J. Environ. Monit. 1999 1 19N † I use the word ‘uncertainty’ (u) to indicate standard uncertainty as defined in the ISO Guide to the Expression of Uncertainty of Measurement and ‘reliability’ to indicate an extended uncertainty the range in which we expect the true value to lie. Viewpoint Sampling the uncertainty that dares not speak its name ‘How reliable are these analytical results?’ This is a question that the end user of analytical data—presumably the person who is paying for it—always should and increasingly does ask. Decisions based on analysis depend not only on the actual result but on its associated reliability. Most analytical chemists respond to the ‘reliability question’ by citing precision estimates that they make during the validation of the method. A proportion of these will know that a major part of the measurement uncertainty arises because of diVerences between laboratories and give you the reproducibility precision which incorporates this extra source of variation.Perhaps some will be able to say that their estimate of reliability includes terms that allow for any bias that might be present in the analytical method. Yet even the best of these answers fails to address what the enduser is really asking. Why does this failure occur? Simply because the end-user is usually seeking information about the composition of a ‘target’ a large body of material say the soil in a field or the atmosphere in a building. In contrast the analyst’s result with its associated uncertainty uan refers to the sample the usually much smaller amount of material that is subjected to the analytical procedure.† These two things are not identical.Almost everything that is worth analysing is actually or potentially heterogeneous. Consequently any sample is likely to have a composition that is diVerent from the mean composition of the target and no two samples will have the same composition. This variation in composition even among properly collected samples is quantified as the sampling uncertainty usam. The failure accurately to inform the end-user arises because we do not normally take the sampling variations into account when we are assembling an uncertainty budget. As the squares of the uncertainties are cumulative that is utotal2=usam2+uan2 potentially serious misunderstandings could occur if the sampling uncertainty were larger than the analytical uncertainty.Nowhere is this problem likely to be greater than when we sample environmental materials contamination after all is often very uneven in both space and time so sampling precisions are correspondingly high. So how do we address this sampling uncertainty? In fact little has been done so far on the subject so we have no well established guidelines. A practical approach would be to list all of the concepts and practices relating to quality in analysis and see if they can be sensibly applied to quality in sampling. So we need to consider the following topics as potentially useful in sampling error accuracy bias trueness precision uncertainty reference materials proficiency tests collaborative trials and internal quality control. Things are simpler than this agenda suggests at first sight however.Accuracy is no more than lack of error which itself is simply the sum of the random error (characterised by precision) and any systematic error engendered by bias. Trueness is lack of bias. Uncertainty (or lack of reliability) is a measure that encompasses all types of error. Reference materials address bias collaborative trials and internal quality control mainly address aspects of precision while proficiency tests look at the accuracy of single results. It seems that we need consider only precision and bias as the fundamental concepts that might apply to sampling all the rest should follow. Basic concepts Precision in principle is easy to estimate because experimentally it requires only the ‘Two Rs’ randomness and repetition. So for sampling precision we would need to replicate the taking of samples according to a definite protocol but randomise the method in some way for each sample.For instance if the protocol required that 10 increments were collected and combined to make the aggregate sample the positions of those increments (in space or time) would have to be randomised for each sample. In practice however this might be very diYcult or costly to execute. Furthermore we cannot know exactly the true compositions of the aggregate samples we have to estimate them by analysis which adds an extra layer of error to the final result. Hence we need to use a designed experiment and employ analysis of variance to apportion the precision between sampling and analysis. Sampling bias is a more diYcult issue. Some experts on sampling even deny the validity of the concept.The basis for such a view is that if sampling is carried out correctly (that is according to the accepted protocol) it cannot be biased. (This is equivalent to regarding an analytical method as ‘empirical’ or ‘definitive’.) However it is easy to see that bias could be introduced into sampling in a number of ways for instance by systematically using an incorrect procedure or by contaminating the material with the sampling tools. And what can happen sooner or later does! Bias in analysis is sought (among other methods) by comparing the results of the candidate analytical method with the results obtained by using an independent reference method. This strategy in sampling using a reference sampling method for comparison at least seems feasible. The diYculties of the alternative setting up and using the sampling analogue of a reference material seem to be insurmountable.A useful design for studying sampling bias would be to apply both methods of to a number of diVerent targets so as to encompass within the study the typical ranges of both the concentration of the analyte and any variations in the nature of the defined target material. The paired samples could then be analysed together (so that any analytical bias cancels out) and any sampling bias appraised by a suitable statistical method. This simple idea apparently has not been exploited as yet. At the moment it seems we need to find out 20N J. Environ. Monit. 1999 1 Viewpoint Certainly the idea of replication (essential to estimate precision) and randomness (essential to avoid bias) seem at first sight to be undermined here.So can the ideas previously established for static sampling be adapted here for these commonplace situations? I believe that they can. First monitoring is no more than sampling for contiguous short time intervals. We can never really get a continuous signal any recording device will smear the signal out over a certain time interval. So there is no precision problem unique to monitoring it is simply an extreme example of sampling in time. (Normally of course we assume that the system is suYciently stable to obviate any time eVect.) So we can obtain random replicate samples in time simply by restricting our activities to a time-frame appropriate for the sampling target under consideration. Second consider the need to sample in a specific place rather than at random.Duplication could be achieved by having two parallel monitors adjacent to each other for example passive monitors on both sides of a worker’s overall collar. It seems that there is no insuperable scientific problem about extending the ideas of data quality to environmental sampling although economic and political diYculties might become apparent if we tried to carry it out. To exercise quality assurance on sampling would undoubtedly require expenditure in the first instance just as it did when it was introduced for analysis. But in the longer run the knowledge provided could bring about an overall saving by helping us make the best possible use of the available resources. We could employ an optimal apportionment of cash between the cost of sampling and the cost of analysis if we knew about their uncertainties.For instance we might find that we could obtain more information at lower cost by collecting twice as many samples and then subjecting them to a relatively crude analytical method. The political problems would arise when end-users found out just how poor sampling reliability is in some instances. They might even conclude that the whole process was not worth doing if the result is so unreliable. Fitness for purpose This article began with a question about the reliability of an analytical a particular sampler. Internal quality control in sampling seems to be considerably more promising method as we can restrict our interest to precision. Moreover there is only a small financial penalty involved in executing it. It seems that we need worry only about sampling precision under repeatability conditions.(Reproducibility precision is impossible to monitor as a matter of routine and between-run precision would be diYcult because the sampling target would tend to disappear before we could get back to it for a second try!) Therefore some simple and inexpensive strategies should suYce for an IQC procedure. Suppose for example that the sampling protocol called for the aggregation of n increments selected at random. The within-run sampling precision could be monitored by aggregating two subsets each comprising n/2 increments selected at random and analysing the two subaggregates separately. The mean of these two results would be the reported analytical result and the diVerence between the results would have a precision (standard deviation) of s=2Óssam2+san2/2.This s could be used to set up limits for a control chart with zero mean which would reflect variation in sampling and analysis jointly. However unless san>0.7ssam (which is unlikely in environmental analysis) analytical variation would make a negligible contribution to s so the chart could be regarded for practical purposes as monitoring within-run sampling precision alone. Moving targets Up to this point I have treated sampling as if sampling targets were static as if we could return to them a number of times and find them pretty well unchanged. However many environmental materials are rapidly changing in both time and space. We may be interested in the composition of something that is potentially always changing such as the composition of a river subject to sporadic contamination ‘You cannot sample the same river twice’ according to Heraclitus the famous Greek analyst from the fifth century BCE.Alternatively the sampling target may be moving in space for instance the atmosphere in the vicinity of a worker who is moving about. This broader perspective for sampling raises the diVerence (if any) between sampling and monitoring. more about bias before trying to incorporate it into sampling uncertainty. Practical methods? Having examined the basic ideas we can now consider the practical measures that might be taken in relation to sampling. The ‘Full Monty’ method for estimating sampling precisions for a particular sampling protocol would be the equivalent of a collaborative trial (method performance study).We must envisage a number of samplers visiting the target independently and collecting duplicate samples at random. After analysis of all the samples (under randomised repeatability conditions) we could estimate the sampling precisions of repeatability (within-sampler) and reproducibility (between-sampler) using a nested analysis of variance. A few such trials have been carried out in experiments involving several diVerent type of material (soils sediments crops) and for some of these have demonstrated a distinct betweensampler eVect. Collaborative trials are certainly expensive but throw interesting light on the quality of sampling in specific methods. Proficiency testing in analysis is organised by distributing samples of a homogeneous material to the participants who independently analyse the material and report the result(s) back to the organiser.The organiser then assesses the results and reports the outcome back to the participants. This provides an opportunity for the participants to address the cause of any unsuspected discrepancies in their results. Proficiency testing in sampling is at least conceivable so long as all of the participants could visit the sampling target within its period of stability. That would often be impracticable for example in the analysis of workplace atmospheres. Moreover it is clearly not feasible to send environmental-type targets to the samplers! So again a considerable use of resources would be required. Sampling proficiency tests have been carried out on an experimental basis and are certainly practicable but it is not clear whether they will prove to be cost-eVective for general use.However our experience in analysis shows that the proficiency test analogue is the only device that is capable of demonstrating an unsuspected problem in sampling by J. Environ. Monit. 1999 1 21N Viewpoint result and concludes with a diVerent but related question namely ‘How reliable do these results need to be?’ The simple answer is that the uncertainty of the result should be suYciently small so that decisions based on the result should be correct with a given high probability but no smaller than that because reliability costs money. In quantitative terms we should seek to employ sampling and analytical methods with uncertainties of a magnitude that minimises the statistical expectation of all financial losses related to the uncertainty.(Obviously sampling and analysis cost money and the smaller the uncertainty the greater the costs. There are also costs associated with providing the end user with inaccurate data and these cost will rise with the uncertainty.) This minimisation is easy to do in principle but may require help from other professionals in practice because it is diYcult to quantify both the probability and the cost of certain remote possibilities. At present for the sampling of almost anything there is a protocol regarded as best practice in that field. In contrast there is an almost total lack of quantitative information about how well these protocols perform. We have seen that most of the problems of assessing sampling uncertainty can in principle be addressed by methods similar to those used for analytical uncertainty. In practice there are often considerable diYculties because of the sheer size (and often the financial value) of the sampling target. Moreover there is an understandable lack of enthusiasm for rousing the sleeping dogs of sampling when there is a fair chance of being severely bitten. Nevertheless unless analytical chemists can address these problems we cannot give the customers what they really want. Michael Thompson Birkbeck College London UK