Assessing compatibility of two laboratories: formulations as a statistical hypothesis testing problem

A decision problem frequently occurring in metrology is that of compatibility of data obtained by two (or several) different laboratories, methods or instruments. One laboratory can be a prestigious national metrology institute whose data are considered to be a gold standard or a certified reference material interval. When each laboratory presents its results in the form of a coverage interval for the measurand, several statistical approaches to this conformity assessment problem are reviewed including the classical 'equality of means' hypotheses tests. A new compatibility hypothesis is formulated in terms of consistency of laboratory results and compliance with a maximum permitted uncertainty. The power functions of these tests are compared numerically. The Kullback–Leibler information number is suggested as a directional (asymmetric) interchangeability index.