01Define the result before assigning uncertainty

Eurachem's uncertainty guide begins by specifying the measurand and its relationship to input quantities. For a peptide assay, that means deciding whether the result concerns concentration in a prepared solution, target peptide mass in a vial or a mass fraction on a stated basis.Eurachem/CITAC — Quantifying uncertainty in analytical measurement (opens in a new tab)

Those quantities can share measurements while needing different calculations. Converting a solution concentration into vial content introduces preparation and volume information. Expressing content on a dry basis introduces a different basis correction. An uncertainty statement should follow the actual result being reported.

02Combine contributions on a compatible basis

NIST describes combined standard uncertainty as combining standard-uncertainty contributions with covariance where appropriate. The familiar root-sum-of-squares calculation is a useful special case when contributions are appropriately expressed and independent.NIST TN 1297 — Combined standard uncertainty (opens in a new tab)

In an original simplified assay model, suppose four independent relative standard-uncertainty contributions are 1.0%, 0.5%, 0.4% and 1.5%, each with unit relative sensitivity in the multiplicative result. The combined value is the square root of 1.0² + 0.5² + 0.4² + 1.5², approximately 1.91%.

For a result of 10.00 mg, that corresponds to a combined standard uncertainty of about 0.19 mg. Adding the percentages directly would give 3.4%, which follows a different assumption and is not the independent-contribution calculation used here.

03Distinguish standard from expanded uncertainty

Expanded uncertainty U is obtained by multiplying the combined standard uncertainty by a coverage factor k. NIST explains that k = 2 corresponds to approximately 95% coverage under suitable distributional and uncertainty-estimation assumptions; it is not an unconditional identity for every measurement.NIST TN 1297 — Expanded uncertainty (opens in a new tab)

Applying k = 2 to the original example gives an expanded uncertainty of approximately 0.38 mg. The result could be written 10.00 ± 0.38 mg, with k = 2 and an explanation of the coverage basis. The plus/minus number is not a permitted manufacturing tolerance or a known correction to add to the measured value.

More printed digits do not narrow the interval. Conversely, two results with slightly different central values may be compatible within their measurement uncertainties. A comparison should consider their definitions and any shared sources of uncertainty rather than comparing rounded numbers alone.

04Make the uncertainty budget honest about its reach

Eurachem describes using validation and quality-control data to capture groups of effects and warns against double counting. A repeatability study can already include some preparation variation, while repeated injections from one preparation capture a narrower set of effects.Eurachem/CITAC — Quantifying uncertainty in analytical measurement (opens in a new tab)

A small calculated uncertainty does not compensate for an unidentified peak or an incorrect molecular assumption. Those issues need investigation, correction or an explicit limit on the claim. The budget should describe the evidence it includes, rather than absorb every possible problem into an unexplained percentage.

Finally, uncertainty for the tested sample does not automatically describe all vials in a lot. Extending the target of inference requires suitable sampling evidence. Keep that broader question separate from the calculation for one prepared sample.