One design uses a high reliability test and an external anchor, and the other uses a relatively low reliability test and an internal anchor. The chained linear equation functions derived from the total sample are used as the criterion equating function in both assessments. The results from each of these methods were compared to the criterion equating function with respect to the linking bias and error. The study indicates that the synthetic functions might be a better choice than the chained linear equating method when samples are neither large nor representative.