This report sets out the mathematics for solving the `linking comparison' problem. The degrees of equivalence (DoE) for participants in a regional measurement comparison should be linked to a primary comparison. This can be achieved when some laboratories participate in both comparisons, because the DoEs of linking participants will be known from their prior participation in a primary comparison. The analysis of a linking comparison is complicated by multiple sources of correlation between values used in the analysis. This report provides a rigorous description of the solution to linking comparison problem. It identifies sources of correlation and shows how to manage and account for them in the determination of the DoEs of all new participants. The report describes the analysis of a primary comparison, using the fixed effects with weighted mean model, before presenting an analysis of linking comparisons that is (somewhat) independent of the choice of primary comparison analysis method. A linear algebra formulation (using generalised least squares) is also given, which can simplify the mechanics of calculation. The CCPR is intending to revise its guidance for linking comparisons and so several issues specific to the CCPR and its comparison analysis guidelines are also addressed.

The only change is to the OrcID hyperlinks on the title page, which did not work correctly in version 1.