= Measurement trueness
<Measurement trueness> describes how closely the mean of indefinitely many replicate measured values would agree with a reference value. It concerns <systematic error>, rather than the random spread described by <measurement precision>. The VIM treats <measurement trueness> as qualitative: a numerical error or bias estimate is not itself a numerical value of trueness.<International vocabulary of metrology by JCGM>[VIM3 entry 2.14, definition and notes 1–3]{ref}
An original <measurement model> separates the two issues:
$$
X=x_{\mathrm{ref}}+b+\varepsilon,\qquad
\mathbb E[\varepsilon]=0,\qquad
\operatorname{Var}(\varepsilon)=\sigma^2.
$$
Here $b$ is a fixed offset from the stipulated reference and $\varepsilon$ is <random measurement error>. Thus $\mathbb E[X]-x_{\mathrm{ref}}=b$, while the <standard deviation> of individual readings is $\sigma$. For $n$ <independent random variables> following this same model, averaging gives
$$
\mathbb E[\bar X]-x_{\mathrm{ref}}=b,\qquad
\operatorname{SD}(\bar X)=\frac{\sigma}{\sqrt n}.
$$
More readings reduce the random scatter of the mean without removing $b$.
For a stipulated length example, instrument A has $b=0.40\,\mathrm{mm}$ and $\sigma=0.10\,\mathrm{mm}$; instrument B has $b=0$ and $\sigma=0.50\,\mathrm{mm}$. A is more precise, while B's limiting mean agrees better with the reference. With 25 independent readings each, the means have <standard deviations> $0.02\,\mathrm{mm}$ and $0.10\,\mathrm{mm}$ respectively, and their expected offsets remain $0.40\,\mathrm{mm}$ and zero. These are chosen model parameters, not experimental determinations.
Experimentally, compare repeated readings of a stable <measurement standard> with its assigned value under specified conditions. A finite observed mean difference estimates an offset; its interpretation includes sampling variation and the reference's <measurement uncertainty>. Determine an appropriate correction through <measurement calibration>, apply it in the <measurement model>, and check it with further reference measurements. Neither a small sample spread nor a single reading equal to the reference establishes <measurement trueness>.
Back to article page
