Pairwise comparison scale extension using core linking sets

Pairwise comparisons can be used to equate two sets of educational performances. In this article, a simple method for the joint scaling of two or more sets of assessment performances is described and illustrated. This method is applicable where a scale of student abilities has already been formed, and the scale is to be extended to include additional performances. It requires a subset of already scaled performances, which is designated as a core linking set for the purpose of scale extension. The article illustrates the application of the method to construct a scale with a larger range of latent abilities, using fewer additional comparisons compared to the standard method of pairwise comparisons. The design differs from standard pairwise comparisons in the way performances are paired. The method of pairing performances can also be used to efficiently place individual performances on an existing scale.