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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.

Intermediate measurement precision is measurement precision under declared intermediate precision conditions of measurement. The measurement procedure and location remain the same, measurements extend over a longer period, and specified changes can include operators, measuring systems or measurement calibration. It lies between a tightly restricted measurement repeatability study and a comparison across locations for measurement reproducibility.^[ref]

For a concrete study, one laboratory could measure the same stable reference block each working day with a differential length comparator, taking four complete placements per day. Keep the procedure fixed, record temperature and operator, and retain the day labels. The labels let the study distinguish variation between days from rapid reading-to-reading variation.

An original measurement model makes that distinction explicit:Here $D_d$ is a shared daily offset, while ${\epsilon }_{dj}$ varies between placements. Assume zero-mean independent random variables, independent also between days. A single measurement then has standard deviation $\sqrt{{\tau }^2+{\sigma }^2}$. For stipulated $\tau =0.30\mu \mathrm{m}$ and $\sigma =0.10\mu \mathrm{m}$, this is $0.316\mu \mathrm{m}$, even though within-day scatter reflects only $0.10\mu \mathrm{m}$.

For four readings from one day, the daily arithmetic mean hasAveraging four such means from independent days reduces that modelled standard deviation to $0.152\mu \mathrm{m}$. Four same-day readings do not average away their shared daily offset. The numbers illustrate the model, not measured comparator performance. A real study must estimate its components from enough days and investigate trends: deterministic instrumental drift is not automatically an independent daily offset.

Measurement precision describes agreement among repeated indications or measured values obtained under stated conditions. It is commonly characterized using a standard deviation, variance or coefficient of variation, which describe the observed spread. Measurement repeatability is precision under a particular restricted set of conditions; intermediate measurement precision and measurement reproducibility concern other specified conditions.^[ref]

For an original balance example, take three repeat readings of a reference object: $100.100$, $100.080$ and $100.120\mathrm{g}$. Their arithmetic mean and sample standard deviation areSuppose the reference object's assigned mass is $100.000\mathrm{g}$ with standard uncertainty $0.002\mathrm{g}$. The observed mean differs from that reference by $0.100\mathrm{g}$, much more than the within-series scatter. These chosen readings therefore illustrate why close repeat readings do not establish agreement with a reference. They do not determine the true systematic offset from only three trials.

Measurement accuracy and measurement trueness answer different questions from precision. A common additive offset leaves the deviations $x_j-\bar{x}$, and hence $s$, unchanged. Averaging more independent readings can reduce random uncertainty in the mean but does not by itself remove that common offset.^[ref]

A useful physical study repeatedly removes and replaces the reference object while recording load procedure, environmental conditions and elapsed time. Specify which parts of the measurement were repeated: repeated display readings alone may omit placement variation or instrumental drift. The statistic describes the stated experiment, not an unconditional property of the instrument.

Measurement repeatability is measurement precision under a declared set of repeatability conditions. The VIM's repeatability condition of measurement includes the same procedure, operators, measuring system, operating conditions and location, with repeated measurements over a short time.^[ref] The complete measurement cycle must be specified before its repeatability can be assessed.

For an original length-comparator study, one operator measures the same reference block using the same differential length comparator over a short session. Three readings without disturbing the setup happen to be $20.000,20.000,20.000\mathrm{mm}$. Their sample spread is zero. In a separate series, the operator removes and reseats the block for every trial, obtaining $19.980,20.000,20.020\mathrm{mm}$. That series givesThe two procedures repeat different parts of the experiment. The first data cannot establish the repeatability of the full remove-and-reseat procedure, nor does its zero observed spread prove an absence of readout noise or finite measurement resolution.

A repeatability experiment keeps the declared conditions stable and records each completed trial, including placement and settling when those belong to the procedure. Positioning repeatability applies this reasoning to repeated returns of a moving stage. Repeating a study over longer periods with selected changes can instead assess intermediate measurement precision; studies changing locations, operators and measuring systems concern measurement reproducibility.^[ref] Report those changes rather than describing every repeated experiment as the same repeatability test.

Measurement reproducibility is measurement precision under specified reproducibility conditions of measurement. These include changed locations, operators and measuring systems; the measurement procedures may also differ. The comparison must state what changed and what remained common.^[ref] This is a metrological use of reproducibility, concerned with agreement of measured values under declared conditions.

An original comparison sends a stable reference block to three laboratories. Each laboratory uses its own differential length comparator and operator, measures the same specified measurand, and reports three length errors relative to the common reference, in micrometres:Each laboratory has sample standard deviation $1\mu \mathrm{m}$, yet their arithmetic means differ by as much as $6\mu \mathrm{m}$. Relative to the grand mean $2/3\mu \mathrm{m}$, the total squared deviation separates into within-laboratory and between-laboratory terms:Consequently the nine chosen values have pooled sample standard deviation $\sqrt{62/8}\approx 2.78\mu \mathrm{m}$. This is a descriptive statistic for these observations, not a universal estimator prescribed by the definition of measurement reproducibility. Reporting only the three within-laboratory spreads would conceal the disagreement.

The physical comparison must also monitor transport damage, reference stability and temperature corrections. A changing reference block could imitate a laboratory difference. Measurement reproducibility alone does not establish measurement trueness: all laboratories could share the same erroneous reference value or correction. The changed apparatus and conditions belong alongside the reported statistic.

Paul Willetts is an analytical chemistry researcher associated with studies of laboratory performance and analytical sampling. The recovery-information report lists him at the MAFF Food Science Laboratory in Norwich, establishing the identity independently of unrelated authors with the same name.^[ref]

With Michael Thompson, Sharron Anderson, Paul Brereton and Roger Wood, Paul Willetts studied collaborative sampling of wheat and green coffee from bulk lots. Multiple samplers allowed the study to distinguish variation under different sampling conditions. Between-sampler variation contributed significantly for two wheat analytes; the coffee results showed significant sampling-repeatability variation without a detected significant sampling-reproducibility contribution.^[ref]

The measurement begins before material reaches the instrument. For an original illustration, two perfectly repeatable preparations might contain $10$ and $14\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$ because the collected portions differ. Repeating each instrument reading a hundred times would not make those portions identical. Measurement repeatability within a portion and measurement reproducibility across the relevant procedures therefore cannot be inferred from the same replication design.

Paul Willetts also coauthored the recovery-information guidance. Together these contributions emphasize that sample matrix, material selection, preparation loss and stated measurement uncertainty belong in the interpretation of an analytical result. They cannot all be assessed by repeatedly reading a single prepared solution.

A repeatability condition of measurement belongs to a specified set of conditions used to assess measurement repeatability. The VIM set includes a common measurement procedure, operator, measuring system, operating conditions and location, with repeated measurements of the same or similar objects over a short period.^[ref] A condition is therefore meaningful relative to the whole declared set, rather than being a property supplied by the word repeat alone.

For a physical length experiment, specify one operator, one differential length comparator, a reference block, the contact orientation, the remove-and-replace cycle, the settling rule and a short session after thermal equilibration. Keep the measurement calibration fixed during that series. Record every completed measurement, including the elapsed time and block temperature. Reading the unchanged display repeatedly and replacing the block between readings are different measurement procedures, even if the displayed numbers happen to coincide.

An original thermal calculation explains why the operating conditions matter. Suppose a metal reference block has length $L_0=100\mathrm{mm}$ at $T_0$, with stipulated constant linear thermal expansion coefficient $\alpha =12\times 10^{-6}{\mathrm{K}}^{-1}$. In the small-expansion model,A temperature rise of $2\mathrm{K}$ changes its length by $0.0024\mathrm{mm}=2.4\mu \mathrm{m}$. If the intended measurand is length at $T_0$, that change requires an appropriate correction; it should not be silently interpreted as random comparator scatter. This calculation holds other thermal effects fixed and does not model expansion of the comparator itself.

The same room and a short elapsed time do not prove that the relevant conditions were stable. Record observed deviations and assess their effect. Deliberately varying operators over several days at the same location leads to a study of intermediate measurement precision; varying locations and measuring systems leads toward measurement reproducibility.

A reproducibility condition of measurement belongs to a declared set of conditions used to assess measurement reproducibility. The VIM set includes different locations, operators and measuring systems, with replicate measurements on the same or similar objects. The systems may also use different measurement procedures; the specification should identify both changed and unchanged conditions.^[ref]

For an original physical comparison, laboratories A and B measure the same stable reference block's length at a stated reference temperature. Each laboratory uses its own operator and differential length comparator. Record the block identity, temperature observations, applied corrections, procedure version and instrument reference in each result. Measurements before and after transport help distinguish reference changes from laboratory differences.

Suppose the stipulated readings, in millimetres, areThe laboratory means are $50.001$ and $50.011\mathrm{mm}$, differing by $10\mu \mathrm{m}$. Each pair has sample standard deviation $\sqrt{2}\mu \mathrm{m}$. Small within-laboratory scatter therefore does not remove the difference between laboratory means.

Because location, operator and system changed together, this comparison alone cannot identify which caused the difference. In a chosen additive measurement model,a $10\mu \mathrm{m}$ difference could be assigned entirely to a system contribution or entirely to a location contribution, with the same predicted means. Separating those explanations needs additional comparisons that vary their combinations.

The conditions describe the experiment's scope; they are not a numerical precision result by themselves. Report the complete measurand and what remained common, including any shared measurement standard. A common reference error can affect both laboratories, so agreement under changed conditions does not by itself establish measurement trueness.