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Analytical sampling uncertainty is the contribution to measurement uncertainty arising when collected material is used to infer a property of a specified sampling target. The target might be a bulk lot or a defined location and time interval. Its composition need not equal that of one convenient portion. Sampling and physical preparation therefore belong in the measurement model when the measurand concerns the larger target.^[ref]

A duplicated experiment can separate two random components. Within each target, collect two independent samples by the stated protocol, prepare them separately, and analyse each twice. For a simple model,where $i=1,2$ labels collection and $j=1,2$ labels analysis; all random terms are centered and independent except for the shared $S_i$ within a sample. The within-sample difference has variance $2{\sigma }_a^2$. The difference between the two sample means has variance $2{\sigma }_s^2+{\sigma }_a^2$. Repeating this design across targets supports estimation of both components; different target means cancel in each within-target difference.^[ref]

For original stipulated difference standard deviations2and5milligrams per kilogram, respectively,in squared concentration units. One analysis on one sample has combined standard deviation $\sqrt{13.5}\approx 3.67$milligrams per kilogram. Averaging two analyses of that same sample gives $\sqrt{11.5+2/2}\approx 3.54$; averaging one analysis from each of two independent samples gives $\sqrt{(11.5+2)/2}\approx 2.60$. More laboratory replication and more independent collection address different contributions.

A collaborative wheat-and-coffee trial varied the sampler as well as the collected material. Its contrasting reproducibility and repeatability findings show why the uncertainty depends on which collection conditions are allowed to vary.^[ref]

Duplicate sampling with one sampler and protocol does not establish absence of a shared sampling bias. Reference comparisons, alternative protocols or inter-organisational trials can test additional effects. Common preparation losses or measurement calibration errors also require covariance terms beyond the independent model.

Michael H. Ramsey is a researcher credited as chair of the working group and co-editor of the 2019 guide to measurement uncertainty arising from analytical sampling. The editorial page gives his affiliation as the University of Sussex and names fellow editors Stephen L. R. Ellison and Peter Rostron.^[ref]

The scientific problem is the difference between the collected material and the material about which a conclusion is wanted. For a measurand defined over a larger target, excellent measurement repeatability on one extract does not establish small analytical sampling uncertainty. The guide treats collection and analysis as stages of the measurement process.^[ref]

An original measurement model illustrates why replication at the right level matters:Here $\mu$ is the target mean, $S_i$ is the zero-mean deviation associated with independently collected sample $i$, and $A_{ij}$ is zero-mean analytical variation in repeat $j$. Suppose all these effects are mutually independent, with variances ${\sigma }_S^2$ and ${\sigma }_A^2$. Averaging $m$ analyses on each of $n$ collected samples givesFor stipulated variance components ${\sigma }_S^2=9$ and ${\sigma }_A^2=4$ in squared concentration units, three collections analysed twice give variance $9/3+4/6=11/3$, or standard uncertainty about $1.915$ concentration units. Six analyses of only one collection instead give variance $9+4/6=29/3$, or about $3.109$ units. Both plans use six analyses; only the first averages over independently collected material.

The calculation assumes independent collections and an appropriate model for the target; a shared systematic collection error is not removed by increasing $n$. It explains the measurement-design issue addressed by the guide without presenting these invented numbers as Ramsey's experimental observations.

Peter Rostron is a co-editor, with Michael H. Ramsey and Stephen L. R. Ellison, of the 2019 guide to measurement uncertainty arising from analytical sampling. Its editorial page identifies him with the University of Sussex. The guide connects laboratory analysis with the earlier act of collecting material.^[ref]

An illuminating experimental design question is where to place replication. Repeating an analysis of one collected sample reveals a different source of variation from collecting another sample from the target material. A nested design can distinguish the corresponding variance components. The guide also describes an unbalanced sampling-uncertainty design with two analyses of one field sample and one analysis of its field duplicate.^[ref]

An original counting example makes the design concrete. At each of ten targets, two collected samples each analysed twice require $10\times 2\times 2=40$ analytical results. Analysing the first sample twice and its field duplicate once instead requires $10\times (2+1)=30$. The design retains a within-sample analytical contrast at each target and a contrast between separately collected samples, with fewer analytical results. The information content and the appropriate analysis of variance must nevertheless follow the actual replication pattern; thirty results do not automatically have the same precision as forty.

This distinction matters when deciding whether to spend effort on another instrument reading or on another collection. Rostron's verified contribution here is editorial participation in the shared guidance, rather than sole authorship of every method it discusses. Repeated collection can reveal variability without, by itself, proving the absence of a common collection bias.

An unbalanced sampling-uncertainty design estimates collection and analytical contributions while performing different numbers of analyses on the collected samples. One useful duplicate design collects two samples independently at each target, analyses one twice and the other once. The Eurachem guide presents this three-result arrangement as a less costly alternative to analysing both samples twice.^[ref]

An original variance calculation shows why both components remain identifiable. At target $i$, letHere $j=1,2$ labels independently collected samples; only $j=1$ has analytical replicates $r=1,2$. Assume centered independent random effects, common variance components and the same analytical precision for each result. Define within-target contrastsThe target mean cancels. The first contrast also cancels the sample effect; the second compares independent collections with unequal analytical averaging. Consequently,The coefficient $3/2$ matters: one sample mean contains half the analytical variance, while the other result contains all of it. Applying the balanced-design coefficient would misallocate uncertainty.

For stipulated contrast variances $s_D^2=4$ and $s_Q^2=25$ in squared concentration units, the corresponding method-of-moments estimates areA single analysis of a single collected sample then has modeled standard uncertainty $\sqrt{11+2}\approx 3.61$ in concentration units. These are invented values illustrating the model, not measurements from the guide.

Across eight targets, this design requires sixteen collections and twenty-four analyses, compared with thirty-two analyses for two analytical replicates on each collection. The saving is in analytical runs; equal cost does not imply equal statistical precision. Repeat the nested design across targets to estimate the contrast variances. One triple of results does not reliably estimate the collection variance, and duplicate collection by one unchanged protocol does not reveal a bias shared by every sample. A negative estimated variance component signals finite-data or model issues requiring an appropriate estimation method, rather than a physically negative uncertainty.