Explaining Measurement Uncertainty Without Losing Trust

A customer asks whether a sensor reads 72.4 °C or 72.0 °C, and the honest answer is “both are inside what we can claim.” That sounds evasive unless the measurement uncertainty is stated clearly. Measurement uncertainty is the part of a result that engineers often leave out of datasheets, test reports and product pages, partly because it’s awkward to explain and partly because of a fear that admitting doubt looks weak. This article explains what uncertainty is, how the standard method calculates it, a worked uncertainty budget, and how to report it so that it builds trust rather than undermining it.

Key Takeaways

• The International Vocabulary of Metrology (VIM, JCGM 200:2012) defines measurement uncertainty as a non-negative parameter characterizing the dispersion of the values attributed to a measurand. It describes doubt; error is the difference from a true value, which is usually unknown.
• The GUM (JCGM 100:2008) classifies evaluations as Type A (statistical analysis of repeated observations) or Type B (other means: certificates, specifications, resolution, experience). Both produce standard uncertainties that combine the same way.
• Independent standard uncertainties combine as a root sum of squares. The expanded uncertainty U = k × u_c, and k = 2 gives about 95% coverage when the distribution is approximately normal.
• ISO/IEC 17025:2017 requires accredited laboratories to evaluate measurement uncertainty, and to state a decision rule when they report conformity with a specification.
• In experiments by van der Bles and colleagues (PNAS, 2020), communicating numeric uncertainty about facts reduced trust only slightly; the small decreases were mostly associated with verbal uncertainty statements.

The problem: a number without its doubt

A single number invites false precision. If a test report says a part measures 10.02 mm and the limit is 10.00 mm, the part looks out of spec. If the measurement’s uncertainty is ±0.03 mm, the honest conclusion is that you can’t tell from this measurement alone. Leaving out the uncertainty doesn’t remove the doubt; it hides it from the person making the decision.

The same applies to product claims. A datasheet that says “accuracy ±0.5 °C” without saying under what conditions, over what range or with what confidence leaves the engineer to guess. As we covered in how to read a sensor datasheet, an accuracy figure only means something together with its conditions.

What the standards say

Error, accuracy and uncertainty are different things

The VIM, published by the Joint Committee for Guides in Metrology (JCGM 200:2012), separates terms that everyday language mixes. Measurement error is the measured value minus a reference value. Measurement accuracy is the closeness of agreement between a measured value and a true value, and the VIM treats it as a concept, not a quantity with a number. Measurement uncertainty is the quantified parameter: it characterizes the spread of values that could reasonably be attributed to what you’re measuring.

The practical consequence: “accuracy ±0.5 °C” on a datasheet is shorthand, and what it really should communicate is an uncertainty or a maximum permissible error under stated conditions.

The GUM method

The Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100:2008) is the reference method, and NIST’s Technical Note 1297 (Taylor and Kuyatt, 1994) is a widely used shorter guide to applying it. The steps are:

1. Define the measurand and the measurement model: what you’re measuring and how the inputs combine to give the result.
2. List the sources of uncertainty: calibration of the reference, resolution, repeatability, environmental effects, drift and so on.
3. Evaluate each as a standard uncertainty. A Type A evaluation uses statistics of repeated observations, for example the standard deviation of the mean. A Type B evaluation uses other information: a calibration certificate, a manufacturer’s specification, the resolution of a display. A specification given as ±a with no other information is often treated as a rectangular distribution, whose standard uncertainty is a / √3.
4. Combine. For independent inputs with unit sensitivity, the combined standard uncertainty is the root sum of squares of the contributions. Correlated inputs and non-unit sensitivity coefficients need the GUM’s full law of propagation.
5. Expand. Multiply the combined standard uncertainty by a coverage factor k to get the expanded uncertainty U. With k = 2 and an approximately normal distribution, the interval covers about 95% of the values that could reasonably be attributed to the measurand.
6. Report the result with U, k and the approximate coverage.

What accredited labs must do

ISO/IEC 17025:2017, the general requirements for the competence of testing and calibration laboratories, requires laboratories to identify the contributions to measurement uncertainty and evaluate it. When a laboratory reports a statement of conformity with a specification, it must state the decision rule it applied, which defines how uncertainty is accounted for in a pass or fail decision. That’s the formal answer to the 10.02 mm problem above.

An uncertainty budget, worked through

Illustrative example, not a real calibration: a temperature reading of 72.4 °C from a digital thermometer, averaged from 10 readings.

Source	Information	Type	Distribution	Standard uncertainty (°C)
Calibration of the thermometer	Certificate: U = 0.2 °C, k = 2	B	Normal	0.100
Display resolution	0.1 °C, half-width 0.05 °C	B	Rectangular	0.029
Repeatability	s = 0.15 °C from 10 readings, mean used	A	Normal	0.047
Drift since calibration	Manufacturer: ±0.3 °C	B	Rectangular	0.173
Combined standard uncertainty	Root sum of squares			0.207
Expanded uncertainty	k = 2			0.41

Reported result: 72.4 °C ± 0.4 °C (k = 2, approximately 95% coverage).

Two things stand out. The largest contribution is drift, not the calibration itself, so recalibrating more often would shrink the uncertainty more than buying a finer display. And the budget makes the reasoning auditable: anyone can see where the ±0.4 °C comes from and challenge the inputs.

Communicating uncertainty to people who will decide

Numbers cost less trust than people fear

Van der Bles and colleagues reviewed the field in “Communicating uncertainty about facts, numbers and science” (Royal Society Open Science, 2019). In a follow-up, “The effects of communicating uncertainty on public trust in facts and numbers” (PNAS, 2020), they ran five experiments with 5,780 participants in total, including a field experiment on the BBC News website. Communicating uncertainty made people perceive more uncertainty, as intended, but it reduced trust in the numbers and in the source only slightly, and those small decreases were mostly associated with verbal statements of uncertainty rather than numeric ranges. Their topics were public facts, not engineering measurements, but the lesson transfers: a clear numeric interval is a reasonable thing to show.

What a good statement includes

• The value and the expanded uncertainty in the same units.
• The coverage factor and approximate coverage probability.
• The conditions: temperature range, time since calibration, input range.
• For conformity statements, the decision rule.

What to actually do

Write the measurement model first

Before calculating anything, write down what’s being measured and how. Many uncertainty arguments are actually disagreements about the measurand.

Build a budget, even a rough one

List every contribution you can think of, estimate each, and combine. A rough budget that shows the dominant term is more useful than a precise number with no reasoning.

Fix the dominant term

The root-sum-of-squares combination means the largest contribution dominates. Reducing a small term barely helps.

Report numbers, not adjectives

“72.4 ± 0.4 °C (k = 2)” is more trustworthy than “highly accurate.” Avoid vague verbal hedges; the research suggests they cost more trust than numeric ranges.

Agree a decision rule before testing

For pass or fail decisions near a limit, agree in advance whether you’ll use guard bands, simple acceptance or another rule.

How to put it to work

If you have an hour

Take one result you report regularly, from a test report or a datasheet, and write down every source of uncertainty you can think of. Mark the one you suspect dominates.

If you have a sprint

Build a full budget for that measurement, with Type A data from repeated readings and Type B values from certificates and specs. Add the expanded uncertainty and coverage factor to the report template.

If you want it to last the product’s lifetime

Keep the budget alongside the calibration records, update it when instruments or methods change, and write the product’s accuracy claims from it, with conditions stated.

The question to ask yourself: “If someone challenged this number, could I show where its uncertainty came from?”

Frequently asked questions

What is measurement uncertainty?

It’s a quantified parameter that characterizes the spread of values that could reasonably be attributed to what you measured. It describes how much doubt remains about a result, not how wrong it is.

What’s the difference between error and uncertainty?

Error is the difference between a measured value and the true or reference value, which is usually unknown. Uncertainty describes the range within which the true value is believed to lie, with a stated confidence.

What are Type A and Type B uncertainty?

They’re ways of evaluating a contribution. Type A uses statistical analysis of repeated observations. Type B uses other information, such as calibration certificates, specifications or resolution. Both produce standard uncertainties that combine the same way.

What does k = 2 mean?

It’s the coverage factor used to expand the combined standard uncertainty. For an approximately normal distribution, k = 2 gives an interval with about 95% coverage.

Does reporting uncertainty make customers trust a product less?

Research on public facts suggests numeric uncertainty reduces trust only slightly, and less than vague verbal hedges. In engineering, a clear uncertainty statement also makes claims auditable, which tends to help credibility with technical buyers.

Related reading: how to read a sensor datasheet, sensor calibration: offset, gain and linearity and oscilloscope bandwidth and rise time.

Sources

1. JCGM (2008). Evaluation of measurement data — Guide to the expression of uncertainty in measurement. JCGM 100:2008. https://doi.org/10.59161/JCGM100-2008E
2. JCGM (2012). International Vocabulary of Metrology — Basic and general concepts and associated terms (VIM). JCGM 200:2012. https://doi.org/10.59161/JCGM200-2012
3. Taylor, B. N., & Kuyatt, C. E. (1994). Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. NIST Technical Note 1297. https://www.nist.gov/pml/nist-technical-note-1297
4. ISO/IEC 17025:2017. General requirements for the competence of testing and calibration laboratories. https://www.iso.org/standard/66912.html
5. van der Bles, A. M., van der Linden, S., Freeman, A. L. J., Mitchell, J., Galvão, A. B., Zaval, L., & Spiegelhalter, D. J. (2019). Communicating uncertainty about facts, numbers and science. Royal Society Open Science, 6(5), 181870. https://doi.org/10.1098/rsos.181870
6. van der Bles, A. M., van der Linden, S., Freeman, A. L. J., & Spiegelhalter, D. J. (2020). The effects of communicating uncertainty on public trust in facts and numbers. PNAS, 117(14), 7672–7683. https://doi.org/10.1073/pnas.1913678117