Chi-squared statistics for KCRV candidates

We examine chi-squared statistics that are appropriate for analysing the adequacy of different key comparison reference value (KCRV) 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. In this context, we discuss when it is important to view the KCRV as a method and not merely as a number. To use these statistics for the usual chi-squared tests of consistency, the required distributions (that can depart from the exact chi-squared distribution) can readily be evaluated by Monte Carlo simulation, for any KCRV algorithm that uses only the peer results of the comparison. Similarly, the effects of non-Gaussian distributions (such as the Student distribution implied when a participant has reported finite degrees of freedom) can be evaluated with the requisite precision.