Measurement Uncertainty: The Number Next to the Number

A certificate that reads 98.2% looks more authoritative than one reading 98.2 ± 1.4%. It is less informative. The first number tells you what one measurement produced; the second tells you what the measurement is capable of telling you. Only the second can be compared to anything.

Quick answer

What is measurement uncertainty? A quantitative statement of the range within which the true value is expected to lie, derived from every identified source of variation in the measurement process. A 2023 study developing a certified reference material for a protein biomarker reported a certified value of 66.2 ± 8.8 µg/g — an interval of about 13 percent around the stated value, produced by a national metrology institute using two independent isotope dilution mass spectrometry techniques. That is what a careful, well-resourced, fully documented measurement looks like when it states its own limits honestly.

The implication is worth sitting with. If a metrology institute reaches ±13% on a characterised material, a bare percentage on a research-grade certificate, with no interval at all, is not a tighter measurement. It is an unstated one.

Where uncertainty comes from

It is not a single number estimated at the end. It is assembled from contributions, each quantified separately and then combined. A reference method for protein determination published in 2020 lists the work involved explicitly: the estimation of uncertainty contributions and of the combined uncertainty of the final result, alongside the use of conversion factors, were named among its principal challenges. Typical contributors for a peptide assay:

These combine in quadrature, not by addition, which has a practical consequence: the largest contributor dominates. Halving a small term barely moves the total. Finding and reducing the biggest term is the only efficient route to a tighter interval — and you cannot find it without having itemised them.

The term that gets left out

The most instructive example in this literature is an omission. A multi-laboratory study comparing quantification approaches for oxytocin found that the chromatographic assay gave the lowest variability between laboratories — and stated plainly that this coefficient of variation was calculated without counting the uncertainty associated with the purity assignment of the standard by mass balance. The number was real; the comparison it invited was not symmetric, because one method's largest uncertainty term sat outside the figure being compared.

This is the general shape of the problem. An uncertainty figure is only interpretable alongside a list of what it includes. A smaller interval with fewer terms in it is not better than a larger interval with more. It is less complete. The same study's design issue — the chromatographic method using the same bulk material as its own standard — is covered in how much quantification methods agree.

What a 13 percent interval actually permits

Take the certified value above. With ±8.8 on 66.2:

• A single result of 60 and a single result of 73 are both consistent with the certified value. Neither indicates a problem.
• Two measurements of 62 and 71 are not evidence of a difference between the two materials. They are within what the method does to one material.
• A result of 45 is outside the interval and worth investigating — which is the whole value of having the interval.

Without the interval, all four of those numbers look like findings. With it, three are noise and one is a signal. That is not a technicality; it is the difference between chasing an artefact for a week and not.

The validation metrics that feed it

Published validation work gives a sense of realistic magnitudes. A fully validated mass spectrometry method for quantifying a protein in a food matrix, via a signature peptide released by digestion, reported recoveries of 83.1–91.6% with relative standard deviation below 5.4%, and repeatability below 7.7% RSD. Note the recovery range: a method capturing 83–92% of what is present either needs a correction factor (which carries its own uncertainty) or accepts a systematic low bias. Neither option is wrong. Leaving it undeclared is.

What to do with this as a buyer

• Treat a bare number as a point estimate, not a boundary. A certificate reading 98.1% does not mean the material is not 97.2%.
• Estimate your own repeatability once. Measure the same sample six times on different days. The spread is your floor for detecting any difference, and it costs one afternoon.
• Do not treat differences smaller than that spread as real. This single rule prevents most false lot-to-lot findings — see lot-to-lot variability.
• Record the interval, not just the value. A record of 66 is less useful in six months than a record of 66 ± 9 by method X.
• Ask what an uncertainty figure includes when one is given. The excluded terms are where the information is.

Key takeaways

• A published certified reference value for a protein biomarker was 66.2 ± 8.8 µg/g — about 13 percent, from a national metrology institute using two independent techniques.
• Uncertainty is assembled from itemised contributions and combined in quadrature, so the largest term dominates the total.
• A reference method publication named the estimation of uncertainty contributions and the combined uncertainty among its explicit challenges.
• In a multi-laboratory oxytocin study, the lowest reported inter-laboratory CV was calculated without the mass balance purity uncertainty of the standard — a smaller interval with a term left out.
• An uncertainty figure is interpretable only alongside what it includes.
• With a 13 percent interval, results spanning roughly 60–73 on a value of 66 are consistent with one another, not evidence of difference.
• Measuring your own repeatability once establishes the smallest difference you can legitimately call real.

Frequently asked questions

Why does nobody state uncertainty on a research-grade certificate?

Because producing a defensible figure requires itemising and quantifying every contribution, which is a substantial undertaking — the published reference method cited here treats it as a named challenge. Absence of an interval reflects the cost of producing one, not confidence in the number.

Is 13 percent unusually wide?

It is what a national metrology institute reported for a characterised material using two independent techniques in parallel. Read it as a reference point for what rigorous looks like, not as an upper bound on what is acceptable.

How do I estimate uncertainty without doing full metrology?

You generally cannot produce a complete figure, but you can produce the most useful single component: repeatability. Measure one sample several times across days and calculate the spread. That alone tells you the smallest difference your measurements can resolve.

Does a recovery of 85 percent mean the material is 15 percent impure?

No. Recovery describes how much of the analyte the method captures, not how much is present. A method with 85 percent recovery reads low on a pure sample. It is a property of the method, which is why validation reports it separately.

Should uncertainty change what I buy?

It should change what you conclude from a certificate. The number is a point estimate from the supplier's method against their reference — the limits of which are discussed in metrological traceability. Your own repeatability, measured once, is more useful than any certificate for interpreting your own results.

Sources

• Zhu M, Li J, Chu Z, Li L, Meng B, Zhao Y, et al. Development of cancer biomarker heat shock protein 90α certified reference material using two different isotope dilution mass spectrometry techniques. Anal Bioanal Chem. 2024;416(4):913–923. DOI
• Martinez-Esteso MJ, O'Connor G, Nørgaard J, Breidbach A, Brohée M, Cubero-Leon E, et al. A reference method for determining the total allergenic protein content in a processed food: the case of milk in cookies as proof of concept. Anal Bioanal Chem. 2020;412(30):8249–8267. DOI
• Li C, Bhavaraju S, Thibeault MP, Melanson J, Blomgren A, Rundlöf T, et al. Survey of peptide quantification methods and comparison of their reproducibility: a case study using oxytocin. J Pharm Biomed Anal. 2019;166:105–112. DOI
• Yuan M, Feng C, Wang S, Zhang W, Chen M, Jiang H, Feng X. Selection of possible signature peptides for the detection of bovine lactoferrin in infant formulas by LC-MS/MS. PLoS One. 2017;12(9):e0184152. DOI

Citations retrieved via PubMed. The validation and metrology principles transfer across analytes; the specific values belong to the materials studied, which are proteins rather than short synthetic peptides.

This article describes analytical measurement only. It contains no usage instructions, no dosing information and no protocols of any kind.

For laboratory and in-vitro research use only. Not for human or veterinary use.