Key comparisons: applying the scientific method to validate uncertainty

We examine chi-squared statistics that are appropriate for analysing the adequacy of different key comparison reference value candidates in accounting for the observed dispersion of results of a key comparison, about the candidate estimator, and within the stated uncertainty claims. We extend the analysis to cover cases where the uncertainty budgets incorporate low degrees of freedom or have significant correlations. To use these statistics for the usual chi-squared tests of consistency, the required distributions can readily be evaluated by Monte Carlo simulation, including the effects of non-Gaussian uncertainty distributions. Pair-difference chi-squared statistics are a useful method for analysing metrologica, being independent of the choice of estimator of central tendency, and so may expedite the process of analysis, consensus building and publication