Evaluation of Measurement Comparisons Using Generalised Least Squares: the Role of Participants' Estimates of Systematic Error

TL;DR

This paper examines how to evaluate laboratory measurement practices using generalized least squares, focusing on the impact of participants' estimates of systematic errors and the treatment of fixed and random effects.

Contribution

It demonstrates that random effects can be ignored when estimating participant fixed effects and provides an adjustment for variance estimates in measurement comparisons.

Findings

Random effects can be ignored in fixed effects estimation.

Derived adjustment improves variance estimation accuracy.

Clarifies the role of systematic error estimates in measurement evaluation.

Abstract

We consider the evaluation of laboratory practice through the comparison of measurements made by participating metrology laboratories when the measurement procedures are considered to have both fixed effects (the residual error due to unrecognised sources of error) and random effects (drawn from a distribution of known variance after correction for all known systematic errors). We show that, when estimating the participant fixed effects, the random effects described can be ignored. We also derive the adjustment to the variance estimates of the participant fixed effects due to these random effects.