**Abbreviations**

The following abbreviations are used in this manuscript:


#### **Appendix A. Weights for Evaluating DoEs in a CIPM Key Comparison**

The CCPR uses weights in the determination of DoEs that depend on the uncertainties reported by the participants ([6], Appendix A). These weights are calculated from the arithmetic mean of the combined standard uncertainties reported by each participant. For participant *i*, with a mean combined standard uncertainty *u*(*y*∗ *i* ),

$$w\_i = \frac{\left(\overline{u}(y\_i^\*)\right)^{-2}}{\sum\_j \left(\overline{u}(y\_j^\*)\right)^{-2}},\tag{A1}$$

where the sum is over all participants and *u*(*y*∗ *<sup>j</sup>* ) is the arithmetic mean of the combined standard uncertainties reported by participant *j*.

CCPR guidelines recommend a cut-off to limit the influence of any measured values with very low uncertainty. The minimum uncertainty value is taken to be the mean of those *u*(*y*∗ *<sup>i</sup>* ) values that are less than or equal to the median of the uncertainties reported by all participants:

$$\mu\_{\text{Cut}} = \text{mean}(\ \overline{u}(y\_i^\*) \ ) \quad \text{for all} \quad \overline{u}(y\_i^\*) \le \text{median}(\{\ u(y\_i^\*) \ \}) \,. \tag{A2}$$

The weighting factor is evaluated by Equation (A1) while taking the greater of *u*(*y*∗ *i* ) and *<sup>u</sup>*cut as the mean uncertainty for participant *<sup>i</sup>*. In this work, *<sup>u</sup>*cut = 1.92 × <sup>10</sup>−<sup>4</sup> and the weights obtained were:

$$\begin{array}{ll}w\_{\text{A}} = 0.047, & w\_{\text{E}} = 0.025, & w\_{\text{I}} = 0.191, \\ w\_{\text{B}} = 0.004, & w\_{\text{F}} = 0.067, & w\_{\text{J}} = 0.073, \\ w\_{\text{C}} = 0.191, & w\_{\text{G}} = 0.000, & w\_{\text{K}} = 0.012, \\ w\_{\text{D}} = 0.009, & w\_{\text{H}} = 0.191, & w\_{\text{Q}} = 0.191. \end{array}$$

A cut off was imposed on participants C, H, I and Q. The results from those laboratories were weighted most heavily, followed by those from participants J and F.
