= Interlaboratory consensus value
{title2=$x_c$}
An \b[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>.<Selection, Use and Interpretation of Proficiency Testing (PT) Schemes by Brian Brookman and Ian Mann>[§7.2.2 and Annex D.2, expert-laboratory and participant-consensus assignment]{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 $0.10/\sqrt3\approx0.0577$. 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.<Selection, Use and Interpretation of Proficiency Testing (PT) Schemes by Brian Brookman and Ian Mann>[§7.1, printed p. 15, robust statistics; §7.2.3 and AnnexD, consensus versus assessment criteria]{ref}
When laboratories supply valid, mutually uncorrelated standard uncertainties $u_i$ for unbiased estimates of the same quantity, an <inverse-variance weighted mean> uses
$$
w_i=u_i^{-2},\qquad x_c=\frac{\sum_iw_ix_i}{\sum_iw_i},\qquad
u^2(x_c)=\frac1{\sum_iw_i}.
$$
The 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.
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