Extending chi-squared statistics for key comparisons in metrology

We examine different χ2χ2 statistics appropriate for high-level metrology. “Key” measurement comparisons often need statistics that can be used before a reference value is chosen. One such statistic is the pair-difference χ2χ2, presented here. This is also a natural way to examine bilateral equivalences essential for trade. Monte Carlo simulation is a practical means to extend rigor beyond conventional χ2χ2 testing, and permits the use of a wide variety of reference values for familiar null-hypothesis testing. Further, simulation enables the handling of measurements purportedly drawn from Student distributions or with reported inter-laboratory covariances.