01Find the meaning of the plus-or-minus value

The GUM defines expanded uncertainty through a coverage factor multiplying combined standard uncertainty. It calls for the factor to be stated so the standard uncertainty can be recovered for subsequent calculations.JCGM 100:2008 — Guide to the expression of uncertainty in measurement (opens in a new tab)

A report may instead give a standard deviation of replicate readings, a confidence interval for a mean or a specification tolerance. Those are not interchangeable simply because they appear beside a plus-or-minus symbol.

Locate the definition in the report or its referenced method before dividing anything. If the type of interval is not identified, the appropriate first conclusion is that the uncertainty statement is incomplete for comparison.

02Compare two apparently different uncertainties

In an original hypothetical pair of reports, both estimate 10.0 mg. Report A gives expanded uncertainty U = 0.40 mg with k = 2. Report B gives U = 0.30 mg with k = 1.5. The displayed interval is narrower in B.

Both imply the same standard uncertainty under their stated multiplication model. Calling B more precise solely because 0.30 is smaller than 0.40 would confuse the expansion choice with the underlying uncertainty magnitude.

Conversely, equal expanded uncertainties can conceal different standard uncertainties. If two reports both give U = 0.40 mg but use k = 2 and k = 4, the implied standard uncertainties are 0.20 and 0.10 mg respectively.

03Do not infer coverage probability from k alone

The GUM relates coverage factors to the distribution and available information, including degrees of freedom. For a normal distribution, k = 2 corresponds to approximately 95.45% coverage, but that relationship is not universal.JCGM 100:2008 — Guide to the expression of uncertainty in measurement (opens in a new tab)

The invented k = 1.5 example illustrates arithmetic; it does not recommend that factor or assign its report a particular confidence claim. Read the laboratory’s stated distribution and coverage interpretation.

If an interval is asymmetric or was obtained directly from a simulated distribution, one division may not reconstruct the underlying standard uncertainty. The U = k × u model must actually apply.

Nor does dividing by k change the original measurement. It changes the scale on which uncertainty is expressed so one aspect of the statements can be compared.

04Check what each uncertainty budget covers

Even equal standard uncertainties can describe different scopes. One budget may include sampling variation while another begins with the submitted test portion. Numerical normalisation does not add a missing component.

Units and reporting bases must also agree. A relative uncertainty of 2% corresponds to 0.20 mg at 10.0 mg, but 0.40 mg at 20.0 mg. Comparing relative and absolute numbers without their associated results is misleading.

For a defensible comparison, retain the original uncertainty statements and add a clearly labelled common-basis calculation. Note differences in quantity definition, included components and coverage interpretation rather than ranking laboratories from one number.

If the purpose is to assess a difference between results, their possible correlation is a further question. Two standard uncertainties alone do not determine the uncertainty of that difference when the measurements share important inputs.