Issues related to linking tests with constructed response items were explored, specifically by comparing single-group and anchor-test designs to link raw scores from alternate forms of performance-based student assessments in the context of Delaware's assessment program using performance-based assessment. This study explored use of the two test designs for the mathematics assessments administered in 1993 and 1994. In the single-group design the equating study was conducted with 300 to 460 out-of-state students from 16 schools at grades 3, 5, 8, and 10. To equate the performance-based assessments using the anchor-test design (a sample of about 13,000 students each year), each student's 1993 performance-based assessment raw score was equated to the norm-referenced scale score from the Iowa Tests of Basic Skills for grades 3, 5, and 8 and the Tests of Achievement and Proficiency for grade 10. The same procedure was used for the 1994 performance-based assessment. Results suggested that, based solely on considerations of sample size, correlations, and sample matching, the anchor-test design would be expected to produce more accurate results than the single-group design. Commonality of content coverage between the performance assessment and the norm referenced test is essential. (Contains 3 figures, 18 tables in an appendix, and 10 references.) (SLD)