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Analytical sampling selects and collects material from a larger target for chemical measurement. It connects the material actually measured with the batch, location or time period about which a conclusion is wanted. A small, well-measured portion need not represent the larger material merely because its instrument reading is precise.

An original two-region example has90% of a batch's mass at $1\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$ and10% at $100\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$ of an analyte. The batch-average mass fraction isTaking equal masses from the two regions instead produces $50.5\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$. That sample answers a different weighted question. Probability sampling or a justified stratified sampling design can connect selection probabilities and weights to the intended target.

A sampling increment is an individual collected portion. Combining increments and reducing material to a laboratory portion can introduce further variation, so the protocol should state where, when, how much and how material was handled. Repeated readings of one prepared solution chiefly test later measurement stages.

For an original nested model, let independent collected portions have sampling variance ${\sigma }_s^2$, and repeated analyses within a portion have variance ${\sigma }_a^2$. Averaging $m$ analyses on each of $n$ independent portions givesWith stipulated ${\sigma }_s=4$, ${\sigma }_a=1$, $n=4$ and $m=3$ in compatible units, the mean's standard uncertainty is approximately2.02. Increasing laboratory replication alone cannot eliminate the sampling component. Correlated portions or shared biases require an expanded model.

A primary collaborative trial had multiple samplers collect wheat and green coffee from bulk lots. Its contrasting findings for between-sampler and within-condition variation demonstrate why analytical sampling uncertainty needs a design that actually varies the collection stage.^[ref]

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.

A sampling increment is an individual portion collected by one operation of a sampling device. One scoop, one probe withdrawal or one defined cut through a moving stream can produce an increment, provided the collection operation and its extent are specified. IUPAC uses this definition for bulk materials and large units.^[ref]

Several sampling increments may be combined into a composite sample. Their number describes collection operations; repeated instrument readings of the same prepared material do not create more sampling increments. Nor is an increment necessarily representative of the entire lot on its own: its location, time, amount and selection mechanism connect it to the analytical sampling target.

An original mass-balance example combines a0.10kilogram increment containing2milligrams per kilogram of an analyte with a0.30kilogram increment containing10milligrams per kilogram. With complete transfer and no chemical change, the composite mass fraction isThe unweighted average of the two concentrations would be6milligrams per kilogram. Equal weighting of reported increment concentrations is therefore different from physically combining unequal increment masses. Whether either result estimates the intended lot mean also depends on the collection design.

Sparse contamination supplies a second distinction. In a stipulated model where each independent increment has probability0.01of intercepting a contaminated region, $k$ increments all miss it with probability $0.99^k$. Even100such increments have a miss probability of about0.366. This is an illustrative detection model, not a universal sample-count rule; spatial dependence and changing increment size alter it.

A collection record should identify the sampling device, each increment's position or collection interval, its amount and any combining or reduction step. Different increment plans can change analytical sampling uncertainty even when the same analytical instrument is used. The collection stage must be varied to assess that uncertainty, rather than only remeasuring one final extract.

Sharron Anderson is an author of research on analytical sampling and laboratory measurement of food. The primary byline of the2002 collaborative sampling study identifies her with Michael Thompson, Paul Willetts, Paul Brereton and Roger Wood.^[ref]

The team had multiple samplers collect portions of wheat and green coffee from bulk material. Its findings separated variation under different collection conditions, showing that the variability observed for one food could not simply be assumed for the other.^[ref]

An original example illustrates the experimental logic. Repeated readings of one extract might give10.0,10.1 and9.9 concentration units, while a second independently collected portion gives14.0,14.1 and13.9. Each extract is measured consistently, but the collection-to-collection difference is much larger. A study replicating only instrument readings would miss that component of measurement uncertainty.

Sharron Anderson's documented coauthorship concerns this joint experimental investigation. The scientific lesson is to replicate the stage whose variation is at issue: additional measurements of the same material cannot substitute for independent collections when assessing analytical sampling uncertainty.