The Eurachem Guide on “Selection, Use and Interpretation of Proficiency Testing (PT) Schemes” [1] recommends participants to consider the statistical approach used by the PT provider when selecting a PT scheme. This leaflet is intended to help participants in quantitative PT schemes to better understand the statistical parameters that describe the data distribution in the PT report. The PT report should also provide information on how the assigned value (xpt), the corresponding uncertainty (u (xpt)) and the standard deviation for proficiency assessment (σpt) were obtained [2].&nbsp;Summary statistics reported in PT schemes typically describe two features of a data set or of an underlying normal distribution of technically valid results. One feature is the location, usually described by some kind of average. The second is the dispersion, or spread of the data. A further important summary statistic is the (standard) uncertainty associated with the location, which can help to determine whether the chosen location estimator differs from (for example) an external reference value or from individual reported results. The different statistics used for these purposes are summarised below.&nbsp;<h4>Location of the results reported by participants&nbsp;</h4>An estimated location is usually reported even if it is not used as the assigned value. ISO 13528 [3] describes different ways to estimate the location using the arithmetic mean or median, or applying sophisticated robust statistical methods (Table 1).&nbsp;<h5>Key points to note:&nbsp;</h5><ul><li>When data sets contain outliers or when symmetry of the data set cannot be verified, ISO 13528 strongly recommends to use robust estimators.&nbsp;</li><li>When using the arithmetic mean, the PT provider would normally have checked the data set and removed any outliers.&nbsp;</li><li>All estimates of location can be unreliable for data sets with a small number of results.&nbsp;</li><li>A significant difference between the estimated location and a reference value may indicate a bias of the analytical methods (maybe just one, some or for all methods) that have been used by the participants.&nbsp;</li><li>If the participants used different analytical methods, the PT provider might report different estimated locations for each of these methods.&nbsp;</li></ul><h4>Dispersion of results reported by participants&nbsp;</h4>The standard deviation is an estimate of dispersion of a data set. There are various possibilities to estimate the despersion of data including MADe, nIQR, Algorithm A, Qn or Q method (Table 1). Often, they are normalised to allow direct comparability to the standard deviation of a normally distributed data set.&nbsp;<h5>Key points to note:&nbsp;</h5><ul><li>The dispersion is expressed in the same units as the measurand or reported as a percentage.&nbsp;</li><li>When estimating the classical standard deviation, the PT provider would normally have checked the data set and removed any outliers.&nbsp;</li><li>All estimates of dispersion can be unreliable for data sets with a small number of results.</li></ul><img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Table_1_Pros_and_cons_of_the_various_statistical_approaches_89d477c289.jpg" alt="Eurachem: Table 1 - Pros &amp; cons of the various statistical approaches" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Table_1_Pros_and_cons_of_the_various_statistical_approaches_89d477c289.jpg 245w," sizes="100vw" width="1600" height="911"><h4>Standard uncertainty of the location&nbsp;</h4>The standard uncertainty of the location is a measure of the reliability of the mean that can be important for participants.&nbsp;<h5>Key points to note:&nbsp;</h5><ul><li>The standard uncertainty of the arithmetic mean is calculated as:<ul><li>&nbsp;<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Snimek_obrazovky_2026_06_04_195552_9d4102aaef.png" alt="" width="226" height="70"></li><li>where s is the classical standard deviation, and p the number of reported results.&nbsp;</li></ul></li><li>For other estimators of the mean ISO 13528 suggests to use an additional (conservative) multiplication factor set to 1.25, hence:<ul><li><img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Snimek_obrazovky_2026_06_04_195606_d264be5dd8.png" alt="" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Snimek_obrazovky_2026_06_04_195606_d264be5dd8.png 245w," sizes="100vw" width="301" height="49"></li><li>where s* is the robust standard deviation from MADe, nIQR, Algorithm A, Qn or Q method, and p the number of reported results.</li></ul></li></ul>

Understanding PT statistics

This leaflet is intended to help participants in quantitative proficiency testing (PT) schemes to better understand the performance assessment made by the PT provider [1-4].<h3>Performance assessment parameters&nbsp;</h3><h4>Assigned value&nbsp;</h4>In order to assess individual performances, the results reported by participants are compared to the value assigned by the PT provider (xpt). ISO 13528 [1] suggests five different ways to obtain xpt (Figure 1). In this context, the design of the PT scheme must reflect the objectives of the scheme, comparing results either to a predetermined xpt (independent from the participant results), or to a value derived from the reported results. The PT provider is responsible for defining xpt , taking into account the advantages and disadvantages of the various possibilities when establishing metrological traceability or estimating the uncertainty of the assigned value, u(xpt).<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Figure_1_e5ef5d1f9c.jpg" alt="Eurachem - Figure 1 Options for obtaining the assigned value, Xpt" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Figure_1_e5ef5d1f9c.jpg 245w," sizes="100vw" width="640" height="382"><h4>Uncertainty of the assigned value&nbsp;</h4>The uncertainty of the assigned value u(xpt) can be estimated in at least five different ways [1], each corresponding to the value assignment strategy illustrated in Figure 1. The different uncertainty evaluation methods are listed in Figure 2. This uncertainty can be reported as a standard uncertainty (u (xpt)), or as an expanded uncertainty U (xpt) with a coverage factor k, where U (xpt) = k . u (xpt). The choice of k will impact the level of confidence (e.g. approximately 95 % for k = 2).<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Figure_2_f41ebc0c61.jpg" alt="Eurachem: Figure 2 Options for obtaining the uncertainity of the assigned value, u(Xpt)" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Figure_2_f41ebc0c61.jpg 245w," sizes="100vw" width="727" height="378"><h4>Standard deviation for proficiency assessment&nbsp;</h4>Five possibilities are suggested by ISO 13528 to set the standard deviation for proficiency assessment spt (Figure 3). The chosen approach must comply with the objectives of the PT scheme.&nbsp;<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Figure_3_f09cb3969e.jpg" alt="Eurachem: Figure 3 Options for obtaining the standard deviation for proficiency assesment" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Figure_3_f09cb3969e.jpg 245w," sizes="100vw" width="638" height="355">Two approaches for performance assessments use spt as shown in Table 1.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Table_1_Scoring_for_performance_assessment_3dd03aa3fb.jpg" alt="Eurachem: Table 1 - Scoring for performance assessment." srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Table_1_Scoring_for_performance_assessment_3dd03aa3fb.jpg 245w," sizes="100vw" width="1390" height="571"><h3>Performance assessment&nbsp;</h3>All performance assessments are based on the difference between the participant’s results (xi) and the assigned value (xpt) divided by a normalisation factor (Table 1).&nbsp;<ul><li>The percent difference D% is the normalised difference expressed as a percentage of xpt , for which a prescribed maximum relative permissible error (dE% = dE / xpt) is defined by the PT provider.&nbsp;</li><li>The z score (unitless) compares the participant’s deviation from the assigned value with the standard deviation for proficiency assessment (spt). When the uncertainty of the assigned value is significant (u(xpt) &gt; 0.3 spt), the z’ score should be used instead, to include the contribution of u(xpt) in the denominator.&nbsp;</li><li>The zeta (ζ) score (unitless) states whether the laboratory’s result agrees with the assigned value within the respective uncertainty. The denominator is the combined (standard) uncertainty of the assigned value u(xpt) and the (standard) measurement uncertainty reported by the laboratory u(xi). An unsatisfactory zeta score can either be caused by an inappropriate estimation of the measured quantity value (e.g. concentration, content), or of its measurement uncertainty, or both.&nbsp;</li><li>The En score (unitless), unlike the zeta score, uses a combination of expanded uncertainties as the normalisation factor. This combination corresponds to a confidence interval of approximately 95 %. En scores are often used in metrology comparisons among calibration laboratories.</li></ul><h3>Interpretation of performance scores&nbsp;</h3>According to ISO 13528:2022 clause 9.4.2, the conventional interpretation of the z, z’ and ζ scores is as follows:&nbsp;<ul><li>A result that gives |score| ≤ 2.0 is considered to be acceptable, indicating satisfactory performance.&nbsp;</li><li>A result that gives 2.0 &lt; |score| &lt; 3.0 is considered to give a warning signal, indicating questionable performance.&nbsp;</li><li>A result that gives |score| ≥ 3.0 is considered to be unacceptable (or action signal), indicating unsatisfactory performance.&nbsp;</li></ul>Similarly, |En| &lt; 1 and |D%| &lt; dE% indicate successful (acceptable) performance.

Understanding PT performance assessment

Interlaboratory comparisons (ILCs) have been used for more than a century and many important concepts are linked to them. This leaflet addresses the basic terminology of ILCs, why some colloquial terms can be misleading or misunderstood, and the importance of harmonisation.&nbsp;An ‘ILC’ is the organisation, performance and evaluation of measurements or tests on the same or similar items by two or more laboratories in accordance with predetermined conditions [1]. ILCs have a variety of overall – and detailed – objectives, the three most common [2] being:<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Let_s_call_a_PT_scheme_a_PT_scheme_3_9993b9fb0f.jpg" alt="Eurachem: Let’s call a PT scheme a PT scheme" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Let_s_call_a_PT_scheme_a_PT_scheme_3_9993b9fb0f.jpg 245w," sizes="100vw" width="1516" height="472"><h4>Some comparisons have special names&nbsp;</h4>The evaluation of participant (laboratory, organisation or individual) performance is typically referred to as ‘proficiency testing’ (PT) or ‘external quality assessment’ [1]. When the main objective is evaluating the performance of, for example, a candidate standard method, the ILC is often called a ‘method performance study’ or a ‘collaborative study’ [2, 3]. The former is quite clear whereas wording such as “collaborative” and “cooperative” just stresses joint effort. A project aimed at producing a new certified reference material may involve several laboratories conducting analyses on agreed properties [4]. Not surprisingly, this work is sometimes labelled as a ‘material certification study’. Special ILCs used to demonstrate measurement capabilities of National Metrology Institutes are called ‘key comparisons’, ‘supplementary comparisons’, and ‘pilot studies’ [5].&nbsp;<h4>Some terms can be confusing&nbsp;</h4>Other terms for ILCs, including ‘ring test’, ‘round robin’ and ‘circle analysis’, are common in the literature. They have, however, been used for different objectives and different designs and may be ambiguous or understood differently by laboratory staff. The use of these terms may, for example, imply a specific way of distributing the ILC sample. ISO/IEC 17043 uses ‘sequential scheme’, for a PT where a unique item is transferred between the participants and ‘simultaneous scheme’, in which similar items from a batch are distributed simultaneously to the participants [1].&nbsp;Terms like ‘measurement audit’, ‘interlaboratory testing scheme’, ‘measurement comparison scheme’, ‘rapid performance evaluation scheme’ and ‘intercalibration’ may not correctly reflect the category of laboratory involved, or the type of work participants do during the ILC.&nbsp;When in 1994 the IUPAC defined and described three major types of ‘interlaboratory studies’, the word ‘study’ was preferred to synonyms such as ‘trial’, ‘exercise’, ‘test’, ‘evaluation’ or ‘check’ [2].<h4>Let’s try to harmonise&nbsp;</h4>Many laboratory staff are unaware of official terms related to ILCs but recognise the acronym PT and words like ‘ring test’. Ideally, we would use a common scientific language, but harmonisation is time consuming. Terms appear and disappear and definitions change. The same term can be defined differently, even in different international standards. Lack of standards and guidelines in local languages can cause confusion and contribute to spreading of less appropriate terms.&nbsp;<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Let_s_call_a_PT_scheme_a_PT_scheme_2_820043ce8b.jpg" alt="Eurachem: Let’s call a PT scheme a PT scheme" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Let_s_call_a_PT_scheme_a_PT_scheme_2_820043ce8b.jpg 234w," sizes="100vw" width="1006" height="671">Much confusion can be avoided by clear reference to relevant standards and sectoral guides. ISO/ IEC 17043 [1] and ISO 13528 [6] contain many important concepts related to PT schemes and other ILCs. Some of these are also incorporated into ISO/IEC 17025 [7]. Additional useful, and free, tools are the Eurachem PT Guide [8] and the ISO online browsing platform [9].&nbsp;In writing guidance and instructions, remember that the term ‘interlaboratory comparison’ has a broad meaning and can be used for all cases described above. Sometimes this is clear enough for the reader. In other cases, use acknowledged terms that reflect the detailed objective of the ILC. Let’s call a PT scheme a PT scheme!

Let’s call a PT scheme a PT scheme!

The international standard ISO/IEC 17025 [1] clause 7.7.2 with regards to ensuring the validity of results, requires a laboratory to participate in proficiency testing (PT) and/or to participate in interlaboratory comparisons (ILCs) other than PT. However, no guidance as to what these other ILCs might be, or indeed how they might compare in relation to PT, is provided. This leaflet aims to outline other ILCs available, pointing out some of the limitations as compared to PT.&nbsp;There are three major types of ILCs in which a group of laboratories analyses identical portions from a homogeneous, stable test sample, with each type being characterized by its intended purpose [2,3]:<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Interlaboratory_comparisons_other_than_proficiency_testing_2_d9263807fb.jpg" alt="Eurachem: Interlaboratory comparisons other than proficiency testing" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Interlaboratory_comparisons_other_than_proficiency_testing_2_d9263807fb.jpg 245w," sizes="100vw" width="1507" height="607">A key point is that PT is an ILC that is designed to specifically evaluate the performance of participants, providing them with an infrastructure to monitor and assess the validity of their results. This is not the key purpose of the two other ILCs, and thus depending on their intended purpose they have a number of limitations that laboratories need to be aware of when using them rather than PT. Only proficiency testing should have been conducted in full compliance to the competency standard ISO/IEC 17043 [4].&nbsp;<h4>Evaluation of measurement procedure performance&nbsp;</h4>These ILCs, are designed to assess how a particular measurement procedure performs and whether it is fit for its intended purpose. These ILCs are often referred to as a ‘method performance study’ or a ‘collaborative study’ [2]. Some limitations of using such ILCs for monitoring laboratory performance as an alternative to PT are:&nbsp;<ul><li>All participants use the same measurement procedure i.e. the measurement procedure that is being validated. Unless the measurement procedure is being routinely used by the participating laboratory such an ILC will not assess the routine performance of the laboratory using their own routine measurement procedure. Nor does it enable them to compare their performance with other laboratories using alternative measurement procedures.&nbsp;</li><li>The measurement procedure is likely to be new, so participants may not have established stable procedures and quality control, so performance may not reflect routine use.&nbsp;</li><li>The report from such an ILC would not provide information on the performance of the participant, if the statistical model used makes the assumption that all laboratories perform with equal variability.</li><li>The design of the study may require the participants to assess multiple samples and/or to undertake multiple replicate analysis on the test materials. This may not be representative of the routine measurements or tests undertaken by the laboratory.&nbsp;</li><li>The conclusion of the ILC might be that the measurement procedure being assessed is not valid.&nbsp;</li></ul><img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Interlaboratory_comparisons_other_than_proficiency_testing_3_a53ecd2f5d.jpg" alt="Eurachem: Interlaboratory comparisons other than proficiency testing" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Interlaboratory_comparisons_other_than_proficiency_testing_3_a53ecd2f5d.jpg 157w," sizes="100vw" width="570" height="566"><h4>Characterisation of candidate reference materials&nbsp;</h4>These are ILCs that assign a property value to a candidate reference material, usually with a stated measurement uncertainty. These are often referred to as a ‘material certification study’ [2]. Limitations of using such ILCs as an alternative to PT are:&nbsp;<ul><li>The analysis of the candidate reference material is likely to require additional care in exercising the routine measurement procedure, such as substantially more replication, and/or may require quite different reporting formats (e.g. all valid replicates instead of a mean result). Thus, such an ILC will not necessarily provide an evaluation of the performance of the laboratory based on the routine use of their measurement procedures.&nbsp;</li><li>The report from such an ILC may include the results from the participating laboratories but would not provide information on the performance of each laboratory.&nbsp;</li><li>Participating laboratories may be required to assess multiple samples and/or to undertake multiple replicate analysis on the candidate reference materials. Thus this may not be representative of the routine measurements or tests undertaken by the laboratory.&nbsp;</li></ul><h4>Other ILCs&nbsp;</h4>Some other ILCs, whilst not being conducted in full compliance of the requirements of ISO/IEC 17043, may be designed to evaluate participant performance. These would include small ILCs as defined by EA‑2/21 [5] or split sample ILCs i.e. where a portion of a single sample is sent to two or three laboratories. Whilst these ILCs are specifically designed to evaluate participant performance, they may not provide a comprehensive comparison that a PT might provide. In such cases the laboratory needs to evaluate carefully the competence of the organization managing the ILC and the suitability of the service externally provided (ISO/IEC 17025 clause 6.6).

Interlaboratory comparisons other than proficiency testing

<h4>Do you use results of chemical analyses as a basis for your decisions and judgements?</h4>Those of us working in accredited laboratories or dealing with issues concerning the quality of measurements, would like to inform you about some important changes concerning the way the results of measurements are presented. These changes make it easier for you as an end-user to make correct decisions.<h4>Nobody is perfect!</h4>Results of analyses cannot be perfect! We hope this does not come as a big surprise to you. We use the term measurement uncertainty to describe this lack of perfection.<h4>The analytical process</h4>In each step of the analytical work, from sampling to the final measurement, deviations from the true value occur and measurement conditions vary. We take measures and perform controls regularly to assure that these deviations and variations together are small enough to make sure the end result fulfils your requirements. When we don’t have full information about all of the steps, e.g. when sampling and initial sample preparation are performed by you as a customer, you can assist us by providing detailed information about how that work was performed. Our experts are ready to advise on all matters regarding sampling. Please contact the laboratory beforehand.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Important_information_to_our_customers_concerning_the_quality_of_measurements_2_d885f6b051.jpg" alt="Eurachem: The analytical process" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Important_information_to_our_customers_concerning_the_quality_of_measurements_2_d885f6b051.jpg 139w," sizes="100vw" width="562" height="630"><h4>Results should be fit-for-the-purpose</h4>The accuracy of the results must of course not be too low nor too high since this would increase the costs. It should be fit for the intended purpose. If you are unsure on what level of accuracy you need, do not hesitate to contact the laboratory.<h4>Uncertainty and limiting values</h4>Many analyses are made to assure that limiting values are not exceeded. Without information about the measurement uncertainty it may appear to be very easy to make decisions, but these decision may be incorrect, with, e.g. economical consequences when rejecting instead of accepting a product, judicial consequences when returning a verdict of guilty instead of not guilty, or medical consequences when carrying out an unnecessary treatment. There are numerous examples!<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Important_information_to_our_customers_concerning_the_quality_of_measurements_3_f0ef8edc77.jpg" alt="Eurachem: Uncertainty and limiting values" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Important_information_to_our_customers_concerning_the_quality_of_measurements_3_f0ef8edc77.jpg 245w," sizes="100vw" width="932" height="453">With a realistic measurement uncertainty the information included in the result becomes much more useful.<h4>It will be easier to compare results</h4>Most laboratories have until now chosen not to state measurement uncertainty in the test report. Instead, such information has only been given when the customer has asked for itIn the future, information about the measurement uncertainty will appear more frequently in the test report. It is also possible that you will bump into new and unfamiliar quality terms. This is due to the fact that there are new international guides and standards describing a common and partly new terminology. One of the objectives is to make it easier for you as a customer to compare test results.<h4>What could it look like?</h4>When reporting the test result we will give the normal information about what we have measured. When the results are followed by uncertainty statements, they are presented as intervals within which the true values are expected to lie with a certain level of confidence (usually 95%). In the example below the lead content is 1.65 ± 0.15 mmol·kg-1, that is between 1.50 and 1.80. The measurement uncertainty is also often reported relatively, in %.<ul><li>Total lead content (Pb): 1.65 mmol·kg-1&nbsp;</li><li>Measurement uncertainty: 0.15 mmol·kg-1 (9.1%)&nbsp;</li></ul>The stated uncertainty is an expanded measurement uncertainty (U). It was obtained by multiplying the combined standard uncertainty uc with a coverage factor k equal to 2. This corresponds approximately to a 95 % confidence interval.<h4>All’s well that ends well...</h4>The requirements for a consistent way of reporting test results are increasing. Therefore, those of us involved in measurements are eager to assure ourselves that we understand your needs. You will notice this in your contacts with us before, during and after the test assignment. We hope that you will be satisfied with the final result.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Important_information_to_our_customers_concerning_the_quality_of_measurements_4_f870b1a7b8.jpg" alt="Eurachem: All’s well that ends well..." srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Important_information_to_our_customers_concerning_the_quality_of_measurements_4_f870b1a7b8.jpg 159w," sizes="100vw" width="713" height="701">

Important information to our customers concerning the quality of measurements

<h4>Traceability in the 19th century&nbsp;</h4>Once a dairymaid bought one kilo of flour from the local shop. Next day she returned to sell one kilo of butter to the shopkeeper. He then complained that 50 grams of the kilo were missing.&nbsp;<blockquote>Oh that is odd, the dairymaid said, to get the correct weight I used the kilo of flour you sold to me yesterday to weigh the butter!&nbsp;</blockquote><h4>Traceability today&nbsp;</h4>Traceability is the ability to trace, for example, the ancestors of a person or the origin of a product. The word can be derived from the Latin tractus = drawn or the verb trahere = to draw.&nbsp;Traceability can refer to documentation (e.g. a sampling procedure), a laboratory, analyst or method. But as in ISO/IEC 17025, this leaflet deals with traceability of measurement results. That is, measurement results have to be traceable to the metrological1 references used. To be specific, we use the term metrological traceability.&nbsp;<blockquote>The current VIM2 definition of metrological traceability is: property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations each contributing to the measurement uncertainty2&nbsp;</blockquote><h4>The references&nbsp;</h4>Ideally the references should be the values of national and international standards expressed in SI units. The traceability is realised through chains of calibrations, the traceability chain. For temperature and many other physical quantities such as mass and time, the traceability is easily established.&nbsp;In addition, in chemistry the working standards are substances with defined purity, solutions of pure substances and matrix reference materials.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Metrological_Traceability_of_Analytical_Results_2_b809be57bc.jpg" alt="Douglas Hasbun: An “analyst” not knowing the traceability of his/her values for volume, time, mass, calibration solution concentration and temperature." srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Metrological_Traceability_of_Analytical_Results_2_b809be57bc.jpg 157w," sizes="100vw" width="852" height="847"><h4>Temperature example - Traceability to SI&nbsp;</h4>The temperature of a sample can be traced back through a chain of calibrations to the reference, an SI traceable value of temperature at 0 °C.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Metrological_Traceability_of_Analytical_Results_3_9933347331.jpg" alt="Douglas Hasbun: Temperature example - Traceability to SI" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Metrological_Traceability_of_Analytical_Results_3_9933347331.jpg 245w," sizes="100vw" width="926" height="432"><h4>Example – Mercury in tuna fish&nbsp;</h4>A measurement result (mass fraction) obtained for mercury in a tuna fish sample is 4.03 ± 0.11 mg/kg. The result is reported as total Hg on dry weight basis (105 ºC, 12 h determined on a separate sample portion) and the measurement uncertainty is reported with a 95 % level of confidence (coverage factor, k=2). In this case mercury was determined with a mercury analyser (cold vapour atomic spectroscopy) after a microwave digestion.&nbsp;The samples are weighed on a balance with a calibration certificate relating the weight measured to the SI unit of mass (kg).&nbsp;The acid digest is diluted in a volumetric flask where the manufacturer documents the traceability of the volume of the flask to a national standard.&nbsp;The calibration curve was prepared using a CRM (certified reference material) – a mercury standard with a certificate stating a quantity value of 0.998 ± 0.005 mg/L (k=2) and with traceability to pure mercury.&nbsp;The method is validated using an appropriate matrix CRM with a total mercury mass fraction of 1.97 ± 0.04 mg/kg (k=2). The purpose of the validation is to check the method performance.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Metrological_Traceability_of_Analytical_Results_4_1ef2bc4b97.jpg" alt="Douglas Hasbun: An “analyst” knowing the traceability of his/her values for volume, time, mass, calibration solution concentration and temperature" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Metrological_Traceability_of_Analytical_Results_4_1ef2bc4b97.jpg 119w," sizes="100vw" width="808" height="1062"><h4>How can a laboratory demonstrate metrological traceability?&nbsp;</h4>The evidence required by the laboratory to demonstrate traceability for the mercury result is shown below:&nbsp;<ol><li>concentration of the Hg solution – a certificate for the CRM solution;&nbsp;</li><li>mass of sample – calibration certificate for the balance;&nbsp;</li><li>volume of volumetric flask – calibration certificate of the manufacturer;&nbsp;</li><li>drying temperature – calibration of oven temperature;&nbsp;</li><li>digestion conditions – calibration of e.g. temperature;&nbsp;</li><li>drying time – ordinary clock or stopwatch&nbsp;</li></ol>Point 1 would need special attention to assure the quality and traceability for the calibration standard. Traceability for points 2, 3 and 6 is easily achieved with adequate uncertainty using commercial equipment.&nbsp;Points 4 and 5 need additional attention by the lab.&nbsp;The use of the matrix CRM in the method validation is vital but not part of the traceability chain, since it is not used for calibration. If this CRM is used for recovery correction it should be part of the traceability chain.&nbsp;<h4>Measurement quality&nbsp;</h4><ul><li>Method validation demonstrates that the method (set of conditions) used in a particular laboratory at a certain time was fit for purpose and all significant effects were identified.&nbsp;</li><li>Calibration of critical equipment completes the metrological traceability chains.</li><li>Measurement uncertainty is estimated from the method validation and the traceability.&nbsp;</li><li>Quality control (internal and external) assures that the measurement results (including uncertainty) are of the same quality as at the time of validation.</li></ul><h4>Conclusion</h4>The traceability of a measurement result refers to metrological traceability as defined by VIM. It relates the result to SI units or other agreed standards/references.&nbsp;Traceability is essential for comparability of results and is a requirement of ISO/IEC 17025. Traceability is easily achieved following good laboratory practice.

Metrological Traceability of Analytical Results

When test results are used to assess compliance, i.e. to decide whether specifications or regulations are met, the measurement uncertainty of the test results has to be taken into account. Assessment of compliance for cases i and v in the Figure below is clear – the measurement results including the uncertainty interval are clearly above or below the limit value. In the other cases the decision is not clear since the uncertainty interval overlaps the limit value. The Eurachem/CITAC guide [1] gives guidance on cases ii, iii and iv.&nbsp;<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Upper_control_limit_9366d8f597.jpg" alt="Eurachem: Upper control limit" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Upper_control_limit_9366d8f597.jpg 245w," sizes="100vw" width="1536" height="585"><h4>We need acceptance &amp; rejection zones&nbsp;</h4>In order to judge whether the results in cases ii, iii, and iv comply with the limit value we need a decision rule, based on the risks associated with making a wrong decision. This decision rule enables a guard band, g, to be calculated which defines an acceptance zone and a rejection zone. If the measurement value is within the acceptance zone the specifications are met and we can conclude compliance. If the measured value is in the rejection zone, we can conclude non-compliance. The intersection between these two zones is called the decision limit. A guard band is normally chosen so that for a measured value in the acceptance zone the probability of correct acceptance is more than or equal to a defined confidence value α. Note that a guard band, g = 0 can also be used. This is called simple acceptance.&nbsp;<h4>Decision rule&nbsp;</h4>A decision rule should have a well-documented method of determining the location of acceptance and rejection zones, ideally including acceptable levels of probability, P, that the value of the measurand 1) lies within the specification limit, high confidence of correct acceptance (low probability of false acceptance) or 2) lies outside the specification limit, high confidence of correct rejection (low probability of false rejection).<h4>Information needed for assessing compliance&nbsp;</h4>The following information is needed:&nbsp;<ul><li>measurand clearly specified;&nbsp;</li><li>specification stating upper or lower limit or both;&nbsp;</li><li>decision rule;&nbsp;</li><li>measured value:&nbsp;</li><li>measurement uncertainty for a measured value at the limit(s).</li></ul><h4>Example focusing on correct acceptance&nbsp;</h4><ul><li>Measurand: Mass fraction of nickel, Ni in a batch of steel delivered to a customer.&nbsp;</li><li>Uncertainty: U = 0.2 % Ni, k = 2 (95 %). Standard uncertainty, u = 0.1 % Ni. This uncertainty includes both sampling uncertainty for the batch and analytical uncertainty.&nbsp;</li><li>Specification: The specification zone is from the lower limit 16.0 % Ni to the upper limit 18.0 % Ni.&nbsp;</li><li>Decision rule High confidence of correct acceptance: The acceptance range is the mass fraction where it can be decided with a confidence level of approximately 95 % (α = 0.05) that the batch has a mass fraction above the lower limit and below the upper limit.&nbsp;</li><li>Guard band: Each guard band is calculated as 1.64u ≈ 0.17 % (rounded upward for safety) with k value 1.64 from the one-tailed upper 95 % quantile of the normal distribution.&nbsp;</li><li>Acceptance zone: 16.2 % Ni to 17.8 % Ni , after rounding to one decimal place.&nbsp;</li><li>Measured value: 16.1 % Ni</li></ul><img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Guard_bands_g_and_acceptance_and_a_rejection_zones_based_on_a_lower_and_upper_bedc4769b3.jpg" alt="Eurachem: Guard bands (g), and acceptance and a rejection zones based on a lower and upper limit and a decision rule stating high confidence of correct acceptance" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Guard_bands_g_and_acceptance_and_a_rejection_zones_based_on_a_lower_and_upper_bedc4769b3.jpg 245w," sizes="100vw" width="1091" height="447">The measured value, 16.1 % Ni, is below the lower acceptance limit of 16.2 %; that is, in the rejection zone. The batch is non-compliant.&nbsp;<blockquote>Note – if the decision rule stated simple acceptance the acceptance zone would be 16.0 % to 18.0 % and the batch would be compliant.&nbsp;</blockquote><h4>Example focusing on correct rejection&nbsp;</h4><ul><li>Measurand: Mass fraction of a banned substance in a sample.&nbsp;</li><li>Uncertainty: The relative standard uncertainty urel is 35 %.&nbsp;</li><li>Specification: Upper limit is 2 ng/g.&nbsp;</li><li>Decision rule High confidence of correct rejection: The concentration of the banned substance will be deemed to be above the limit if the probability of the value of the concentration being greater than the limit is 95 % or greater.</li><li>Guard band: The guard band g for correct rejection is 1.6 ng/g assuming a lognormal distribution (due to the high relative uncertainty – see further Guide Annex A, Case 4 [1]).&nbsp;</li><li>Acceptance limit: 3.6 ng/g&nbsp;</li><li>Measured value: 3.3 ng/g&nbsp;</li></ul><img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Guard_band_g_and_acceptance_and_a_rejection_zones_based_f0f8f140db.jpg" alt="Eurachem: Guard band (g), and acceptance and a rejection zones based on a decision rule stating high confidence of correct rejection" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Guard_band_g_and_acceptance_and_a_rejection_zones_based_f0f8f140db.jpg 245w," sizes="100vw" width="883" height="392">The measured value, 3.3 ng/g, is below the acceptance limit of 3.6 ng/g; that is, in the acceptance zone. The sample is compliant. Note that the assumption of the type of distribution is crucial. If assuming a normal distribution in this case the acceptance limit would be 3.2 ng/g and the sample would not be compliant.

Use of uncertainty in compliance

The standard uncertainty arising from random effects is often derived from repeated experiments and is quantified in terms of the standard deviation s of the measured values of the quantity. If it is the standard uncertainty arising from random effects on a single measurement that is required, then the observed standard deviation s is used without change. However, for a result which is the mean x of n measurements the standard uncertainty decreases as n increases, so that:<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Using_repeated_measurements_to_improve_the_standard_uncertainty_equation_1_19f8f07f8f.jpg" alt="Eurachem: Using repeated measurements to improve the standard uncertainty - Equation 1" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Using_repeated_measurements_to_improve_the_standard_uncertainty_equation_1_19f8f07f8f.jpg 245w," sizes="100vw" width="485" height="138">Example 1 shows how Eq (1) applies when estimating the uncertainty of a mean value, but not when considering the uncertainty of individual observations.<blockquote>Example 1 A volumetric pipette is calibrated with 12 measurements; the mean and the standard deviation are calculated. Eq. 1 applies to estimate the standard uncertainty of the mean value. However, when using the pipette to deliver one aliquot, Eq. 1 does not apply and the standard uncertainty due to random variation on this single measurement is the standard deviation s</blockquote>For Eq (1) to be valid, it is a requirement that all the measurements are independent and from a stable test sample under the same measurement conditions. The measurement conditions for all the measurements could be, for example, 1) repeatability conditions, 2) intermediate precision (within laboratory reproducibility) conditions or 3) reproducibility conditions&nbsp;It is very important to be aware that the standard uncertainty given by Eq. 1 only gives the estimated uncertainty due to random variation under the conditions of measurement under which the observations were taken, and is only strictly valid for independent observations.&nbsp;It can be hard to decide whether observations are sufficiently independent for Eq. 1 to apply, as there is no simple, general, rule. The following paragraphs therefore give examples of different circumstances to help identify circumstances when Eq. 1 can safely be used.<h3>Example where Equation (1) applies&nbsp;</h3><h4>Measurement of inhomogeneous samples&nbsp;</h4>If inhomogeneity for test samples is a major part of the uncertainty the analyst may choose to measure more test portions from each test sample in order to reduce the standard uncertainty. If all these measurements are made under repeatability conditions, i.e. the same measurement conditions following the whole procedure, including repeated random sampling from the test sample, the standard deviation of the mean, given by Eq. (1), should be used to estimate the uncertainty arising from variation under repeatability conditions.&nbsp;<h3>Examples where Equation (1) does not apply&nbsp;</h3>The following paragraphs give two examples where neither the standard deviation nor the standard deviation of the mean can be directly applied without further analysis of the data.&nbsp;<h4>Measurements taken in groups&nbsp;</h4>One example is when we have data from internal quality control from a measurement procedure that includes a calibration before analysis each day. We want to calculate the standard uncertainty of the mean value used to set the central line in the QC chart. The data consist of duplicate QC measurements performed on a stable test sample each day over a longer period of time (say, p days), giving a total of 2p observations; that is, p groups of two measurements. Because each pair of duplicate measurements has a single calibration error in common; the duplicates within the data set are not strictly independent and Eq. (1) cannot be directly used for all 2p observations. The uncertainty of the mean can most easily be calculated by taking the standard deviation of the p means for each day and dividing that standard deviation by √p . Analysis of variance can also be useful in similar cases. Similar principles apply to other kinds of grouping, including grouping by operator, instrument etc.&nbsp;<h4>Measurement when the test item or measurement system is not stable over time</h4>Another common example is time dependent data. The time dependence could be due to instrument drift or to actual change in concentration by time. In such cases the error for a given observation is partly random and in part ‘carried over’ from the previous observation. Again the errors affecting each observation are not independent because some part of the error is common to successive observations; Eq. (1) can not be used and more complex statistical techniques, that allow for correlation, must be used to process the data.&nbsp;For further guidance on the treatment of correlated data in uncertainty evaluation, see Eurolab Technical Report 1/2006: Guide to the Evaluation of Measurement Uncertainty for Quantitative Test Results, Appendix A.5

Using repeated measurements to improve the standard uncertainty

In this leaflet we discuss whether or not you should correct for an observed significant bias and the impact this may have on the measurement uncertainty (MU). How to apply the correction and how to increase the uncertainty to take account of an uncorrected bias is outside the scope of this leaflet.&nbsp;Important issues for deciding on how to treat an observed significant bias are:&nbsp;<ul><li>whether we understand the cause of the bias, and&nbsp;</li><li>whether its size can be reliably determined.&nbsp;</li></ul>Further we must decide:&nbsp;<ul><li>whether the bias is consistent for all test samples within the scope of the method and&nbsp;</li><li>whether any correction for bias should be multiplicative or additive, depending on whether the magnitude of the bias is constant or changes with the concentration level.</li></ul><img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Treatment_of_an_observed_bias_2_d221a32b8b.jpg" alt="Eurachem: Treatment of an observed bias" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Treatment_of_an_observed_bias_2_d221a32b8b.jpg 245w," sizes="100vw" width="1528" height="448"><h4>Should we correct, and should we increase the measurement uncertainty?&nbsp;</h4>The ISO Guide to the expression of uncertainty in measurement, GUM [1], assumes that “the result of a measurement has been corrected for all recognised significant systematic effects” (GUM 3.2.4). This implies that when developing a measurement method all known sources of bias should be investigated and if possible, eliminated or their effect minimised. If this cannot be achieved, then, if appropriate, a correction should be applied and the measurement uncertainty revised.&nbsp;Let’s assume we have available a standardised method or a fully developed in-house method, with a clear description of the measurand, where any known bias has been minimised during method development (e.g. the effect of interferences has been minimised or a correction is included in the method). The next step, as a part of the validation, is to reliably determine any additional bias for the concentration interval and different matrices specified within the scope of the method. On the next page we present a roadmap outlining how to handle any additional significant bias.&nbsp;Note that the observed bias in a laboratory could be due to laboratory as well as method bias. For empirical methods where the measurand is operationally defined by the method, the method bias is by definition zero, however, the laboratory bias still needs to be considered.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Treatment_of_an_observed_bias_3_5d99940abd.jpg" alt="Eurachem: Treatment of an observed bias" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Treatment_of_an_observed_bias_3_5d99940abd.jpg 62w," sizes="100vw" width="426" height="1060"><ol><li>There is no point in trying to eliminate or correct a small bias, since both elimination and correction need resources.&nbsp;</li><li>If bias is not negligible then the best approach, if possible, is to try to eliminate it by modifying the method.&nbsp;</li><li>If bias is not negligible, but eliminating it is either impossible or impractical, then we can consider correcting for bias. There are three possibilities:&nbsp;<ul><li>Correction may be required (e. g. by regulations).&nbsp;</li><li>Correction may be forbidden, in which case no correction should be made.&nbsp;</li><li>Correction may be allowed. Then we should look at two more criteria to determine whether correction is justified.&nbsp;</li></ul></li><li>If bias can be reliably determined and a correction method can be applied that is relevant for all test samples within the scope of the method we may decide to correct for bias. However, if the cause of bias is not known then correcting for bias cannot be generally recommended. If bias cannot be reliably determined then we should not correct for it. If we correct the result on the basis of an unreliable bias estimate then we may even increase the uncertainty of the results.&nbsp;</li><li>Correcting for bias is meaningful only if a useful reduction of measurement uncertainty (MU) is achieved. Correcting for the bias is only meaningful if the MU of the correction is smaller than the component of the MU arising from not applying the correction.&nbsp;</li></ol>If a significant bias is not corrected, it is difficult to give clear guidance on what action to take. For the case of recovery correction, IUPAC [2] lists some possibilities if no correction is applied:&nbsp;<ol><li>No action;&nbsp;</li><li>Report recovery separately, including the uncertainty of both the result and the recovery&nbsp;</li><li>Take the bias into account in the uncertainty estimate of the results</li></ol>These principles can be applied to other forms of bias. Further options have also been reviewed in the literature: See, for example, reference [3]

Treatment of an observed bias

Measurement results are only fit for purpose if the measurement uncertainty (MU) is reliable and has a magnitude small enough for the intended use. The target MU is the maximum admissible uncertainty defined for a specific measurement goal.&nbsp;In compliance assessment, the MU should be small enough to enable identification of deviations from compliance relevant to the interests to be protected (such as public health or industrial productivity). Too large an uncertainty would not provide the required protection, while an uncertainty that is too small could mean the use of unnecessary expensive measurements.&nbsp;The Eurachem/CITAC guide on ‘Setting and Using Target Uncertainty in Chemical Measurement’ suggests how to set upper boundaries for the uncertainty based on the intended use of the result [1].&nbsp;The impact of the MU on decisions is illustrated in a fictional scenario.&nbsp;<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Setting_Target_Measurement_Uncertainty_2_daf2cb4ec8.jpg" alt="Eurachem: Setting Target Measurement Uncertainty" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Setting_Target_Measurement_Uncertainty_2_daf2cb4ec8.jpg 150w," sizes="100vw" width="740" height="770">Mr. Reis is a farmer planning to sell oranges to a juice producer. The juice producer checks oranges for thiabendazole pesticide residues and Brix level (degrees Brix provides a measure of orange juice sweetness). The producer only accepts oranges with thiabendazole residues below 1 mg kg-1 and a Brix level above 55 °Bx, paying more if the Brix level is above 65 °Bx.&nbsp;Mr. Reis contracted Laboratory C to analyse his oranges before shipping them to the producer knowing that the customer also checks the oranges in its laboratory. Mr. Reis was very happy with the results provided by Laboratory C although the pesticide residue analyses were expensive.&nbsp;The producer accepted the oranges but decided to pay less than expected.&nbsp;After asking the juice producer, the detailed results of both laboratories were compared. This showed that although the results were metrologically compatible they supported different decisions on the oranges’ price.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Setting_Target_Measurement_Uncertainty_3_aa7c28e61a.jpg" alt="Eurachem: Setting Target Measurement Uncertainty - Laboratory C" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Setting_Target_Measurement_Uncertainty_3_aa7c28e61a.jpg 245w," sizes="100vw" width="927" height="192"><img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Setting_Target_Measurement_Uncertainty_4_4588f40881.jpg" alt="Eurachem: Setting Target Measurement Uncertainty - Juice producers Laboratory" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Setting_Target_Measurement_Uncertainty_4_4588f40881.jpg 245w," sizes="100vw" width="911" height="195">The measurement of thiabendazole residues performed by Laboratory C is associated with an extremely low uncertainty making measurements more expensive than necessary. However, the uncertainty associated with the determination of the Brix level is too large, making compliance decisions too uncertain.Measurement results are only fit for the intended use if the measurement uncertainty (MU) is smaller than a maximum acceptable value (i.e. the target MU).&nbsp;Even if the customer or the regulator does not define the target MU, the laboratory should define it to decide if the measurement is fit for the intended use. The Eurachem/CITAC guide [1] suggests the use of different indicators of the measurement quality requirement to define the target MU. Information used to define the target MU is presented from the most likely to become harmonised to the ones supported with less adequate data. The following figure presents this hierarchy of adequacy with numbers from #1 to #9.<img src="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/Eurachem_Setting_Target_Measurement_Uncertainty_01cd73bb2c.jpg" alt="Eurachem: Setting Target Measurement Uncertainty" srcset="https://storage.googleapis.com/labrulez-bucket-strapi-h3hsga3/thumbnail_Eurachem_Setting_Target_Measurement_Uncertainty_01cd73bb2c.jpg 245w," sizes="100vw" width="1600" height="900"><blockquote>Approaches to defining the target MU described in the Eurachem/CITAC Guide, where utg and Utg represent the target standard and expanded uncertainties, respectively. (the numbers in the bottom of the circles identify the sections of the Guide)</blockquote>

Setting Target Measurement Uncertainty

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Eurachem is a European network promoting international traceability of chemical measurements and good analytical practice. It provides expert guidance, supports method validation, uncertainty evaluation, proficiency testing, and facilitates discussion on technical and policy issues in analytical quality.

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