= Recovery correction
A \b[recovery correction] adjusts an analytical result to account for an estimated loss of <analyte> during a specified preparation stage. If the recovered amount $y$ follows $y=rq$, with original amount $q$ and <extraction recovery> $r>0$, the corrected estimate is $\widehat q=y/r$. Its validity depends on whether the recovery estimate applies to that analyte, <sample matrix> and procedure.
For an original example, $y=6\,\mathrm{nmol}$ and $r=0.60$ give $\widehat q=10\,\mathrm{nmol}$. The calculation estimates the amount before loss; it does not restore molecules to the sample. It also does not separately correct a <mass spectrometry matrix effect> unless that effect has been included consistently in the measurement model.
<Recovery-correction uncertainty> follows from the quotient, not just from the measured amount. First-order <propagation of uncertainty> gives
$$
u^2(\widehat q)\approx\frac{u_y^2}{r^2}+\frac{y^2u_r^2}{r^4}-\frac{2y\operatorname{Cov}(y,r)}{r^3}.
$$
If the two inputs are independent, the covariance term vanishes. With stipulated standard uncertainties $u_y=0.3\,\mathrm{nmol}$ and $u_r=0.06$, the two variance contributions are $0.25$ and $1.00\,\mathrm{nmol^2}$, giving $u(\widehat q)\approx1.12\,\mathrm{nmol}$. The recovery estimate dominates this example; dividing by recovery has not created extra precision.
A recovery inferred from a spiked preparation need not reproduce the behavior of analyte originally embedded in a sample. Likewise, applying a single recovery at every concentration assumes a common model. Near-zero or very uncertain recovery can make quotient inference unreliable beyond the linear uncertainty approximation.
Reporting whether a correction was applied, its size and how it was derived makes results comparable. These reporting provisions appear in the harmonised recovery guidelines and their Codex adoption text.<Harmonised guidelines for the use of recovery information in analytical measurement by Michael Thompson and others>[Recommendation1 reporting provisions, reproduced at the linked FAO Codex text.]{ref}
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