The effects of anchor test characteristics in the accuracy and precision of test equating in the "common items, nonequivalent groups design" were studied. The study also considered the effects of nonparallel based and new forms on the equating solution, and it investigated the effects of differential weighting on the success of equating under these conditions of nonrepresentative anchor tests and nonparallel test forms. Data were generated for this simulation study using a multidimensional item response theory approach to data from the American College Testing Program assessment in mathematics. The three weighting models included the traditional unweighted approach and two differential weighting methods, one with item weights obtained using the proportion of items in the anchor test relative to the proportion in the total test and one based on the proportion of item response theory information provided in each content area in the anchor test relative to the proportion in the total test. For the conditions examined in this study, the traditional unit weighting method outperformed both alternative methods. Despite the limited performance of the alternative methods in this study, they merit further study. (Contains 8 tables, 4 figures, and 17 references.) (SLD)