occurs in some analytical methods, and also when the uncertainty includes that arising from the primary sampling of highly heterogeneous materials. The upper and lower confidence limits of the uncertainty interval are calculated by multiplying and dividing the measurement result by the uncertainty factor, rather than adding and subtracting the traditional uncertainty value.

This Technical Brief describes the evolution of hand-held X-ray fluorescence instrumentation designed for inorganic elemental analysis outside the confines of a laboratory, thereby offering the capability for in situ analysis. As well as providing an overview of the instrumentation, it aims to inform both analysts and less-technically aware users how the technique may be used for a comprehensive assessment of a complex measurement problem and enable on-site decision making.

Laser-induced breakdown spectroscopy (LIBS) is a versatile technique that provides nearly instant elemental analysis of materials, both in the laboratory and in the field. This is done by focusing a short laser pulse on the surface of the sample, or object, studied and analysing the resulting spectrum from the laser-induced plasma. LIBS has been employed in the analysis of archaeological and historical objects, monuments and works of art for assessing the qualitative, semi-quantitative and quantitative elemental content of materials such as pigments, pottery, glass, stone, metals, minerals and fossils. It is also used in robotic planetary rovers. This Technical Brief describes the basic concepts of LIBS, presents relevant aspects of instrumentation and discusses how the technique is applied in the context of cultural heritage studies.

A significance test can be performed by calculating a test statistic, such as Student's t or chi-squared, and comparing it with a critical value for the corresponding distribution. If the test statistic crosses the critical value threshold, the test is considered "significant". The critical value is chosen so that there is a low probability - often 5% (for "95% confidence") - of obtaining a significant test result by chance alone. Routine use of computers has changed this situation; software presents critical values at traditional probabilities, but now also calculates a probability, the "p-value", for the calculated value of the test statistic. A low p-value - say, under 0.05 - can be taken as a significant result in the same way as a test statistic passing the 95% critical value. This applies to a wide variety of statistical tests, so p-values now pop-up routinely in statistical software. However, their real meaning is not as simple as it seems, and the widespread use of p-values in science has recently been challenged - even banned. What does this mean for p-values in analytical science?

X-ray micro computed tomography (μCT) can reveal the internal structure of several types of objects by exploiting differences in their X-ray absorption. It can: provide information about the objects' relative composition and density without taking any samples or causing any damage; reveal invisible defects, cracks or damage; show if there are any inclusions and if the object is a single piece or is made of different parts joined together; and, uncover methods of construction and even show if repairs and additions have been made. For this reason, it has increasingly been used in archaeology and cultural heritage.

The past 30 years have seen increasing availability of methods and equipment using thermal desorption for the measurement of airborne pollutants. These methods: offer greater sensitivity than methods using solvent desorption; are more amenable to automation; and, are better suited to mass spectrometry (MS)-based detection. The greater sensitivity offered by thermal desorption means it is well suited to the analysis of samples collected through diffusive sampling with the additional benefits that this offers. This Technical Brief informs both analysts and less technically aware users of the capabilities and limitations of thermal desorption equipment and measurement methods.

Once a suitable experimental design has been used to find the most important factors affecting the outcome of an experiment, and maybe to find any significant interactions between them, we can use an optimisation method to find the best levels (values) for those factors. This Technical Brief outlines the basic principles of optimisation, and introduces some of the most commonly used approaches.