• Table of Content
• Foreword
• Scope
• Uncertainty
• Analytical Measurement
• The Process
• Step 1: Specification
• Step 2: Identification
• Step 3: Quantification
• Step 4: Calculation
• Reporting Uncertainty
• Appendix A: Examples
  • Example 1: Calibration Standard
  • Example 2: Standardising NaOH
  • Example 3: An Acid/Base Titration
  • Example 4: In-house Validation Studies
  • Example 5: Determ. Cadmium Release
  • Example 6: Crude Fibre in Animal Feed
  • Example 7: Lead in Water - double IDMS
• Appendix B: Definitions
• Appendix C: Analytical Proc.
• Appendix D: Analyse U Sources
• Appendix E: Statistics
• Appendix F: MU at the Limit
• Appendix G: Common Sources
• Appendix H: Bibliography

7. Step 3: Quantifying Uncertainty

7.1. Introduction

7.1.1. Having identified the uncertainty sources as explained in step 2 (chapter 6), the next step is to quantify the uncertainty arising from these sources. This can be done by

• evaluating the uncertainty arising from each individual source and then combining them as described in chapter 8. Examples a1 to a3 illustrate the use of this procedure.

or

• by determining directly the combined contribution to the uncertainty on the result from some or all of these sources using method performance data. Examples a4 to a6 represent applications of this procedure.

In practice, a combination of these is usually necessary and convenient.

7.1.2. Whichever of these approaches is used, most of the information needed to evaluate the uncertainty is likely to be already available from the results of validation studies, from QA/QC data and from other experimental work that has been carried out to check the performance of the method. However, data may not be available to evaluate the uncertainty from all of the sources and it may be necessary to carry out further work as described in sections 7.10. to 7.14.

7.2. Uncertainty Evaluation Procedure

7.2.1. The procedure used for estimating the overall uncertainty depends on the data available about the method performance. The stages involved in developing the procedure are

• reconcile the information requirements with the available data
  First, the list of uncertainty sources should be examined to see which sources of uncertainty are accounted for by the available data, whether by explicit study of the particular contribution or by implicit variation within the course of whole-method experiments. These sources should be checked against the list prepared in Step 2 and any remaining sources listed to provide an auditable record of which contributions to the uncertainty have been included.

• plan to obtain the further data required
  For sources of uncertainty not adequately covered by existing data, either seek additional information from the literature or standing data (certificates, equipmentspecifications etc.), or plan experiments to obtain the required additional data. Additional experiments may take the form of specific studies of a single contribution to uncertainty, or the usual method performance studies conducted to ensure representative variation of important factors.

7.2.2. It is important to recognise that not all of the components will make a significant contribution to the combined uncertainty; indeed, in practice it is likely that only a small number will. Unless there is a large number of them, components that are less than one third of the largest need not be evaluated in detail. A preliminary estimate of the contribution of each component or combination of components to the uncertainty should be made and those that are not significant eliminated.

7.2.3. The following sections provide guidance on the procedures to be adopted depending on the data available and on the additional information required. Section 7.3. presents requirements for the use of prior experimental study data, including validation data. Section 7.4. briefly discusses evaluation of uncertainty solely from individual sources of uncertainty. This may be necessary for all, or for very few of the sources identified, depending on the data available, and is consequently also considered in later sections. Sections 7.5. to 7.9. describe the evaluation of uncertainty in a range of circumstances. Section 7.5. applies when using closely matched reference materials. Section 7.6. covers the use of collaborative study data and 7.7. the use of in-house validation data. 7.8. describes special considerations for empirical methods and 7.9. covers ad-hoc methods. Methods for quantifying individual components of uncertainty, including experimental studies, documentary and other data, modelling, and professional judgement are covered in more detail in sections 7.10. to 7.14. Section 7.15. covers the treatment of known bias in uncertainty estimation.

7.3. Relevance of Prior Studies

7.3.1. When uncertainty estimates are based at least partly on prior studies of method performance, it is necessary to demonstrate the validity of applying prior study results. Typically, this will consist of

• Demonstration that a comparable precision to that obtained previously can be achieved.

• Demonstration that the use of the bias data obtained previously is justified, typically through determination of bias on relevant reference materials (see, for example, ISO Guide 33) [h.8], by appropriate spiking studies, or by satisfactory performance on relevant proficiency schemes or other laboratory intercomparisons

• Continued performance within statistical control as shown by regular QC sample results and the implementation of effective analytical quality assurance procedures.

7.3.2. Where the conditions above are met, and the method is operated within its scope and field of application, it is normally acceptable to apply the data from prior studies (including validation studies) directly to uncertainty estimates in the laboratory in question.

7.4. Evaluating Uncertainty by Quantification of Individual Components

7.4.1. In some cases, particularly when little or no method performance data is available, the most suitable procedure may be to evaluate each uncertainty component separately.

7.4.2. The general procedure used in combining individual components is to prepare a detailed quantitative model of the experimental procedure (cf. sections 5. and 6., especially 6.4.), assess the standard uncertainties associated with the individual input parameters, and combine them using the law of propagation of uncertainties as described in section 8.

7.4.3. In the interests of clarity, detailed guidance on the assessment of individual contributions by experimental and other means is deferred to sections 7.10. to 7.14. Examples a1 to a3 in appendix a provide detailed illustrations of the procedure. Extensive guidance on the application of this procedure is also given in the ISO Guide [h.2].

7.5. Closely Matched Certified Reference Materials

7.5.1. Measurements on certified reference materials are normally carried out as part of method validation or re-validation, effectively constituting a calibration of the whole measurement procedure against a traceable reference. Because this procedure provides information on the combined effect of many of the potential sources of uncertainty, it provides very good data for the assessment of uncertainty. Further details are given in section 7.7.4.

NOTE: ISO Guide 33 [h.8] gives a useful account of the use of reference materials in checking method performance.

7.6. Uncertainty Estimation using Prior Collaborative Method Development and Validation Study Data

7.6.1. A collaborative study carried out, for example according to AOAC/IUPAC or ISO 5725 standards, to validate a published method, is a valuable source of data to support an uncertainty estimate. The data typically include estimates of reproducibility standard deviation, s_R, for several levels of response, a linear estimate of the dependence of s_R on level of response, and may include an estimate of bias based on CRM studies. How this data can be utilised depends on the factors taken into account when the study was carried out. During the 'reconciliation' stage indicated above (section 7.2.), it is necessary to identify any sources of uncertainty that are not covered by the collaborative study data. The sources which may need particular consideration are:

• sampling. Collaborative studies rarely include a sampling step. If the method used in house involves sub-sampling, or the measurand (see Specification) is estimating a bulk property from a small sample, then the effects of sampling should be investigated and their effects included.

• pre-treatment. In most studies, samples are homogenised, and may additionally be stabilised, before distribution. It may be necessary to investigate and add the effects of the particular pre-treatment procedures applied in-house.

• method bias. Method bias is often examined prior to or during interlaboratory study, where possible by comparison with reference methods or materials. Where the bias itself, the uncertainty in the reference values used, and the precision associated with the bias check, are all small compared to s_R, no additional allowance need be made for bias uncertainty. Otherwise, it will be necessary to make additional allowances.

• variation in conditions. Laboratories participating in a study may tend towards the mean of allowed ranges of experimental conditions, resulting in an underestimate of the range of results possible within the method definition. Where such effects have been investigated and shown to be insignificant across their full permitted range, however, no further allowance is required.

• changes in sample matrix. The uncertainty arising from matrix compositions or levels of interferents outside the range covered by the study will need to be considered.

7.6.2. Each significant source of uncertainty not covered by the collaborative study data should be evaluated in the form of a standard uncertainty and combined with the reproducibility standard deviation s_R in the usual way (section 8.)

7.6.3. For methods operating within their defined scope, when the reconciliation stage shows that all the identified sources have been included in the validation study or when the contributions from any remaining sources such as those discussed in section 7.6.1. have been shown to be negligible, then the reproducibility standard deviation s_R, adjusted for concentration if necessary, may be used as the combined standard uncertainty.

7.6.4. The use of this procedure is shown in example a6 (appendix a)

7.7. Uncertainty Estimation using In-House Development and Validation Studies

7.7.1. In-house development and validation studies consist chiefly of the determination of the method performance parameters indicated in section 3.1.3. Uncertainty estimation from these parameters utilises:

• The best available estimate of overall precision

• The best available estimate(s) of overall bias and its uncertainty

• Quantification of any uncertainties associated with effects incompletely accounted for in the above overall performance studies.

Precision Study

7.7.2. The precision should be estimated as far as possible over an extended time period, and chosen to allow natural variation of all factors affecting the result. This can be obtained from

• The standard deviation of results for a typical sample analysed several times over a period of time, using different analysts and equipment where possible (the results of measurements on QC check samples can provide this information).

• The standard deviation obtained from replicate analyses performed on each of several samples.

  NOTE: Replicates should be performed at materially different times to obtain estimates of intermediate precision; within-batch replication provides estimates of repeatability only.

• From formal multi-factor experimental designs, analysed by ANOVA to provide separate variance estimates for each factor.

7.7.3. Note that precision frequently varies significantly with the level of response. For example, observed precision often increases significantly and systematically with analyte concentration. In such cases, the uncertainty estimate should be adjusted to allow for the precision applicable to the particular result. Appendix e4 gives additional guidance on handling level-dependent contributions to uncertainty.

Bias Study

7.7.4. Overall bias is best estimated by repeated analysis of a relevant CRM, using the complete measurement procedure. Where this is done, and the bias found to be insignificant, the uncertainty associated with the bias is simply the combination of the standard uncertainty on the CRM value with the standard deviation associated with the bias.

NOTE: Bias estimated in this way combines bias in laboratory performance with any bias intrinsic to the method in use. Special considerations may apply where the method in use is empirical; see section 7.8.1.

• When the reference material is only approximately representative of the test materials, additional factors should be considered, including (as appropriate) differences in composition and homogeneity; reference materials are frequently more homogeneous that test samples. Estimates based on professional judgement should be used, if necessary, to assign these uncertainties (see section 7.14.).

• Any effects following from different concentrations of analyte; for example, it is not uncommon to find that extraction losses differ between high and low levels of analyte.

7.7.5. Bias for a method under study can also be determined by comparison of the results with those of reference method. If the results show that the bias is not statistically significant, the standard uncertainty is that for the reference method (if applicable; see section 7.8.1.), combined with the standard uncertainty associated with the measured difference between methods. The latter contribution to uncertainty is given by the standard deviation term used in the significance test applied to decide whether the difference is statistically significant as explained below.

EXAMPLE

7.7.6. Overall bias can also be estimated by the addition of analyte to a previously studied material. The same considerations apply as for the study of reference materials (above). In addition, the differential behaviour of added material and material native to the sample should be considered and due allowance made. Such an allowance can be made on the basis of

• Studies of the distribution of the bias observed for a range of matrices and levels of added analyte.

• Comparison of result observed in a reference material with the recovery of added analyte in the same reference material.

• Judgement on the basis of specific materials with known extreme behaviour. For example, oyster tissue, a common marine tissue reference, is well known for a tendency to co-precipitate some elements with calcium salts on digestion, and may provide an estimate of 'worst case' recovery on which an uncertainty estimate can be based (e.g. By treating the worst case as an extreme of a rectangular or triangular distribution).

• Judgement on the basis of prior experience.

7.7.7. Bias may also be estimated by comparison of the particular method with a value determined by the method of standard additions, in which known quantities of the analyte are added to the test material, and the correct analyte concentration inferred by extrapolation. The uncertainty associated with the bias is then normally dominated by the uncertainties associated with the extrapolation, combined (where appropriate) with any significant contributions from the preparation and addition of stock solution.

NOTE: To be directly relevant, the additions should be made to the original sample, rather than a prepared extract.

7.7.8. It is a general requirement of the ISO Guide that corrections should be applied for all recognised and significant systematic effects. Where a correction is applied to allow for a significant overall bias, the uncertainty associated with the bias is estimated as paragraph 7.7.5. described in the case of insignificant bias.

7.7.9. Where the bias is significant, but is nonetheless neglected for practical purposes, additional action is necessary (see section 7.15.).

Additional Factors

7.7.10. The effects of any remaining factors should be estimated separately, either by experimental variation or by prediction from established theory. The uncertainty associated with such factors should be estimated, recorded and combined with other contributions in the normal way.

7.7.11. Where the effect of these remaining factors is demonstrated to be negligible compared to the precision of the study (i.e. statistically insignificant), it is recommended that an uncertainty contribution equal to the standard deviation associated with the relevant significance test be associated with that factor.

EXAMPLE

7.7.12. Where an effect is detected and is statistically significant, but remains sufficiently small to neglect in practice, the provisions of section 7.15. apply.

7.8. Evaluation of Uncertainty for Empirical Methods

7.8.1. An 'empirical method' is a method agreed upon for the purposes of comparative measurement within a particular field of application where the measurand characteristically depends upon the method in use. The method accordingly defines the measurand. Examples include methods for leachable metals in ceramics and dietary fibre in foodstuffs (see also section 5.2. and example a5)

7.8.2. Where such a method is in use within its defined field of application, the bias associated with the method is defined as zero. In such circumstances, bias estimation need relate only to the laboratory performance and should not additionally account for bias intrinsic to the method. This has the following implications.

7.8.3. Reference material investigations, whether to demonstrate negligible bias or to measure bias, should be conducted using reference materials certified using the particular method, or for which a value obtained with the particular method is available for comparison.

7.8.4. Where reference materials so certified are unavailable, overall control of bias is associated with the control of method parameters affecting the result; typically such factors as times, temperatures, masses, volumes etc. The uncertainty associated with these input factors must accordingly be assessed and either shown to be negligible or quantified (see example a6).

7.8.5. Empirical methods are normally subjected to collaborative studies and hence the uncertainty can be evaluated as described in section 7.6.

7.9. Evaluation of Uncertainty for ad-hoc Methods

7.9.1. Ad-hoc methods are methods established to carry out exploratory studies in the short term, or for a short run of test materials. Such methods are typically based on standard or well-established methods within the laboratory, but are adapted substantially (for example to study a different analyte) and will not generally justify formal validation studies for the particular material in question.

7.9.2. Since limited effort will be available to establish the relevant uncertainty contributions, it is necessary to rely largely on the known performance of related systems or blocks within these systems. Uncertainty estimation should accordingly be based on known performance on a related system or systems. This performance information should be supported by any study necessary to establish the relevance of the information. The following recommendations assume that such a related system is available and has been examined sufficiently to obtain a reliable uncertainty estimate, or that the method consists of blocks from other methods and that the uncertainty in these blocks has been established previously.

7.9.3. As a minimum, it is essential that an estimate of overall bias and an indication of precision be available for the method in question. Bias will ideally be measured against a reference material, but will in practice more commonly be assessed from spike recovery. The considerations of section 7.7.4. then apply, except that spike recoveries should be compared with those observed on the related system to establish the relevance of the prior studies to the ad-hoc method in question. The overall bias observed for the ad-hoc method, on the materials under test, should be comparable to that observed for the related system, within the requirements of the study.

7.9.4. A minimum precision experiment consists of a duplicate analysis. It is, however, recommended that as many replicates as practical are performed. The precision should be compared with that for the related system; the standard deviation for the ad-hoc method should be comparable.

NOTE: It recommended that the comparison be based on inspection. Statistical significance tests (e.g. an F-test) will generally be unreliable with small numbers of replicates and will tend to lead to the conclusion that there is 'no significant difference' simply because of the low power of the test.

7.9.5. Where the above conditions are met unequivocally, the uncertainty estimate for the related system may be applied directly to results obtained by the ad-hoc method, making any adjustments appropriate for concentration dependence and other known factors.

7.10. Quantification of Individual Components

7.10.1. It is nearly always necessary to consider some sources of uncertainty individually. In some cases, this is only necessary for a small number of sources; in others, particularly when little or no method performance data is available, every source may need separate study (see examples 1, 2 and 3 in appendix a for illustrations). There are several general methods for establishing individual uncertainty components:

• Experimental variation of input variables

• From standing data such as measurement and calibration certificates

• By modelling from theoretical principles

• Using judgement based on experience or informed by modelling of assumptions

These different methods are discussed briefly below.

7.11. Experimental Estimation of Individual Uncertainty Contributions

7.11.1. It is nearly always necessary to consider some sources of uncertainty individually. Often, it is possible and practical to obtain estimates of uncertainty contributions from experimental studies specific to individual parameters.

7.11.2. The standard uncertainty arising from random effects is often measured from repeatability experiments and is quantified in terms of the standard deviation of the measured values. In practice, no more than about fifteen replicates need normally be considered, unless a high precision is required.

7.11.3. Other typical experiments include:

• Study of the effect of a variation of a single parameter on the result. This is particularly appropriate in the case of continuous, controllable parameters, independent of other effects, such as time or temperature. The rate of change of the result with the change in the parameter can be obtained from the experimental data. This is then combined directly with the uncertainty in the parameter to obtain the relevant uncertainty contribution.

  NOTE: The change in parameter should be sufficient to change the result substantially compared to the precision available in the study (e.g. by five times the standard deviation of replicate measurements)

• Robustness studies, systematically examining the significance of moderate changes in parameters. This is particularly appropriate for rapid identification of significant effects, and commonly used for method optimisation. The method can be applied in the case of discrete effects, such as change of matrix, or small equipment configuration changes, which have unpredictable effects on the result. Where a factor is found to be significant, it is normally necessary to investigate further. Where insignificant, the associated uncertainty is (at least for initial estimation) that obtained from the robustness study.

• Systematic multifactor experimental designs intended to estimate factor effects and interactions. Such studies are particularly useful where a categorical variable is involved. A categorical variable is one in which the value of the variable is unrelated to the size of the effect; laboratory numbers in a study, analyst names, or sample types are examples of categorical variables. For example, the effect of changes in matrix type (within a stated method scope) could be estimated from recovery studies carried out in a replicated multiple-matrix study. An analysis of variance would then provide within- and between-matrix components of variance for observed analytical recovery. The between-matrix component of variance would provide a standard uncertainty associated with matrix variation.

7.12. Estimation based on Other Results or Data

7.12.1. It is often possible to estimate some of the standard uncertainties using whatever relevant information is available about the uncertainty on the quantity concerned. The following paragraphs suggest some sources of information.

7.12.2. Proficiency Testing (PT) schemes. A laboratory's results from participation in PT schemes can be used as a check on the evaluated uncertainty, since the uncertainty should be compatible with the spread of results obtained by that laboratory over a number of proficiency test rounds. Further, in the special case where

• the compositions of samples used in the scheme cover the full range analysed routinely

• the assigned values in each round are traceable to appropriate reference values, and

• the uncertainty on the assigned value is small compared to the observed spread of results

then the dispersion of the differences between the reported values and the assigned values obtained in repeated rounds provides a basis for a good estimate of the uncertainty arising from those parts of the measurement procedure within the scope of the scheme. For example, for a scheme operating with similar materials and analyte levels, the standard deviation of differences would give the standard uncertainty. Of course, systematic deviation from traceable assigned values and any other sources of uncertainty (such as those noted in section 7.6.1.) must also be taken into account.

7.12.3. Quality Assurance (QA) data. As noted previously it is necessary to ensure that the quality criteria set out in standard operating procedures are achieved, and that measurements on QA samples show that the criteria continue to be met. Where reference materials are used in QA checks, section 7.5. shows how the data can be used to evaluate uncertainty. Where any other stable material is used, the QA data provides an estimate of intermediate precision (Section 7.7.2.). QA data also forms a continuing check on the value quoted for the uncertainty. Clearly, the combined uncertainty arising from random effects cannot be less than the standard deviation of the QA measurements.

7.12.4. Suppliers' information. For many sources of uncertainty, calibration certificates or suppliers catalogues provide information. For example, the tolerance of volumetric glassware may be obtained from the manufacturer's catalogue or a calibration certificate relating to a particular item in advance of its use.

7.13. Modelling from Theoretical Principles

7.13.1. In many cases, well-established physical theory provides good models for effects on the result. For example, temperature effects on volumes and densities are well understood. In such cases, uncertainties can be calculated or estimated from the form of the relationship using the uncertainty propagation methods described in section 8.

7.13.2. In other circumstances, it may be necessary to use approximate theoretical models combined with experimental data. For example, where an analytical measurement depends on a timed derivatisation reaction, it may be necessary to assess uncertainties associated with timing. This might be done by simple variation of elapsed time. However, it may be better to establish an approximate rate model from brief experimental studies of the derivatisation kinetics near the concentrations of interest, and assess the uncertainty from the predicted rate of change at a given time.

7.14. Estimation based on Judgement

7.14.1. The evaluation of uncertainty is neither a routine task nor a purely mathematical one; it depends on detailed knowledge of the nature of the measurand and of the measurement method and procedure used. The quality and utility of the uncertainty quoted for the result of a measurement therefore ultimately depends on the understanding, critical analysis, and integrity of those who contribute to the assignment of its value.

7.14.2. Most distributions of data can be interpreted in the sense that it is less likely to observe data in the margins of the distribution than in the centre. The quantification of these distributions and their associated standard deviations is done through repeated measurements.

7.14.3. However, other assessments of intervals may be required in cases when repeated measurements cannot be performed or do not provide a meaningful measure of a particular uncertainty component.

7.14.4. There are numerous instances in analytical chemistry when the latter prevails, and judgement is required. For example:

• An assessment of recovery and its associated uncertainty cannot be made for every single sample. One then makes such assessment for classes of samples (e.g. grouped by type of matrix) and applies them to all samples of similar type. The degree of similarity is itself an unknown, thus this inference (from type of matrix to a specific sample) is associated with an extra element of uncertainty that has no frequentistic interpretation.

• The model of the measurement as defined by the specification of the analytical procedure is used for converting the measured quantity to the value of the measurand (analytical result). This model is - like all models in science - subject to uncertainty. It is only assumed that nature behaves according to the specific model, but this can never be known with ultimate certainty.

• The use of reference materials is highly encouraged, but there remains uncertainty regarding not only the true value, but also regarding the relevance of a particular reference material for the analysis of a specific sample. A judgement is required of the extent to which a proclaimed standard substance reasonably resembles the nature of the samples in a particular situation.

• Another source of uncertainty arises when the measurand is insufficiently defined by the procedure. Consider the determination of "permanganate oxidizable substances" that are undoubtedly different whether one analyses ground water or municipal waste water. Not only factors such as oxidation temperature, but also chemical effects such as matrix composition or interference, may have an influence on this specification.

• A common practice in analytical chemistry calls for spiking with a single substance, such as a close structural analogue or isotopomer, from which either the recovery of the respective native substance or even that of a whole class of compounds is judged. Clearly, the associated uncertainty is experimentally assessable provided one is ready to study this recovery at all concentration levels and ratios of measurands to the spike, and all "relevant" matrices. But frequently this experimentation is avoided and substituted by judgements on even that of a whole class of compounds is judged.

• the concentration dependence of recoveries of measurand,
  
  
• the concentration dependence of recoveries of spike,
  
  
• the dependence of recoveries on (sub)type of matrix,
  
  
• the identity of binding modes of native and spiked substances.

7.14.5. Judgement of this type is not based on immediate experimental results, but rather on a subjective (personal) probability, an expression which here can be used synonymously with "degree of belief", "intuitive probability" and "credibility" [h.4]. It is also assumed that a degree ofbelief is not based on a snap judgement, but on a well considered mature judgement of probability.

7.14.6. Although it is recognised that subjective probabilities vary from one person to another, and even from time to time for a single person, they are not arbitrary as they are influenced by common sense, expert knowledge, and by earlier experiments and observations.

7.14.7. This may appear to be a disadvantage, but need not lead in practice to worse estimates than those from repeated measurements. This applies particularly if the true, real-life, variability in experimental conditions cannot be simulated and the resulting variability in data thus does not give a realistic picture.

7.14.8. A typical problem of this nature arises if long-term variability needs to be assessed when no collaborative study data are available. A scientist who dismisses the option of substituting subjective probability for an actually measured one (when the latter is not available) is likely to ignore important contributions to combined uncertainty, thus being ultimately less objective than one who relies on subjective probabilities.

7.14.9. For the purpose of estimation of combined uncertainties two features of degree of belief estimations are essential:

• degree of belief is regarded as interval valued which is to say that a lower and an upper bound similar to a classical probability distribution is provided,
  
  
• the same computational rules apply in combining 'degree of belief' contributions of uncertainty to a combined uncertainty as for standard deviations derived by other methods.

7.15. Significance of Bias

7.15.1. It is a general requirement of the ISO Guide that corrections should be applied for all recognised and significant systematic effects.

7.15.2. In deciding whether a known bias can reasonably be neglected, the following approach is recommended:

i) Estimate the combined uncertainty without considering the relevant bias.

ii) Compare the bias with the combined uncertainty.

iii) Where the bias is not significant compared to the combined uncertainty, the bias may be neglected.

iv) Where the bias is significant compared to the combined uncertainty, additional action is required. Appropriate actions might:

• Eliminate or correct for the bias, making due allowance for the uncertainty of the correction.

• Report the observed bias and its uncertainty in addition to the result.

NOTE: Where a known bias is uncorrected by convention, section 7.8 (empirical methods) applies.