The purpose of this paper is to extend von Davier, Holland, and Thayer's (2004b) framework of kernel equating so that it can incorporate raw data and traditional equipercentile equating methods. One result of this more general framework is that previous equating methodology research can be viewed more comprehensively. Another result is that the standard error of equated score difference (SEED) has a wider application than originally proposed. The methods described in this paper are empirically evaluated in an accompanying simulation study (Moses & Holland, 2007).