This study developed, applied, and evaluated a theory-based method of detecting the underlying causes of differential difficulty. The method was applied to two subgroups taking the Scholastic Aptitude Test-Mathematics (SAT-M), 261 visually impaired students taking Braille forms of the test and 1,985 black students at 3 test administrations. It involved: (1) reviewing the literature to identify possible causes of differential item functioning; (2) forming item categories based on those factors; (3) identifying categories that functioned differentially; (4) assessing the functioning of the items composing deviant categories; and (5) relating item and category functioning. Results were compared to a traditional item-level analysis. In both subgroups, the cluster and traditional methods agreed on the overall extent of differential functioning (substantial in the first group, virtually absent in the second). The method would seem to be applied most productively when a small number of hypotheses can be derived from a reasonably strong research base, overlap among cluster structures can be avoided, and results can be supplemented with experimental studies of protocol analysis. (Contains 27 references, 11 tables, and an appendix of category definitions.) (Author/SLD)