= Interlaboratory comparison
An \b[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.<Selection, Use and Interpretation of Proficiency Testing (PT) Schemes by Brian Brookman and Ian Mann>[§§2–3, printed pp. 3–4: scope and definitions]{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.<Collaborative trials of the sampling of two foodstuffs, wheat and green coffee by Michael Thompson and others>[Abstract: comparison of sampling reproducibility and repeatability for wheat and green coffee]{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 $\sigma_{\mathrm{pt}}>0$. Then
$$
z_i=\frac{x_i-x_{\mathrm{pt}}}{\sigma_{\mathrm{pt}}}.
$$
The 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.<Selection, Use and Interpretation of Proficiency Testing (PT) Schemes by Brian Brookman and Ian Mann>[§7.2.4, printed pp. 16–17, and §8.2.3, p. 21]{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,
$$
x_i=\theta+b+\varepsilon_i,
$$
where $\theta$ is the reference quantity value, $b$ is a common <systematic error>, and $\varepsilon_i$ 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 \b[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>.
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