Measurement result

A measurement result comprises the values attributed to a measurand together with the information needed to interpret those values. It commonly takes the form of a measured quantity value and its measurement uncertainty, but the result can contain a fuller probability distribution. A displayed number alone need not supply this information.^[ref]

For an original electrical resistance example, report a corrected value $R=100.020\Omega$ at $20{}^{\circ }\mathrm{C}$, with standard uncertainty $u(R)=0.010\Omega$. Specify that the uncertainty is a standard uncertainty, identify the resistor and the temperature condition, and retain the measurement procedure and measurement calibration records. Writing only “100.020” omits both the unit and the meaning of the last digits. Writing $100.020\pm 0.010\Omega$ without stating what the second number represents is also incomplete.

An alternative report might use expanded uncertainty $U=0.020\Omega$ with coverage factor $k=2$. This is a different uncertainty convention for the same central estimate; it is not a newly observed change in the resistor. A probability interpretation requires the distributional assumptions accompanying that convention.

An instrument's indication, a corrected measured quantity value and the complete measurement result therefore play different roles. Corrections from the measurement model, the specified measurand, environmental conditions and metrological traceability can all matter when comparing results. Extra displayed digits cannot replace the omitted measurement uncertainty.

A measurement indication is the value supplied by a measurement instrument or measuring system. It may appear as a pointer position, displayed number, printed output or transmitted code. The indication and the corresponding measurand value need not be values of the same kind of quantity.^[ref]

For an original mechanical readout, suppose the indicated pointer position is a length $z$, related to input pressure $p$ byThe measurement indication $z=21.00\mathrm{mm}$ then corresponds to $p=(z-z_0)/S=100.0\mathrm{kPa}$ under this measurement model. The position is observable; the pressure value is inferred using the response relation. A printed pressure scale could carry out part of that conversion physically without changing the underlying distinction.

If the pointer position is uncertain by $0.10\mathrm{mm}$, that contribution corresponds to $0.50\mathrm{kPa}$ in this stipulated linear model. Uncertainty in the zero $z_0$, transducer sensitivity $S$, temperature response and instrumental drift can add further contributions. Closely spaced scale markings therefore do not establish the total measurement uncertainty.

Record the original indication and instrument settings when applying corrections. A corrected measured quantity value can change after improved measurement calibration even though the recorded indication remains the same. For example, revising the assumed zero from $1.00$ to $1.20\mathrm{mm}$ changes the inferred pressure from $100.0$ to $99.0\mathrm{kPa}$. The complete measurement result accompanies the inferred value with its uncertainty and relevant conditions; the raw measurement indication alone cannot supply that information.

A measured quantity value is a value used to represent a measurement result. It may be obtained from one observation or calculated from replicate observations, for example as an arithmetic mean. The VIM distinguishes this value from a raw measurement indication and from the fuller result with its measurement uncertainty.^[ref]

For an original electrical resistance example, suppose three instrument indications are $100.04$, $100.06$ and $100.05\Omega$. A measurement calibration gives additive indication offset $b=0.02\Omega$, so the corrected values are $100.02$, $100.04$ and $100.03\Omega$. Their arithmetic mean is the representative measured quantity valueThis value is a numerical estimate of the specified measurand, such as the resistor's resistance at a stated temperature. It is not established as an exact true value merely by correcting the indications.

The three values have sample standard deviation $s=0.01\Omega$. If repeat deviations are independent, their contribution to the mean's standard uncertainty is $s/\sqrt{3}\simeq 0.0058\Omega$. Suppose the common correction has independent standard uncertainty $u(b)=0.02\Omega$. First-order propagation of uncertainty givesRepeating the readings reduces the first term under these assumptions; it does not repeatedly remeasure and average away the same common correction. These are illustrative uncertainty inputs, not observed equipment data.

Reporting the measured quantity value therefore requires its unit and measurand definition. Reporting the complete measurement result also identifies the associated measurement uncertainty, its convention and relevant conditions. A change from ohms to milliohms changes the numerical expression, while leaving the represented physical value unchanged.