 Participant influence on a consensus assigned value

Participant influence on a consensus assigned value is the dependence created when a result being assessed also contributes to its benchmark. The deviation from that benchmark is then generally smaller than the deviation from a corresponding consensus formed solely from the other participants. This is a property of the estimator, not evidence that the laboratory improved.

For an original equal-weight calculation with $n>1$ results, writewhere ${\bar{x}}_{-i}$ is the leave-one-out interlaboratory consensus computed as the arithmetic mean of the other results. With results $(8,10,10,12)$, the overall mean is 10. The participant reporting 12 differs from it by 2, but differs from the other three laboratories' mean $28/3$ by $8/3$. The factor $3/4$ accounts for the difference exactly.

A fixed-weight version makes the effect more general. If normalized weights $a_j$ sum to one, $0\le a_i<1$, andthen $x_i-x_c=(1-a_i)(x_i-x_{c,-i})$. A participant with weight 0.8 retains only one fifth of its difference from the remaining weighted consensus. These are fixed-weight identities; robust statistics with data-dependent weights requires analysis of the actual estimator, for example through an influence function.

Dependence also enters uncertainty. For independent results $X_i$ having common mean $\theta$ and variance ${\sigma }^2$,Treating $X_i$ and $\bar{X}$ as independent would instead add their variances and give the wrong result. This is a stated sampling model, not a universal uncertainty formula for every interlaboratory comparison.

The primary guide distinguishes assigned values based on participant consensus, expert laboratories, formulation and certified reference materials. It also requires the assigned value's uncertainty to be evaluated and reported.^[ref] Using an independent reference or a documented leave-one-out method changes the dependence, but neither is automatically appropriate for every scheme.

Finally, reducing self-influence does not resolve shared bias in an interlaboratory consensus. All remaining laboratories can still share the same calibration error. Benchmark independence, robustness to an extreme result and absolute accuracy are separate questions.