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An assigned value in proficiency testing $x_{\mathrm{pt}}$ is the benchmark attributed to the proficiency-test item for evaluation of participant results. Its origin, measurement uncertainty and relationship to the specified measurand are part of its meaning. It is not automatically a true value known without uncertainty.

The guide distinguishes assignment by formulation, a certified reference material, results from one laboratory, an expert-laboratory consensus or participant consensus. These methods provide different evidence and dependencies; a simple interlaboratory consensus value is only one possibility.^[ref]

For an original formulation example, suppose the relevant mass concentration is analyte mass divided by final solution volume:The assigned value in this stipulated complete-transfer model is $c=2.00mg/L$. If $u(m)=0.02\mathrm{mg}$ and $u(V)=0.005\mathrm{L}$ are independent standard uncertainties, first-order propagation givesso $u(c)\approx 0.0224mg/L$. Purity, incomplete transfer, stability or nonuniform mixing would require additional model terms. Formulation alone may not reproduce extraction or preparation difficulties encountered in routine samples.^[ref]

Participant consensus introduces a different dependency. If four laboratories report 100 and a fifth reports 110, their arithmetic mean is 102. The fifth laboratory's deviation from this benchmark is 8, whereas its deviation from the other four laboratories' mean is 10. In general,where ${\bar{x}}_{-i}$ is the arithmetic mean excluding participant $i$. This original identity shows participant influence on a consensus assigned value; the same result being assessed helps determine its comparator. It does not imply that every scheme should use a leave-one-out rule, but the dependence must not be mistaken for an independent reference comparison.

The provider should record how the assigned value was obtained and how its uncertainty was evaluated. A precise participant consensus can retain shared bias in an interlaboratory consensus, while an independent reference can itself have substantial uncertainty. Those are distinct limitations requiring different evidence.

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.

An interlaboratory consensus value is a value derived from results supplied by a specified group of laboratories to represent their common location for a stated measurand. It can serve as an assigned value in proficiency testing, but consensus and independent reference assignment are different ways of establishing that benchmark. The procedure must specify the participating results, estimator and associated measurement uncertainty.^[ref]

For an original example, three laboratories report $9.90$, $10.00$ and $10.10$ in the same units. Their arithmetic mean is $10.00$ and their sample standard deviation is $0.10$. Under a model of independent, equally distributed, unbiased laboratory errors, the estimated standard uncertainty of this mean is $0.10/\sqrt{3}\approx 0.0577$. This calculation does not include an unrecognized systematic error common to all three laboratories.

Choosing a location estimator is a substantive decision. For stipulated results $100.0$, $100.2$, $100.4$ and $105.0$, the arithmetic mean is $101.4$, whereas the median is $100.3$. Robust statistics can reduce the influence of an isolated extreme result, but cannot decide from these four numbers whether that result is erroneous or represents a different measurement method or material condition. The guide discusses robust approaches while distinguishing consensus assessment from fitness-for-purpose criteria.^[ref]

When laboratories supply valid, mutually uncorrelated standard uncertainties $u_i$ for unbiased estimates of the same quantity, an inverse-variance weighted mean usesThe last equality belongs to that model. Shared references, method-specific effects or underestimated $u_i$ can invalidate its interpretation. A laboratory reporting a small uncertainty should not receive overwhelming influence merely because that number was submitted.

An interlaboratory consensus value therefore summarizes a specified collection of evidence. It is not automatically the true value, a certified reference material value, or an independent test of those same laboratories. Shared bias in an interlaboratory consensus and the influence of participants on their own benchmark must be considered before interpreting a small deviation as evidence of accuracy.

Shared bias in an interlaboratory consensus occurs when a common systematic error shifts several laboratories' results together. Their interlaboratory consensus value can then be highly reproducible while displaced from an independent reference. Shared calibration standards, a common correction or the same inadequately modeled measurement step can create such dependence. The GUM explicitly warns that using the same instrument, standard or reference datum can correlate input quantities.^[ref]

A simple original model iswhere $\theta$ is the target quantity value, $b$ a common fixed offset and ${\epsilon }_i$ a laboratory-specific deviation. The arithmetic mean is $\bar{x}=\theta +b+\bar{\epsilon }$. Increasing the number of independent laboratories reduces the fluctuations in $\bar{\epsilon }$ but leaves $b$ in place.

The obstacle is also one of identification. For any constant $c$, replacing $(\theta ,b)$ with $(\theta +c,b-c)$ leaves all predicted results unchanged. Pairwise differences $x_i-x_j$ cancel both terms. Thus the comparison's internal agreement cannot determine the absolute common offset without additional information.

To represent residual common-reference uncertainty, use an uncertain zero-centered quantity $B$ with standard uncertainty $u_B$, independent of mutually independent laboratory errors of variance ${\sigma }^2$. ThenThis is a stated uncertainty model, distinct from asserting that an unknown fixed bias has been observed to vary randomly. The common contribution is counted once in the mean's uncertainty; it is not divided by the number of laboratories.

For stipulated $u_B=0.50$, $\sigma =0.20$ and $n=25$, treating everything as independent would retain only $0.20/5=0.04$. The stated correlated model instead gives $u(\bar{x})=\sqrt{0.25+0.0016}\approx 0.502$, in the same units as the measurement. The appropriate covariance terms prevent the implausible conclusion that enough copies of a shared reference can remove its uncertainty.^[ref]

An independently characterized certified reference material, a different measurement principle or an independently calibrated reference can help test the suspected common shift. Independence must itself be checked: a nominally separate reference derived from the same calibration chain may retain the same dependency. Recognized biases should be corrected where appropriate, with the correction's uncertainty retained.