Reporting a Result

A propagated measurement is not yet a reported one. JCGM 100:2008 §7 governs how a result is written down, and what it says is more prescriptive than most software admits: there are four acceptable textual forms, a rule for how many digits to quote, and a separate statement for expanded uncertainty that must name its coverage factor.

report produces them.

The four forms of §7.2.2

The GUM's own worked example is a 100 g mass standard whose calibration gives m_S = 100.02147 g with u_c = 0.35 mg:

using SymbolicUncertainties

report(100.02147, 0.00035; symbol = "m_S", unit = "g")

Measurement result — JCGM 100:2008 §7.2.2
  m_S = 100.02147 g with u_c = 0.00035 g
  m_S = 100.02147(35) g
  m_S = 100.02147(0.00035) g
  m_S = (100.02147 ± 0.00035) g

All four say the same thing. Which one belongs on a certificate is a house-style question, not a metrological one.

How many digits — §7.2.6

u_c is quoted to two significant digits, and the estimate is rounded to that same last significant place. Quoting an estimate to more digits than its uncertainty supports claims a precision the measurement does not have; quoting fewer discards information that was paid for.

The rule is on significant digits of the uncertainty, not on decimal places, so a coarse uncertainty coarsens the estimate with it:

report(1234.5678, 12.0; symbol = "y", unit = "m").forms[4]

"y = (1235 ± 12) m"

Feeding in more digits than the uncertainty can carry changes nothing:

report(100.021473829, 0.000351119; symbol = "m_S", unit = "g").forms[2]

"m_S = 100.02147(35) g"

Pass digits = 1 or digits = 3 where a laboratory's own convention differs; §7.2.6 says "at most two" and leaves room.

Expanded uncertainty — §7.2.4

An expanded uncertainty is a different statement, not an annotation of the standard one, and §7.2.4 asks it to name its coverage factor and the basis for it. Supplying k produces it:

report(
    100.02147, 0.00035;
    symbol = "m_S",
    unit = "g",
    k = 2.26,
    coverage_probability = 0.95,
    dof = 9,
)

Measurement result — JCGM 100:2008 §7.2.2
  m_S = 100.02147 g with u_c = 0.00035 g
  m_S = 100.02147(35) g
  m_S = 100.02147(0.00035) g
  m_S = (100.02147 ± 0.00035) g

Expanded uncertainty — §7.2.4
  m_S = (100.02147 ± 0.00079) g, where the number following the symbol ± is the numerical value of an expanded uncertainty U = k·u_c, with U determined from a combined standard uncertainty u_c = 0.00035 g and a coverage factor k = 2.26 based on the t-distribution for ν = 9 degrees of freedom, and defines an interval estimated to have a level of confidence of 95 percent.

Without k there is no expanded statement to make, and the expanded field is nothing. ± U with no stated k is precisely the ambiguity §7.2.2 warns about, so the package will not write one.

From a model, with units

With DynamicQuantities loaded, report(m, values) takes the measurement and unit-carrying values, and derives the numbers and the unit from the model — the same walk evaluate uses:

using Symbolics, DynamicQuantities

@variables V I σV σI
R = (V ± σV) / (I ± σI)

readings = Dict(
    V => 10.000us"V", σV => 1e-3us"V",
    I => 0.10002us"A", σI => 1e-5us"A",
)

report(R, readings; symbol = "R", unit = "Ω", k = 2, coverage_probability = 0.95)

Measurement result — JCGM 100:2008 §7.2.2
  R = 99.980 Ω with u_c = 0.014 Ω
  R = 99.980(14) Ω
  R = 99.980(0.014) Ω
  R = (99.980 ± 0.014) Ω

Expanded uncertainty — §7.2.4
  R = (99.980 ± 0.028) Ω, where the number following the symbol ± is the numerical value of an expanded uncertainty U = k·u_c, with U determined from a combined standard uncertainty u_c = 0.014 Ω and a coverage factor k = 2, and defines an interval estimated to have a level of confidence of 95 percent.

The dimensional walk composes what it is given, so this model produces A⁻¹ V. report recognises the thirteen coherent derived SI units by their dimension and writes Ω instead — likewise W for A V, and Hz for s⁻¹. The unit = "Ω" above is therefore redundant here, and kept only to show the override.

Two limits on that naming, both deliberate.

A prefixed unit is never renamed. 1 kΩ expands to a thousand base units, so a result computed in kilohms stays in kilohms: calling it Ω would be wrong by a factor of a thousand. Only a unit that is already the coherent SI one is given its name.

A dimension does not determine a kind of quantity (VIM §1.1). Torque and energy are both m² kg s⁻², so the table calls that J and a torque must say otherwise:

@variables F σF d σd
M = (F ± σF) * (d ± σd)

vals = Dict(
    F => 12.0us"N", σF => 0.1us"N",
    d => 0.25us"m", σd => 0.001us"m",
)

(
    default = report(M, vals; symbol = "M").forms[2],
    corrected = report(M, vals; symbol = "M", unit = "N m").forms[2],
)

(default = "M = 3.000(28) J", corrected = "M = 3.000(28) N m")

Hz carries the same caveat, sharing s⁻¹ with an activity in becquerel. check_units refuses to unify such homonyms through Kind; report cannot make that distinction on its own, because a product of two plain quantities carries no kind to propagate — which is exactly why unit exists.

API reference

report(y, u; symbol, unit, digits, k, coverage_probability, dof)
report(m::SymbolicMeasurement; kwargs...)

julia> r = report(100.02147, 0.00035; symbol = "m_S", unit = "g");

julia> r.forms[2]
"m_S = 100.02147(35) g"

UncertaintyReport