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Brian Brookman works on analytical measurement quality and proficiency testing. His official 2026 Eurachem workshop biography describes him as an independent consultant and former Chief Scientific Officer of LGC's global proficiency-testing business. It records work on training, development of testing schemes and accreditation.^[ref]

With Ian Mann, Brookman co-edited the 2021 third edition of Selection, Use and Interpretation of Proficiency Testing (PT) Schemes by Brian Brookman and Ian Mann. The editorial page lists him as chair of its working group. The guide explains how laboratories select comparisons, interpret performance and investigate questionable results.^[ref]

An original statistical example shows one reason scheme design matters. Four reported results $100,100,100,140$ have sample mean110 and sample standard deviation20. Assessing the value140 against that mean and spread gives $(140-110)/20=1.5$. If an independently justified assigned value is100 and the required assessment spread is5, the same reported value gives a proficiency-test z-score of8. The participant values have not changed; the reference and criterion have.

This small invented dataset is not a prescription to estimate a real scheme from four participants. It illustrates how an extreme result can affect a participant-derived consensus and spread. The guide discusses assigned values, standard deviation for proficiency assessment and statistical evaluation as distinct design choices. A laboratory should understand those choices before interpreting a score as a simple accuracy ranking.^[ref]

The scientific role of this work is to connect measurement accuracy, measurement uncertainty and externally defined performance criteria. A comparison can reveal a problem, but determining its cause still requires examination of the method, materials, measurement calibration and data handling.

Ian Mann is a metrology and laboratory-quality specialist credited with Brian Brookman as co-editor of the 2021 third edition of Selection, Use and Interpretation of Proficiency Testing (PT) Schemes by Brian Brookman and Ian Mann. The editorial page identifies him with SAS in Switzerland. This identifies the proficiency-testing author without attributing the careers of other people named Ian Mann to him.^[ref]

The guide connects proficiency testing with practical decisions about laboratory measurements. Its selection criteria ask whether a scheme's material, measurand, concentration range and assessment approach fit the laboratory's actual work. A comparison using an unsuitable material can fail to test the procedure for which competence is being assessed.^[ref]

An original example illustrates why interpretation needs the assessment criterion. For a participant result $x=102$, assigned value $x_{\mathrm{pt}}=100$ and standard deviation for proficiency assessment ${\sigma }_{\mathrm{pt}}=1$ in compatible units, the proficiency-test z-score isA scheme using ${\sigma }_{\mathrm{pt}}=2$ would give $z=1$ for the same result. The result and its difference from the reference did not improve; the assessment scale changed. The chosen standard deviation for proficiency assessment must therefore be read with the score.

A participant's reported standard uncertainty answers another question: how uncertain is that participant's measurement result? It is not automatically the scheme's performance criterion. The guide separates evaluation scores, assessment spread and laboratory investigation of unexpected results.^[ref] Mann's documented editorial contribution is to this shared measurement-quality guidance; no separate invention or personal experimental result is implied.

An interlaboratory comparison organizes measurements of the same or similar items by at least two laboratories under agreed conditions. Its purpose may be to compare measurement reproducibility, evaluate a measurement procedure, or assess participants through proficiency testing. The last purpose evaluates performance against criteria specified beforehand; it is one use of interlaboratory comparison, not a synonym for every such study.^[ref]

A comparison begins with its experimental design. When the aim is to compare laboratory analysis, the organizer needs evidence of reference material homogeneity and reference material stability: unequal or changing test items would otherwise be confounded with differences between laboratories. If collection is part of the measurement procedure, the design must instead include analytical sampling explicitly. In a 2002 collaborative study, several samplers collected wheat and green coffee from bulk lots. The reported between-sampler variation was significant for two wheat analytes; for coffee, a significant repeatability contribution was detected without a significant sampling-reproducibility contribution. Thus even the importance of collection differences depended on the material and analyte.^[ref]

For a common proficiency-test z-score, let laboratory $i$ report $x_i$, let the assigned value in proficiency testing be $x_{\mathrm{pt}}$, and let the standard deviation for proficiency assessment be ${\sigma }_{\mathrm{pt}}>0$. ThenThe denominator describes the scheme's assessment scale. It is not automatically the laboratory's own measurement uncertainty or the observed standard deviation of participants. The guide distinguishes this proficiency-test z-score from scores incorporating uncertainty, and discusses choosing the assessment scale to match the intended use.^[ref]

An original hypothetical example shows why the assigned value matters. Suppose three laboratories report $9.8$, $10.0$ and $10.2$ in the same units, with a stipulated assessment scale ${\sigma }_{\mathrm{pt}}=0.2$. Using their arithmetic mean as an interlaboratory consensus value gives $x_{\mathrm{pt}}=10.0$ and scores $(-1,0,1)$. An independently established assigned value of $11.0$, with the same assessment scale, instead gives $(-6,-5,-4)$. Close agreement between participants is compatible with a shared displacement from an independent reference.

The identifiability issue is visible in a simple model,where $\theta$ is the reference quantity value, $b$ is a common systematic error, and ${\epsilon }_i$ describes laboratory-specific deviations. Pairwise differences eliminate both $\theta$ and $b$. Moreover, replacing $(\theta ,b)$ by $(\theta +c,b-c)$ leaves every predicted $x_i$ unchanged. Consequently agreement alone cannot identify a common bias. Evidence from an independently characterized certified reference material or an independent measurement calibration can help resolve this ambiguity. Its own measurement uncertainty and any shared dependencies must then enter the comparison model; one should not silently interpret the simple proficiency-test z-score as a full uncertainty calculation. This is the practical importance of distinguishing measurement precision, measurement trueness and shared bias in an interlaboratory consensus.

A proficiency-test item is the material, artefact, instrument or information supplied for assessment in a proficiency testing scheme. It is the object to which a specified task and result refer; it is not itself the participant's reported result or the assigned value in proficiency testing. The primary guide's definition covers samples and physical standards as well as data or other information used for assessment.^[ref]

For a material example, the provider can prepare a batch, divide it into sealed units, and distribute one coded unit to each laboratory. The specified measurand, amount to be sampled, preparation instructions, reporting units and handling conditions belong to the comparison design. The material must support the particular measurement procedures being assessed, rather than merely have a convenient nominal concentration.

Reference material homogeneity and reference material stability protect the interpretation. An original counterexample gives two laboratories bottles whose actual mass concentrations are $8$ and $12mg/L$, while both are scored against $10mg/L$ with assessment scale $0.5mg/L$. Perfect measurement of each bottle produces proficiency-test z-scores of $-4$ and $+4$. Those discrepancies arise from unequal items, not from incorrect laboratory measurement. A perfectly stable material can still be nonuniform, and a uniform batch can still change during transport.

A simple item heterogeneity contribution to proficiency-test scores can be written in a measurement model,where ${\delta }_{j(i)}$ describes the supplied unit's deviation, $b_i$ the laboratory effect and ${\epsilon }_i$ residual variation. Observing $x_i$ alone cannot assign all of its difference from $\theta$ to $b_i$. Replicate portions from selected units and stability checks across the relevant interval supply additional evidence.

The required degree of item uniformity depends on the assessment criterion. Narrowing the standard deviation for proficiency assessment can make previously tolerable item differences significant. The guide consequently requires checking whether item homogeneity and stability remain appropriate when choosing a stricter assessment scale.^[ref]

When a single artefact is circulated sequentially, changes between visits can similarly be confounded with laboratory differences. Record the item identifier, its preparation or transport history and the actual observation conditions so the reported value refers to a reproducible task.

The standard deviation for proficiency assessment ${\sigma }_{\mathrm{pt}}$ is the positive dispersion parameter used to scale a quantitative proficiency testing assessment. In a proficiency-test z-score, it specifies how large a deviation is relative to the scheme's performance criterion. It is not necessarily the observed standard deviation of participant results, a standard error of their mean, or one participant's standard uncertainty.^[ref]

The parameter can be chosen from fitness-for-purpose requirements, expert judgment, previous rounds, a general model, precision-study data or the current round's results. The choice must match the intended assessment. The guide favors fitness-for-purpose criteria where possible because a denominator determined by each round's participant spread can change the apparent performance scale.^[ref]

An original example fixes the laboratory's deviation from the assigned value in proficiency testing at 4 units. Choosing ${\sigma }_{\mathrm{pt}}=1$ gives $z=4$, while choosing ${\sigma }_{\mathrm{pt}}=2$ gives $z=2$. The measurement did not improve when the denominator changed. This is why the criterion must be justified independently of a desire to obtain a favorable score.

The assessment scale can also depend on the quantity level. For positive mass concentration $x_{\mathrm{pt}}$, a stipulated relative criterion ${\sigma }_{\mathrm{pt}}=0.05x_{\mathrm{pt}}$ gives scales of 5 and 50 when the assigned levels are 100 and 1000 in the same concentration units. Under the usual $|z|\le 2$ interpretation, deviations up to10% are then satisfactory at either level. A constant absolute scale of 5 would instead impose a much tighter relative criterion at the higher level. Neither choice is universal; the intended measurement use decides which is meaningful.

Uncertainty of the assigned value is a separate input. The guide's criterion $u(x_{\mathrm{pt}})<0.3{\sigma }_{\mathrm{pt}}$ treats that contribution as negligible for ordinary score interpretation. Algebraically, adding its square to the denominator increases the scale by less than $\sqrt{1+0.3^2}\approx 1.044$, illustrating the size of the approximation. If the contribution is not negligible, the provider must account for it through an appropriate evaluation rather than relabel it as participant variation.^[ref]

Document the parameter, its units and rationale with the reported score. A useful assessment criterion remains interpretable across rounds and reflects the performance needed for the task, rather than merely rewarding agreement within a poorly performing group.