= Shared calibration error
A <shared calibration error> is a <measurement error> contribution inherited by several results from the same uncertain <measurement calibration> information. A common reference offset, scale factor or fitted coefficient can couple readings that would otherwise have independent noise. The GUM identifies common measuring instruments, standards and reference data as sources of <correlation>.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[Sections5.2.4–5.2.5]{ref}
Consider an original additive model for repeated readings of a fixed quantity $\theta$:
$$
Y_i=\theta+B+\varepsilon_i,\qquad \operatorname{Var}(B)=\tau^2,\qquad \operatorname{Var}(\varepsilon_i)=\sigma^2.
$$
Here $B$ represents the remaining uncertainty in a common correction, and the centered $\varepsilon_i$ are independent of one another and of $B$. These assumptions imply
$$
\operatorname{Cov}(Y_i,Y_j)=\tau^2\quad(i\ne j),\qquad
\operatorname{Var}(\overline Y)=\tau^2+\frac{\sigma^2}{n}.
$$
This is <covariance induced by a shared latent variable>: the same unknown contribution appears in every reading. A fixed but unknown physical offset need not fluctuate between readings for uncertainty about it to be shared.
With100readings, individual noise <standard deviation>1unit and common-offset <standard uncertainty>0.2unit, the mean has <standard uncertainty> $\sqrt{1/100+0.2^2}\approx0.224$unit. Treating all100readings as independent would instead give $\sqrt{(1+0.2^2)/100}\approx0.102$unit. Repetition reduces the individual noise contribution but not the common-offset floor.
A difference $Y_i-Y_j=\varepsilon_i-\varepsilon_j$ cancels this additive common offset. It does not cancel an arbitrary common gain error. Reference changes and deliberate <systematic-error cancellation by reversal> test different effects; the <measurement uncertainty budget> should identify which quantities actually share the uncertain correction.
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