Measurement uncertainty and significant figures in technical reports

What it is

The NIST guidelines, adapted from Technical Note 1297 and the ISO Guide to the Expression of Uncertainty in Measurement, describe the method used by national metrology institutes. Each input to a measurement has a standard uncertainty, evaluated either statistically (Type A, for example the standard deviation of the mean of repeated observations) or by other means such as specifications and previous data (Type B). These combine into a combined standard uncertainty. Multiplying it by a coverage factor k gives an expanded uncertainty defining an interval; NIST states that k is typically in the range 2 to 3 and that, under a normal distribution, k = 2 corresponds to a level of confidence of approximately 95%. Significant figures are the reporting side of the same idea: digits beyond the uncertainty are noise, and a number written with more of them claims precision it does not have.

Why it matters

Benchmark tables with "latency 12.3478 ms" from three runs, percentages with two decimals from 40 samples, and comparisons of 4.1% against 4.3% without any interval are common in engineering reports. They invite decisions on differences smaller than the run-to-run spread, and they make later readers unable to tell a real change from noise.

How to apply

• Repeat the measurement; report the mean together with the standard deviation of the mean, or a percentile with the spread across runs, and the number of runs.
• Round the uncertainty to one or two significant figures and the value to the same decimal place: "12.35 ± 0.04 ms", not "12.3478 ± 0.0412 ms".
• Say what the interval means (standard uncertainty, expanded with k = 2, or an empirical min-max range) and how it was obtained; do not mix conventions in one table.
• Propagate: for independent inputs, the relative uncertainty of a product or ratio is roughly the root sum of squares of the relative uncertainties; a difference between two numbers with wide intervals may be indistinguishable from zero.
• Respect the instrument's resolution: a timer with 1 ms ticks cannot support sub-millisecond claims from single readings.
• In prose, match the figures to the claim: "about 12 ms" when only the order matters.

Pitfalls

Confusing the standard deviation of the observations (the spread) with the standard deviation of the mean (how well the mean is known). Reporting a percentage without its denominator. Rounding intermediate results and then computing differences. Presenting systematic effects (a warm cache, a busy host, a different compiler flag) as if repetition could average them away; repetition handles random effects only, which is why Type B components exist.