= Michael H. Ramsey
{c}
\b[Michael H. Ramsey] is a researcher credited as chair of the working group and co-editor of the 2019 guide to <measurement uncertainty> arising from <analytical sampling>. The editorial page gives his affiliation as the University of Sussex and names fellow editors <Stephen L. R. Ellison> and <Peter Rostron>.<Measurement uncertainty arising from sampling by Michael H. Ramsey and others>[Editorial page, PDF p. 3, editors and working-group composition]{ref}
The scientific problem is the difference between the collected material and the material about which a conclusion is wanted. For a <measurand> defined over a larger target, excellent <measurement repeatability> on one extract does not establish small <analytical sampling uncertainty>. The guide treats collection and analysis as stages of the measurement process.<Measurement uncertainty arising from sampling by Michael H. Ramsey and others>[Sections 5.2 and 9.3–9.5]{ref}
An original <measurement model> illustrates why replication at the right level matters:
$$
Y_{ij}=\mu+S_i+A_{ij}.
$$
Here $\mu$ is the target mean, $S_i$ is the zero-mean deviation associated with independently collected sample $i$, and $A_{ij}$ is zero-mean analytical variation in repeat $j$. Suppose all these effects are mutually independent, with <variances> $\sigma_S^2$ and $\sigma_A^2$. Averaging $m$ analyses on each of $n$ collected samples gives
$$
\operatorname{Var}(\overline Y)=\frac{\sigma_S^2}{n}+\frac{\sigma_A^2}{nm}.
$$
For stipulated <variance components> $\sigma_S^2=9$ and $\sigma_A^2=4$ in squared concentration units, three collections analysed twice give variance $9/3+4/6=11/3$, or <standard uncertainty> about $1.915$ concentration units. Six analyses of only one collection instead give variance $9+4/6=29/3$, or about $3.109$ units. Both plans use six analyses; only the first averages over independently collected material.
The calculation assumes independent collections and an appropriate model for the target; a shared systematic collection error is not removed by increasing $n$. It explains the measurement-design issue addressed by the guide without presenting these invented numbers as Ramsey's experimental observations.
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